Answer key

Assignment 11Due: 11:59pm on Wednesday, April 30, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 13.2 The gravitational force of a star on orbiting planet 1 is F1 . Planet 2, which is twice as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force F2 . Part A What is the ratio F1 ? F2 ANSWER: F1 = 2 F2 Correct Conceptual Question 13.3 A 1500kg satellite and a 2200kg satellite follow exactly the same orbit around the earth. Part A What is the ratio ANSWER: F1 = 0.682 F2 Correct F1 of the force on the first satellite to that on the second satellite? F2 Part B a1 What is the ratio a of the acceleration of the first satellite to that of the second satellite? 2 ANSWER: a1 a2 = 1 Correct Problem 13.2 The centers of a 15.0kg lead ball and a 90.0g lead ball are separated by 9.00cm . Part A What gravitational force does each exert on the other? Express your answer with the appropriate units. ANSWER: 1.11×10 −8 N Correct Part B What is the ratio of this gravitational force to the weight of the 90.0g ball? ANSWER: 1.26×10−8 Typesetting math: 100% Correct Problem 13.6 The space shuttle orbits 310km above the surface of the earth. Part A What is the gravitational force on a 7.5kg sphere inside the space shuttle? Express your answer with the appropriate units. ANSWER: Fe on s = 67.0 N Correct ± A Satellite in Orbit A satellite used in a cellular telephone network has a mass of 2310kg and is in a circular orbit at a height of 650km above the surface of the earth. Part A What is the gravitational force Fgrav on the satellite? Take the gravitational constant to be G = 6.67×10−11N ⋅ m2 /kg2 , the mass of the earth to be me = 5.97×1024kg , and the radius of the Earth to be re = 6.38×106m . Express your answer in newtons. Hint 1. How to approach the problem Use the equation for the law of gravitation to calculate the force on the satellite. Be careful about the units when performing the calculations. Typesetting math: 100% Hint 2. Law of gravitation According to Newton's law of gravitation, F = Gm1 m2 /r2 , where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of mass of the two objects. Hint 3. Calculate the distance between the centers of mass What is the distance r from the center of mass of the satellite to the center of mass of the earth? Express your answer in meters. ANSWER: r = 7.03×106 m ANSWER: Fgrav = 1.86×104 N Correct Part B What fraction is this of the satellite's weight at the surface of the earth? Take the free-fall acceleration at the surface of the earth to be g = 9.80m/s2 . Hint 1. How to approach the problem All you need to do is to take the ratio of the gravitational force on the satellite to the weight of the satellite at ground level. There are two ways to do this, depending on how you define the force of gravity at the surface of the earth. ANSWER: 0.824 Typesetting math: 100% Correct Although it is easy to find the weight of the satellite using the constant acceleration due to gravity, it is instructional to consider the weight calculated using the law of gravitation: w = Gme m/r2e. Dividing the gravitational force on the satellite Fgrav = Gme m/(re + h)2 by w, we find that the ratio of the forces due to the earth's gravity is simply the square of the ratio of the earth's radius to the sum of the earth's radius and the height of the orbit of the satellite above the earth, [re /(re + h)]2. This will also be the fraction of the weight of, say, an astronaut in an orbit at the same altitude. Notice that an astronaut's weight is never zero. When people speak of "weightlessness" in space, what they really mean is "free fall." Problem 13.8 Part A What is the free-fall acceleration at the surface of the moon? Express your answer with the appropriate units. ANSWER: m gmoon = 1.62 s 2 Correct Part B What is the free-fall acceleration at the surface of the Jupiter? Express your answer with the appropriate units. ANSWER: gJupiter = 25.9 m2 s Correct Typesetting math: 100% 54×104 s Correct Problem 13. what is its gravitational potential energy? Using conservation of energy. How to approach the problem What is conserved in this problem? What is the rocket's initial kinetic energy in terms of its unknown mass. Hint 1. m? When the rocket is very far away from the Earth. For help with math skills.14 A rocket is launched straight up from the earth's surface at a speed of 1. you may want to review: Mathematical Expressions Involving Squares Part A What is its speed when it is very far away from the earth? Express your answer with the appropriate units. You may want to review ( pages 362 . what is the rocket's velocity when it is very far away from the Earth? ANSWER: m 1.365) .13 Part A Typesetting math: 100% . what is the rocket's kinetic energy when it is very far away from the Earth? Therefore. m? What is the rocket's initial gravitational potential energy in terms of its unknown mass.Enhanced EOC: Problem 13.90×104m/s . 17 The asteroid belt circles the sun between the orbits of Mars and Jupiter.2 earth years.85×104 m s Typesetting math: 100% . Part A What is the asteroid's orbital radius? Express your answer with the appropriate units.What is the escape speed from Venus? Express your answer with the appropriate units.89×1011 m Correct Part B What is the asteroid's orbital speed? Express your answer with the appropriate units. One asteroid has a period of 4. ANSWER: vescape = 10.4 km s Correct Problem 13. ANSWER: v = 1. ANSWER: R = 3. Their speeds as they cross the moon's orbit are 2km/s . ANSWER: m 4920 s Correct Problem 13.32 Part A At what height above the earth is the acceleration due to gravity 15.01×10 m Correct Part B What is the speed of a satellite orbiting at that height? Express your answer with the appropriate units. ANSWER: 7 1.0% of its value at the surface? Express your answer with the appropriate units.Correct Problem 13.36 Two meteoroids are heading for earth. Typesetting math: 100% . 0cm mark and the 67. Typesetting math: 100% . What is its speed of impact? Express your answer with the appropriate units. The glider completes 11. ANSWER: v2 = Incorrect.0 oscillations in 32. Try Again Problem 14.2 An air-track glider attached to a spring oscillates between the 11. Part A What is the period of the oscillations? Express your answer with the appropriate units.0s . ANSWER: v1 = 11.Part A The first meteoroid is heading straight for earth.0cm mark on the track. What is its speed at its closest point? Express your answer with the appropriate units.3 km s Correct Part B The second misses the earth by 5500km . ANSWER: 0.91 s Correct Part B What is the frequency of the oscillations? Express your answer with the appropriate units. Typesetting math: 100% .16 rad s Correct Part D What is the amplitude? Express your answer with the appropriate units.344 Hz Correct Part C What is the angular frequency of the oscillations? Express your answer with the appropriate units. ANSWER: 2.ANSWER: 2. in that it represents a special kind of periodic motion called simple harmonic motion. The resistive forces in the system must be reasonably small. or a block attached to a spring oscillating back and forth. The spring can be either stretched or compressed.0 cm Correct Part E What is the maximum speed of the glider? Express your answer with the appropriate units. The100% block slides on a frictionless horizontal surface. F ⃗ = −kx. the restoring force F ⃗ is given by constant that depends on the properties of the oscillating system. There are many examples of periodic motion: the earth revolving around the sun. and its magnitude must be directly proportional to the magnitude of the object's displacement from its equilibrium position. The last example differs from the first two. ANSWER: cm 60. an elastic ball bouncing up and down. There must be a restoring force acting on the oscillating object. as shown. Mathematically.ANSWER: 28. the block is located at x = 0. If the Typesetting math: . Motion that repeats itself over and over is called periodic motion.⃗ where x⃗ is the displacement from equilibrium and k is a In this problem. as shown in the figure. The conditions that lead to simple harmonic motion are as follows: There must be a position of stable equilibrium.5 s Correct Good Vibes: Introduction to Oscillations Learning Goal: To learn the basic terminology and relationships among the main characteristics of simple harmonic motion. When the spring is relaxed. The direction of this force must always point toward the equilibrium. Consider a block of mass m attached to a spring with force constant k. we will introduce some of the basic quantities that describe oscillations and the relationships among them. After x = −A is reached. or hertz (Hz). compressing the spring. The time it takes the block to complete one cycle is called the period. the block will begin its motion to the right. Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block. Part A After the block is released from x = A. is the number of cycles that are completed per unit of time: Typesetting math: 100% f = 1/T . it will ANSWER: remain at rest. pass the equilibrium position and keep moving. if. so by the time the equilibrium position is reached. move to the left until it reaches x = −A and then begin to move to the right. In SI units. there is no friction. Usually. denoted f . completing one . the block has gained some speed. temporarily coming to rest at x = −A. The motion will then repeat. x = A. therefore. it still pulls the block to the left. and the block will slow down.block is pulled to the right a distance A and then released. f is measured in inverse seconds. Although the restoring force decreases as the block approaches equilibrium. it accelerates. A will be the amplitude of the resulting oscillations. The block will pass the equilibrium position and continue until it reaches cycle of motion. pushed by the spring. The frequency. x = −A and stop there. move to the left until it reaches equilibrium and stop there. the motion will repeat indefinitely. as we've assumed. It will. move to the left until it reaches Correct As the block begins its motion to the left. the period is denoted T and is measured in seconds. The spring will now be pushing the block to the right. ANSWER: f = 10 Hz Correct Typesetting math: 100% . halved.10 s to complete one cycle. doubled. the frequency is ANSWER: unchanged. Correct Part C An oscillating object takes 0. its period is 0. that is.10 s.Part B If the period is doubled. What is its frequency f ? Express your answer in hertz. Part E Which points on the x axis are located a distance A from the equilibrium position? ANSWER: Typesetting math: 100% .Part D If the frequency is 40 Hz. Note that the vertical axis represents the x coordinate of the oscillating object. what is the period T ? Express your answer in seconds.025 s Correct The following questions refer to the figure that graphically depicts the oscillations of the block on the spring. and the horizontal axis represents time. ANSWER: T = 0. 12 m and the t coordinate of point K is 0. what fraction of a full wavelength is covered? Call that fraction a.005 s. How to approach the problem In moving from the point Typesetting math: 100% t = 0 to the point K. Part G What is the period T ? Express your answer in seconds.J. Which of the following points on the t axis are separated by the time interval T ? ANSWER: K and L K and M K and P L and N M and P Correct Now assume for the remaining Parts G . that the x coordinate of point R is 0.R only Q only both R and Q Correct Part F Suppose that the period is T . Hint 1. Dividing by the fraction a will give the . Then you can set aT = 0.0050 s. period T .02 s Correct Part H How much time t does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement? Express your answer in seconds.48 m Correct Part J What distance d does the object cover between the moments labeled K and N on the graph? Typesetting math: 100% . ANSWER: d = 0. ANSWER: T = 0. ANSWER: t = 0.01 s Correct Part I What distance d does the object cover during one period of oscillation? Express your answer in meters. 36 m Correct Problem 14.0 cm Correct Typesetting math: 100% . ANSWER: d = 0.4 Part A What is the amplitude of the oscillation shown in the figure? Express your answer to three significant figures and include the appropriate units. ANSWER: A = 20.Express your answer in meters. At t = 0 s the glider is 4.4cm/s .60cm left of the equilibrium position and moving to the right at 33. ANSWER: f = 0. Try Again Problem 14. Part A What is the phase constant? Express your answer to three significant figures and include the appropriate units. ANSWER: ϕ0 = Incorrect.Part B What is the frequency of this oscillation? Express your answer to two significant figures and include the appropriate units.25 Hz Correct Part C What is the phase constant? Express your answer to two significant figures and include the appropriate units.50s . ANSWER: Typesetting math: 100% .10 An air-track glider attached to a spring oscillates with a period of 1. The glider is pushed in 12.ϕ0 = Incorrect. Try Again Part B This question will be shown after you complete previous question(s). Problem 14.12 A 140g air-track glider is attached to a spring. A student with a stopwatch finds that 14. Part D This question will be shown after you complete previous question(s). Part A What is the spring constant? Express your answer with the appropriate units.2cm and released. ANSWER: Typesetting math: 100% . Part C This question will be shown after you complete previous question(s).0s .0 oscillations take 19. ANSWER: 2. If necessary. Determine: Part A The amplitude.14 The position of a 50 g oscillating mass is given by x(t) = (2.628 s Correct Part C Typesetting math: 100% .00 m Correct Problem 14. round your answers to three significant figures. Express your answer to three significant figures and include the appropriate units.0 cm)cos(10t − π/4). ANSWER: 0. where t is in s. Express your answer to three significant figures and include the appropriate units.00 cm Correct Part B The period.N 3. Part F This question will be shown after you complete previous question(s). Try Again Part E This question will be shown after you complete previous question(s). Express your answer to three significant figures and include the appropriate units. ANSWER: Part D The phase constant. Part G Typesetting math: 100% .The spring constant. ANSWER: Incorrect. Express your answer to three significant figures and include the appropriate units. Part H This question will be shown after you complete previous question(s). It is then pulled down 4.391) . How to approach the problem What is the period of oscillation? What is the angular frequency of the oscillations? How is the angular frequency related to the mass and spring constant? What is the mass? Typesetting math: 100% . you may want to review: Differentiation of Trigonometric Functions Part A What is its the mass of the ball? Express your answer to two significant figures and include the appropriate units. You may want to review ( pages 389 .This question will be shown after you complete previous question(s).0cm and released.17 A spring with spring constant 16N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. Hint 1. Part I This question will be shown after you complete previous question(s). The ball makes 35 oscillations in 18s seconds. Enhanced EOC: Problem 14. For help with math skills. approximately what will the pendulum's new period be? Hint 1.ANSWER: m = 110 g Correct Part B What is its maximum speed? Express your answer to two significant figures and include the appropriate units. Part A If the bob's mass is doubled. Period of a simple pendulum Typesetting The math: period 100% T of a simple pendulum of length L is given by . Hint 1. How to approach the problem What is the amplitude of the oscillations? How is the maximum speed related to the amplitude of the oscillations and the angular frequency? ANSWER: vmax = 49 cm s Correct Changing the Period of a Pendulum A simple pendulum consisting of a bob of mass m attached to a string of length L swings with a period T . ANSWER: T /6 T /√6 √6T 6T Typesetting math: 100% . Since the gravitational acceleration appears in the denominator. How to approach the problem Recall the formula of the period of a simple pendulum. where g is the acceleration due to gravity. ANSWER: T /2 T √2T 2T Correct Part B If the pendulum is brought on the moon where the gravitational acceleration is about g/6 . the period must increase when the gravitational acceleration decreases. approximately what will its period now be? Hint 1.−− T = 2π√ Lg . How to approach the problem Recall that the oscillations of a simple pendulum occur when a pendulum bob is raised above its equilibrium position and let go. It will oscillate much faster with a period that approaches zero. where all objects undergo the same acceleration due to the earth's gravity. The gravitational force acts to bring the bob back to its equilibrium position. Part A How long is the string? Express your answer to two significant figures and include the appropriate units. giving them the same acceleration. It will no longer oscillate because there is no gravity in space. the tension in the string is zero and the bob does not fall relative to the point to which the string is attached. Problem 14. It is pulled to an angle of 8. causing the pendulum bob to fall. ANSWER: It will continue to oscillate in a vertical plane with the same period. In the space station. It will no longer oscillate because both the pendulum and the point to which it is attached are in free fall. These objects are said to be in free fall.Correct Part C If the pendulum is taken into the orbiting space station what will happen to the bob? Hint 1.0∘ and released to swing as a pendulum. Correct In the space station.20 A 175g ball is tied to a string. A student with a stopwatch finds that 15 oscillations take 13s . Typesetting math: 100% . the earth's gravity acts on both the station and everything inside it. What is the maximum oscillation amplitude that won't rupture the disk? .35 m Correct Problem 14.0 MHz by an electromagnetic coil.42 An ultrasonic transducer.ANSWER: L = 19 cm Correct Problem 14.4×10 Express your answer to two significant figures and include the appropriate units. of the type used in medical ultrasound imaging.17g ) driven back and forth in SHM at 1. Part A 4 The maximum restoring force that can be applied to the disk without breaking it is 4. ANSWER: lmoon = 0.1-m-long pendulum on the earth? Express your answer to two significant figures and include the appropriate units. is a very thin disk ( m = 0.22 Part A What is the length of a pendulum whose period on the moon matches the period of a 2. ANSWER: amax = 6.6 µm Typesetting math: 100% N . Typesetting math: 100% .Correct Part B What is the disk's maximum speed at this amplitude? Express your answer to two significant figures and include the appropriate units. You received 117.4%.25 out of a possible total of 144 points. ANSWER: vmax = 41 m s Correct Score Summary: Your score on this assignment is 81. m = 4kg . The string is massless and the pulley is frictionless. Correct Conceptual Question 7. Part A Is the force of the truck on the car larger than. 2014 You will receive no credit for items you complete after the assignment is due. Assume that . March 7.7 A small car is pushing a large truck. smaller than. The force of the truck on the car is smaller than the force of the car on the truck.12 The figure shows two masses at rest. Grading Policy Conceptual Question 7.Assignment 6 Due: 11:59pm on Friday. or equal to the force of the car on the truck? ANSWER: The force of the truck on the car is larger than the force of the car on the truck. The spring scale reads in kg. The force of the truck on the car is equal to the force of the car on the truck. They are speeding up. Part A What is the reading of the scale? Express your answer to one significant figure and include the appropriate units. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: . Part A Draw a free-body diagram for the barbells. Draw the force vectors with their tails at the dot. ANSWER: m = 4 kg Correct Problem 7. The orientation of your vectors will be graded.1 A weightlifter stands up at constant speed from a squatting position while holding a heavy barbell across his shoulders. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: .Correct Part B Draw a free-body diagram for the weight lifter. The orientation of your vectors will be graded. Draw the force vectors with their tails at the dot. but you'll have to decide if they're part of the system. and the massless pulley turns on frictionless bearings. but the surface is not frictionless. . The rope and the pulley are among the interacting objects.6 Block A in the figure is sliding down the incline.Correct Problem 7. The rope is massless. Part A Draw a free-body diagram for the block A. ANSWER: Correct . The orientation of your vectors will be graded. The exact length of your vectors will not be graded. ANSWER: Correct A Space Walk Part A . The orientation of your vectors will be graded. The exact length of your vectors will not be graded.Part B Draw a free-body diagram for the block B. Take a tool from her tool belt and throw it away from the shuttle. have equal magnitude and opposite direction. Within each pair. she exerts a force in the direction away from the shuttle. Take the portion of the safety tether still attached to her belt and throw it toward the shuttle. the forces. Take slow steps toward the shuttle. often called action and reaction. For example. ANSWER: . How to approach the problem Recall that the force acting on the astronaut is equal in magnitude and opposite in direction to the force that she exerts on the tool. by Newton's 3rd law. as she throws the tool. What should the astronaut do to get back to the shuttle? Hint 1. Hint 2. Newton's 2nd law Newton's 2nd law states that F = ma. Hint 1. the object with the largest mass will experience the smallest acceleration. a force directed toward the shuttle will act on the astronaut. when the same force is applied to objects of different mass. Part B Assuming that the astronaut can throw any tool with the same force. Then. what tool should be thrown to get back to the shuttle as quickly as possible? You should consider how much mass is left behind as the object is thrown as well as the mass of the object itself. Which of the actions suggested in the problem will result in the force pushing the astronaut back to the shuttle? ANSWER: Attempt to "swim" toward the shuttle. Newton's 2nd law stipulates that the astronaut would acquire an acceleration toward the shuttle. Correct As the astronaut throws the tool away from the shuttle. the tool will exert an opposite force on her. How to approach the problem Newton's 3rd law tells us that forces occur in pairs. then acceleration is inversely proportional to mass. If force is held constant. Thus.An astronaut is taking a space walk near the shuttle when her safety tether breaks. since the mass of the tool would make no difference. if she exerts the same force on any tool. Express your answer in meters per second squared. Correct The force that acts on the astronaut must equal in magnitude the force that she exerts on the tool. Therefore. However. Find the force acting on the astronaut What is the magnitude of the force F acting on the astronaut as she throws the tool? Express your answer in newtons. Hint 1. the force acting on her will be independent of the mass of the tool. what is the magnitude of the acceleration a of the astronaut during the throw? Assume that the total mass of the astronaut after she throws the tool is 80.200 m/s2 m acted upon by a net force F has an acceleration a given by F = ma. the acceleration that the astronaut would acquire is inversely proportional to her mass since she is acted upon by a constant force. the remaining mass (the astronaut plus her remaining tools) would be smallest—and the acceleration the greatest! Part C If the astronaut throws the tool with a force of 16.0 N Hint 2. ANSWER: F = 16.0kg .The tool with the smallest mass. Newton's 2nd law An object of mass ANSWER: a = 0. If she throws the tool with the largest mass. Any tool. .0N . The tool with the largest mass. Correct Problem 7. Part A How much force does the 4kg block exert on the 6kg block? Express your answer to one significant figure and include the appropriate units. ANSWER: F = 50 N Correct Problem 7. ANSWER: F = 30 N Correct Part B How much force does the 4kg block exert on the 2kg block? Express your answer to two significant figures and include the appropriate units. When the driver steps on the accelerator. Rolling friction can . 4kg .9 A 1000kg car pushes a 2100kg truck that has a dead battery.10 Blocks with masses of 2kg . All three are pushed forward by a 60N force applied to the 2kg block. the drive wheels of the car push against the ground with a force of 4500N . and 6kg are lined up in a row on a frictionless table. ANSWER: F = 3000 N Correct Part B What is the magnitude of the force of the truck on the car? Express your answer to two significant figures and include the appropriate units. to be positive. examining special cases will simplify a problem. Often. so that the solution may be found from inspection or from the results of a problem you've already seen. perfect (massless and frictionless) pulley. Part A What is the magnitude of the force of the car on the truck? Express your answer to two significant figures and include the appropriate units. g. .be neglected. take upward to be the positive direction and take the gravitational constant. For all parts of this problem. In this problem you'll investigate some special cases where physical variables describing the Atwood machine take on limiting values. ANSWER: F = 3000 N Correct Atwood Machine Special Cases An Atwood machine consists of two blocks (of masses m1 and m2 ) tied together with a massless rope that passes over a fixed. Try to do this without equations. Let T1 be the magnitude of the tension in the rope connected to the block of mass m1 . Which physical law to use Use Newton's 2nd law on the block of mass m2 . Hint 1. . T2 is greater than T1 by an amount independent of velocity. think about the physical consequences. How to approach the problem If the block of mass m1 is not present. and m2 tension in the rope connected to the block of mass > m1. There is not enough information to determine the relationship between T1 and T2 .Part A Consider the case where m1 and m2 are both nonzero. and the rope connecting the two blocks is massless. will the motion of the block of mass m2 be any different from free fall? Hint 2. Find the magnitude. T . instead. and let T2 be the magnitude of the m2 . Which of the following statements is true? ANSWER: T1 is always equal to T2 . of the tension in the rope. Correct Part B Now. T2 is greater than T1 but the difference decreases as the blocks increase in velocity. consider the special case where the block of mass m1 is not present. ANSWER: a2 = -9. Find the magnitude. and remember that an upward acceleration should be positive. what is the acceleration of the block of mass m2 ? Express your answer in terms of g. . T .80 Correct Part D Next.ANSWER: T= 0 Correct Part C For the same special case (the block of mass m1 not present). of the tension in the rope. and remember that an upward acceleration should be positive. ANSWER: T= 0 Correct Part E For the same special case (the block of mass m2 not present) what is the acceleration of the end of the rope where the block of mass m2 would have been attached? Express your answer in terms of g. consider the special case where only the block of mass m1 is present. ANSWER: a2 = 9. What is the magnitude of the tension in the rope connecting the two blocks? Use the variable m in your answer instead of m1 or m2 . What value does the the magnitude of the tension approach? Hint 1. Acceleration of block of mass m1 . what is the acceleration of the block of mass m2 ? ANSWER: a2 = 0 Correct Part H Finally. ANSWER: T = mg Correct Part G For the same special case (m1 = m2 = m).80 Correct Part F Next. while m2 remains finite. consider the special case m1 = m2 = m. suppose m1 →∞. the finite tension T will have a neglible effect on the acceleration. what value does a1 approach? As ANSWER: a1 = -9. and any other given quantities. g. you can pretend the rope is gone without changing your results for a1 . what value will the acceleration of the block of mass m2 approach? ANSWER: a2 = 9. a1 . Acceleration of block of mass As m2 m1 →∞. T . . Take the upward direction to be positive. As m1 →∞. ANSWER: Fnet = T − m2 g ANSWER: T = 2m2 g Correct Imagining what would happen if one or more of the variables approached infinity is often a good way to investigate the behavior of a system.m1 becomes large. m2 . Net force on block of mass m2 What is the magnitude Fnet of the net force on the block of mass Express your answer in terms of m2 .80 Hint 2.80 Hint 3. If you ignore T . The coefficient of friction between the sleds and the snow is 0. Part A What is the tension at the midpoint of the rope? Express your answer to two significant figures and include the appropriate units.10. what is the tension in rope 2? Express your answer to two significant figures and include the appropriate units. ANSWER: T2 = 180 N .17 A 5.Problem 7.23 The sled dog in figure drags sleds A and B across the snow.9kg rope hangs from the ceiling. ANSWER: T = 29 N Correct Problem 7. Part A If the tension in rope 1 is 100N . you may want to review: Vector Components Part A How long does it take package A to reach the bottom? Express your answer with the appropriate units. For help with math skills.181) .31 Two packages at UPS start sliding down the 20∘ ramp shown in the figure. what is the acceleration of the blocks? What is the initial velocity of the blocks? Given the initial velocity and the acceleration. In your coordinate system. How to approach the problem Start by drawing force identification diagrams for package A and package B separately. Hint 1.) Using the components of the forces and Newton's second law. What is a good coordinate system to use to describe the motion of the blocks down the ramp? Label your coordinate system on the free-body diagram.0kg and a coefficient of kinetic friction of 0. .50kg and a coefficient of kinetic friction of 0.150.Correct Enhanced EOC: Problem 7. What are the four forces acting on each block? Which of the forces are related by Newton's third law? Draw separate free-body diagrams for block A and for block B. compute the x and y components of each force on block A. Package A has a mass of 4. Package B has a mass of 11. You may want to review ( pages 177 . What are the x and y components of the net force on block A? What are the x and y components of the net force on block B? Given that the coefficient of friction of block A is greater than the coefficient of friction of block B. do you think the blocks will stay together as they slide down the ramp? Assuming that they do stay together. how is the acceleration of the two blocks related? (We can check this assumption later.200. The coefficient of kinetic friction at both the lower and upper surfaces of the 2. .0 kg block is µk = 0.48 s Correct Problem 7. If the force is directed toward the bottom of the ramp.33 The 1.how long does it take block A to go the given distance? To check that the blocks do indeed stay together. solve for the force of block B on block A. ANSWER: 1. The lower block is pulled to the right with a tension force of 20 N. then the blocks stay together.420.0 kg block in the figure is tied to the wall with a rope.0 kg block. It sits on top of the 2. ANSWER: 1.38 The 100 kg block in figure takes 5. ANSWER: 4.Part A What is the tension in the rope holding the 1. .60s to reach the floor after being released from rest.77 m s2 Correct Problem 7.0 kg block to the wall? Express your answer with the appropriate units.0 kg block? Express your answer with the appropriate units.12 N Correct Part B What is the acceleration of the 2. 82 and 0. frictionless pulley to a hanging block of mass 2. ANSWER: 98. Part A What is the minimum mass m that will stick and not slip? .41 Figure shows a block of mass m resting on a 20∘ slope.0 kg.7 kg Correct Problem 7. It is connected via a massless string over a massless.Part A What is the mass of the block on the left? Express your answer with the appropriate units. The block has coefficients of friction 0.51 with the surface. The painter's mass is 75kg and the chair's mass is 12kg .80 kg Correct If you need to use the rounded answer you submitted here in a subsequent part.Express your answer to three significant figures and include the appropriate units. instead use the full precision answer and only round as a final step before submitting an answer. Part B If this minimum mass is nudged ever so slightly. ANSWER: m a = 1. it will start being pulled up the incline. ANSWER: m = 1. What acceleration will it have? Express your answer to three significant figures and include the appropriate units.46 A house painter uses the chair and pulley arrangement of the figure to lift himself up the side of a house.35 s 2 Correct Problem 7. . 6%. .5 out of a possible total of 106 points. You received 104.22m/s2 ? Express your answer to two significant figures and include the appropriate units.Part A With what force must he pull down on the rope in order to accelerate upward at 0. ANSWER: F = 440 N Correct Score Summary: Your score on this assignment is 98. or equal to the tension in string B if the balls travel over the top of the circle with equal speed? ANSWER: The tension in string A is less than the tension in string B. The tension in string A is greater than the tension in string B.5 The figure shows two balls of equal mass moving in vertical circles. Grading Policy Conceptual Question 8. less than. The tension in string A is equal to the tension in string B. Correct . 2014 You will receive no credit for items you complete after the assignment is due.Assignment 7 Due: 11:59pm on Friday. Part A Is the tension in string A greater than. March 21. less than. Part A Which of the following sets of vectors best describes the velocity. and net force acting on the cylinder at the point indicated in the diagram? Typesetting math: 100% . or equal to the tension in string B if the balls travel over the top of the circle with equal angular velocity? ANSWER: The tension in string A is less than the tension in string B. Correct A Mass on a Turntable: Conceptual A small metal cylinder rests on a circular turntable that is rotating at a constant rate. acceleration. as illustrated in the diagram. The tension in string A is equal to the tension in string B.Part B Is the tension in string A greater than. The tension in string A is greater than the tension in string B. Now assume that the cylinder is moved to a new location R/2 from the center of the turntable. Typesetting math: 100% . The direction of acceleration can be determined from Newton's second law According to Newton's second law.Hint 1. Which of the following statements accurately describe the motion of the cylinder at the new location? Check all that apply. the acceleration of an object has the same direction as the net force acting on that object. ANSWER: a b c d e Correct Part B Let R be the distance between the cylinder and the center of the turntable. Express your answer in terms of R and T .Hint 1. Assume that the cylinder makes one complete turn in a period of time T . Express your answer in terms of R and T . Centripetal acceleration Recall that the acceleration of an object that moves in a circular path of radius r with constant speed v has magnitude given by a= Note that both the velocity and radius of the trajectory change when the cylinder is moved. . Find the speed of the cylinder Find the speed v of the cylinder at the new location. Assume that the cylinder makes one complete turn in a period of time T . Find the acceleration of the cylinder Find the magnitude of the acceleration a of the cylinder at the new location. Hint 1. ANSWER: v = πR T Hint 2. ANSWER: a= 2π 2 R T2 ANSWER: Typesetting math: 100% v2 r . Acceleration along a curved path Typesetting math: 100% .The speed of the cylinder has decreased. Part A ⃗ be the velocity of the car at point A. What can you say about the acceleration of the car at that point? Let v A Hint 1. Correct Accelerating along a Racetrack A road race is taking place along the track shown in the figure . The speed and the acceleration of the cylinder have not changed. The car at point F is traveling along a straight section of the track. The magnitude of the acceleration of the cylinder has decreased. whereas all the other cars are moving along curved segments of the track. The speed of the cylinder has increased. All of the cars are moving at constant speeds. The magnitude of the acceleration of the cylinder has increased. Correct Part B ⃗ be the velocity of the car at point C. The acceleration is neither parallel nor perpendicular to vA The acceleration is zero. if the speed is constant. an object moving at constant speed along a curved path has nonzero acceleration because the direction of its velocity magnitude of its velocity (the speed) is constant. an object moving at constant speed along a curved path has nonzero acceleration because the direction of its velocity magnitude of its velocity (the speed) is constant. even though the v ⃗ at each point along the curved Since acceleration is a vector quantity. Moreover. ANSWER: Typesetting math: 100% v ⃗ is changing. even though the v ⃗ at each point along the curved . ANSWER: ⃗ . The acceleration is perpendicular to vA ⃗ .v ⃗ is changing. the object's acceleration is always perpendicular to the velocity vector path and is directed toward the center of curvature of the path. the object's acceleration is always perpendicular to the velocity vector path and is directed toward the center of curvature of the path. if the speed is constant. Moreover. The acceleration is parallel to v A ⃗ and directed toward the inside of the track. Acceleration along a curved path Since acceleration is a vector quantity. The acceleration is perpendicular to vA ⃗ and directed toward the outside of the track. What can you say about the acceleration of the car at that point? Let v C Hint 1. The acceleration is parallel to v C ⃗ and pointed toward the inside of the track. The acceleration is neither parallel nor perpendicular to vC The acceleration is zero. the object's acceleration is always perpendicular to the velocity vector path and is directed toward the center of curvature of the path. Correct Typesetting math: 100% v ⃗ is changing. The acceleration is neither parallel nor perpendicular to vD The acceleration is zero. even though the v ⃗ at each point along the curved . ANSWER: ⃗ . The acceleration is perpendicular to vD ⃗ . if the speed is constant. The acceleration is perpendicular to vC ⃗ . What can you say about the acceleration of the car at that point? Let v D Hint 1. The acceleration is parallel to v D ⃗ and pointed toward the inside of the track. an object moving at constant speed along a curved path has nonzero acceleration because the direction of its velocity magnitude of its velocity (the speed) is constant. The acceleration is perpendicular to vC ⃗ and pointed toward the outside of the track. Correct Part C ⃗ be the velocity of the car at point D. Moreover. Acceleration along a curved path Since acceleration is a vector quantity.⃗ . The acceleration is perpendicular to vD ⃗ and pointed toward the outside of the track. Correct Part E Assuming that all cars have equal speeds.Part D ⃗ be the velocity of the car at point F. The acceleration is neither parallel nor perpendicular to vF The acceleration is zero. Acceleration along a straight path The velocity of an object that moves along a straight path is always parallel to the direction of the path. and which one has the acceleration of the least magnitude? Use A for the car at point A. ANSWER: ⃗ . The acceleration is perpendicular to vF ⃗ . and so on. and separate your answers with a comma. The acceleration is perpendicular to vF ⃗ and pointed toward the outside of the track. The acceleration is parallel to v F ⃗ and pointed toward the inside of the track. What can you say about the acceleration of the car at that point? Let v F Hint 1. Hint 1. which car has the acceleration of the greatest magnitude. and the object has a nonzero acceleration only if the magnitude of its velocity changes in time. How to approach the problem Recall that the magnitude of the acceleration of an object that moves at constant speed along a curved path is inversely proportional to the radius of curvature of the path. Express your answer as the name the car that has the greatest magnitude of acceleration followed by the car with the least magnitude of accelation. ANSWER: Typesetting math: 100% . B for the car at point B. Uniform circular motion The magnitude a of the acceleration of an object that moves with constant speed v along a circular path of radius a= r is given by v2 r . how is the magnitude of its acceleration related to that of car E. Find the acceleration of the car at point E Let r be the radius of the two curves along which the cars at points A and E are traveling. Hint 1. what is the acceleration aA of the car at point A? Let r be the radius of the two curves along which the cars at points A and E are traveling. What is the magnitude aE of the acceleration of the car at point E? Express your answer in terms of the radius of curvature r and the speed vE of car E. Find the acceleration of the car at point A If vA = 2vE . Hint 1.Correct Part F Assume that the car at point A and the one at point E are traveling along circular paths that have the same radius. Express your answer in terms of the speed vE of the car at E and the radius r. If the car at point A now moves twice as fast as the car at point E. Typesetting math: 100% . ANSWER: 2 aE = vE r Hint 2. The magnitude of the acceleration of the car at point A is the same as that of the car at point E. ANSWER: Typesetting math: 100% r is given by . Uniform circular motion The magnitude of the acceleration of an object that moves with constant speed v along a circular path of radius a= v2 r . Correct Problem 8. The magnitude of the acceleration of the car at point A is half that of the car at point E. Part A What is the size of the friction force on the car? Express your answer to two significant figures and include the appropriate units.Hint 1. The magnitude of the acceleration of the car at point A is four times that of the car at point E.5 A 1300kg car takes a 50-m-radius unbanked curve at 13m/s . ANSWER: 2 aA = 4vE r ANSWER: The magnitude of the acceleration of the car at point A is twice that of the car at point E. ANSWER: Typesetting math: 100% .2 × 10 −8 m = 9. The inside surface is the deck of the space station.1 × 10−31 kg) orbits a proton at a distance of 5. Suppose a space station is constructed as a 1600-m-diameter cylinder that rotates about its axis.8 s Correct Problem 8.fs = 4400 N Correct Problem 8.10 It is proposed that future space stations create an artificial gravity by rotating.3 × 10−11 m. The proton pulls on the electron with an electric force of N. ANSWER: T = 56. an electron (mass 8.7 In the Bohr model of the hydrogen atom. Part A How many revolutions per second does the electron make? Express your answer with the appropriate units. Part A What rotation period will provide "normal" gravity? Express your answer with the appropriate units. you find the motion somewhat unpleasant. ANSWER: v = 14 m s Correct Problem 8.7 m s Typesetting math: 100% . Part A What is the car's speed at the bottom of the dip? Express your answer to two significant figures and include the appropriate units. you decide to ride the Ferris wheel. and you use your watch to find that each loop around takes 24s . ANSWER: v = 3. Part A What is your speed? Express your answer to two significant figures and include the appropriate units.18 While at the county fair.56×1015 s Correct Problem 8.rev 6. You estimate the radius of the big wheel to be 14m .14 The weight of passengers on a roller coaster increases by 56% as the car goes through a dip with a 38m radius of curvature. Having eaten too many candy apples and elephant ears. To take your mind off your stomach. you wonder about the motion of the ride. ANSWER: m a = 0. ANSWER: Typesetting math: 100% .90 FG Correct Part D What is the ratio of your weight at the bottom of the ride to your weight while standing on the ground? Express your answer using two significant figures.Correct Part B What is the magnitude of your acceleration? Express your answer to two significant figures and include the appropriate units. ANSWER: wtop = 0.96 s 2 Correct Part C What is the ratio of your weight at the top of the ride to your weight while standing on the ground? Express your answer using two significant figures. 46 A heavy ball with a weight of 120N is hung from the ceiling of a lecture hall on a 4. The ball is pulled to one side and released to swing as a pendulum. reaching a speed of 5. you may want to review: Solutions of Systems of Equations Part A What is the tension in the rope at that point? Express your answer to two significant figures and include the appropriate units. You may want to review ( pages 201 . For help with math skills. How to approach the problem Start by drawing a free-body diagram indicating the forces acting on the ball when it is at its lowest point. What is the tension in the rope at this point? ANSWER: T = 210 N Typesetting math: 100% . What is the direction of the acceleration in your chosen coordinate system? What is the magnitude of the acceleration for the mass. which is moving in a circular path? What is Newton's second law applied to the mass at the bottom of its swing? Make sure to use your coordinate system when determining the signs of all the forces and the acceleration. Hint 1.wbottom = 1.4-m-long rope. Choose a coordinate system.6m/s as it passes through the lowest point.204) .1 FG Correct Enhanced EOC: Problem 8. If a rider's mass is 54.80s . ANSWER: 211 N Correct Part B Typesetting math: 100% . After the ring has acquired sufficient speed. with how much force does the ring push on her at the top of the ride? Express your answer with the appropriate units. as shown in the figure . Part A Suppose the ring rotates once every 4.0kg .Correct Problem 8. it tilts into a vertical plane.0m -diameter rotating ring. passengers stand inside a 16.43 In an amusement park ride called The Roundup. Suppose the ring rotates once every 4. Part A What is the object's speed after the impulse? Express your answer as an integer and include the appropriate units. ANSWER: v= 4 m s Typesetting math: 100% . with how much force does the ring push on her at the bottom of the ride? Express your answer with the appropriate units. ANSWER: 5. If a rider's mass is 54. ANSWER: 1270 N Correct Part C What is the longest rotation period of the wheel that will prevent the riders from falling off at the top? Express your answer with the appropriate units.68 s Correct Conceptual Question 9.9 A 2kg object is moving to the right with a speed of 1 ^ i m/s when it experiences an impulse of 6 ^i N s.80s .0kg . Correct Part B What is the object's direction after the impulse? ANSWER: to the right to the left Correct Conceptual Question 9. ANSWER: v= 1 m s Correct Part B What is the object's direction after the impulse? Typesetting math: 100% .10 A 2kg object is moving to the right with a speed of 2 ^ i m/s when it experiences an impulse of -6 ^i N s. Part A What is the object's speed after the impulse? Express your answer as an integer and include the appropriate units. ANSWER: to the right to the left Correct Problem 9.6×103 N Correct Typesetting math: 100% . what value of Fmax gives an impulse of 6.4N s ? Express your answer to two significant figures and include the appropriate units. ANSWER: Fmax = 1.5 Part A In the figure . Part A Assuming that this force is constant. Typesetting math: 100% . The effect of a net force ΣF ⃗ acting on an object is related both to the force and to the total time the force acts on the object. The units of J ⃗ are N ⋅ s or kg ⋅ m/s.Impulse on a Baseball Learning Goal: To understand the relationship between force. His swing applies a force of 12. The physical quantity impulse J ⃗ is a measure of both these effects. causing a change in its velocity. impulse. In a baseball game the batter swings and gets a good solid hit. ANSWER: J = 8.4 N ⋅ s Correct We often visualize the impulse by drawing a graph of force versus time.70 × 10−3 s. For a constant net force such as that used in the previous part. the object will accelerate. and momentum. the impulse is given by ⃗ . A given change in momentum can result from a large force over a short time or a smaller force over a longer time. what is the magnitude J of the impulse on the ball? Enter your answer numerically in newton seconds using two significant figures. In Parts A. the net force multiplied by the time over which the force acts. the graph will look like the one shown in the figure. that is. B. J ⃗ = F ∆t The impulse is a vector pointing in the same direction as the force vector. The impulse-momentum theorem ⃗ . ∆p ⃗ = J ⃗ = F ∆t So the change in momentum of an object equals the net impulse. Hence the object's momentum (p ⃗ describes the effect that an impulse has on an object's motion: = mv)⃗ will also change. Recall that when a net force acts on an object.000 N to the ball for a time of 0. For a constant net force. C consider the following situation. the area of the rectangle corresponds to the impulse. ANSWER: length height For this graph.Part B The net force versus time graph has a rectangular shape. where a large force is applied for a short time. Typesetting math: 100% . Then as the ball loses contact with the bat. slope Correct The assumption of a constant net force is idealized to make the problem easier to solve. It will look like the graph in the figure. A more realistic graph of the force that the swinging bat applies to the baseball will show the force building up to a maximum value as the bat comes into full contact with the ball. the graph will show the force decaying to zero. especially in a case like the one presented in Parts A and B. A real force. Often in physics geometric properties of graphs have physical meaning. is not likely to be constant. Part C If both the graph representing the constant net force and the graph representing the variable net force represent the same impulse acting on the baseball. which geometric properties must the two graphs have in common? ANSWER: maximum force area slope Typesetting math: 100% . J ⃗ = ∆p ⃗ = m(vf⃗ − vi⃗ ). you can simplify the problem by finding the average net force F avg time ∆t. even in a Part D Assume that a pitcher throws a baseball so that it travels in a straight line parallel to the ground. The impulse of an object is also related to its change in momentum. the other momentum can be found. This average net force is treated as a constant force that acts on the ball for time ∆t. it is essential to account for the direction of each vector. ANSWER: Typesetting math: 100% . as in the case of the real net force acting on the baseball. Define the direction the pitcher originally throws the ball as the +x direction. Because both impulse and momentum are vectors. The batter then hits the ball so it goes directly back to the pitcher along the same straight line. or if either the initial or final momentum is known. Keep in mind that one-dimensional problem.Correct ⃗ acting on the baseball during When the net force varies over time. Once the impulse is known. These areas are represented in the figure as the areas shaded in red and blue respectively. The impulse on the ball can then be found as ⃗ ∆t. this method states that the impulse of the baseball can be represented by either the area under the net force versus time curve or the area under the average net force versus time curve. J ⃗ = F avg Graphically. it can be used to find the change in momentum. The batter then hits the ball so it goes directly back to the pitcher along the same straight line.0m/s when it experiences the force shown in the figure.4 N ⋅ s to the baseball? Enter your answer numerically in meters per second using two significant figures. What is the ball's velocity just after leaving the bat if the bat applies an impulse of −8.145-kg baseball parallel to the ground with a speed of 32 m/s in the +x direction.9 A 2.positive The impulse on the ball caused by the bat will be in the negative x direction. Problem 9. ANSWER: v ⃗ = -26 m/s Correct The negative sign in the answer indicates that after the bat hits the ball.6kg object is moving to the right with a speed of 1. the ball travels in the opposite direction to that defined to be positive. Typesetting math: 100% . Correct Part E Now assume that the pitcher in Part D throws a 0. 27 A tennis player swings her 1000 g racket with a speed of 11.0m/s . You may want to review ( pages 226 . ANSWER: v = 0. For help with math skills. you may want to review: Typesetting math: 100% .0m/s .0m/s .62 m s Correct Part B What is the object's direction after the force ends? ANSWER: to the right to the left Correct Enhanced EOC: Problem 9. She hits a 60 g tennis ball that was approaching her at a speed of 19. The ball rebounds at 41.232) .Part A What is the object's speed after the force ends? Express your answer to two significant figures and include the appropriate units. 40 s Correct Part B If the tennis ball and racket are in contact for 8. what are the velocity and speed of the racket after the collision? ANSWER: m 7. what is the initial momentum of the ball–racket system? What is the final momentum of the ball–racket system in terms of the velocity of the racket after the collision? Using conservation of momentum.Solving Algebraic Equations Part A How fast is her racket moving immediately after the impact? You can ignore the interaction of the racket with her hand for the brief duration of the collision. what is the average force that the racket exerts on the ball? Express your answer with the appropriate units.00ms . Keeping in mind that velocity can be either positive or negative in your coordinate system. Express your answer with the appropriate units. what is conserved during the collision? Draw a picture indicating the direction of the racket and ball before the collision and a separate picture for after the collision. Hint 1. How to approach the problem Given that you can ignore the interaction of the racket with her hand during the collision. Hint 1. indicating the positive x direction. How to approach the problem How is the impulse on the ball related to the change in momentum of the ball? What is the change in momentum of the ball? How are the impulse on the ball and the collision time related to the average force on the ball? Typesetting math: 100% . Place a coordinate system on your pictures. Part A What is the car's speed just after the gravel is loaded? Express your answer with the appropriate units.0g insect heading straight toward it with a speed of 34m/s (as measured by an observer on the ground.62 s Correct Problem 9.17 A 330g bird flying along at 5. ANSWER: m 4. ANSWER: Typesetting math: 100% . The bird opens its mouth wide and enjoys a nice lunch.00m/s when a 6000kg load of gravel is suddenly dropped in. not by the bird).0m/s sees a 9. Part A What is the bird's speed immediately after swallowing? Express your answer to two significant figures and include the appropriate units.14 4 A 2.00×10 kg railroad car is rolling at 6.ANSWER: 450 N Correct Problem 9. 20 A 50. Part A What is the recoil speed of the archer? Express your answer with the appropriate units.50m/s collides and sticks together with a 50.0g ball of clay traveling north at 4.25 A 40.0 m s Correct Problem 9.800 s Correct Problem 9.50m/s .v = 4.0kg archer. ANSWER: m 3. standing on frictionless ice.20 s Typesetting math: 100% .0g ball of clay traveling east at 4. Part A What is the speed of the resulting ball of clay? Express your answer with the appropriate units. shoots a 200g arrow at a speed of 200m/s . ANSWER: m 0. Correct Problem 9. Its momentum for t > 0 is given by px = 6t2 kg m/s.32 A particle of mass m is at rest at t = 0. Part A What is the earth's recoil speed after such a collision? (Use a reference frame in which the earth was initially at rest. Suppose an asteroid with a diameter of 2.) Assume that Express your answer to two significant figures and include the appropriate units. ANSWER: v = 9. .98 × 1024 kg.37 Most geologists believe that the dinosaurs became extinct 65 million years ago when a large comet or asteroid struck the earth. the force exerted on the particle as a function of time. throwing up so much dust that the sun was blocked out for a period of many months.0×10−8 m s Typesetting math: 100% MEarth = 5.5×104m/s . ANSWER: Fx = 12t N Correct Problem 9.0km and a mass of 1. where t is in s.2×1013kg hits the earth with an impact speed of 4. Express your answer in terms of the given quantities. Part A Find an expression for Fx (t). 50m/s . A second.42 One billiard ball is shot east at 1.2m/s .Correct Part B What percentage is this of the earth's speed around the sun? (Use the astronomical data in the textbook. The balls have a glancing collision. Typesetting math: 100% . identical billiard ball is shot west at 1. ANSWER: v = 1.6 m s Correct Part B What is the direction of the first ball after the collision? Give the direction as an angle south of east.0×10−10 % of the earth's speed Correct Problem 9. Part A What is the speed of the first ball after the collision? Express your answer to two significant figures and include the appropriate units. not a head-on collision. deflecting the second ball by 90∘ and sending it north at 1. ANSWER: v = 3.8m/s .) Express your answer using two significant figures. It passes all the way through the first block. A 12g bullet is fired at 420m/s toward the blocks. The speed of the first block immediately afterward is 5.49 Two 490g blocks of wood are 2.6 m s Correct Score Summary: Your score on this assignment is 99. You received 156. Typesetting math: 100% . ANSWER: v = 4.5%.Express your answer to two significant figures and include the appropriate units. ANSWER: θ = 68 ∘ Correct Problem 9. Part A What is the speed of the second block after the bullet stops? Express your answer to two significant figures and include the appropriate units.6m/s . then embeds itself in the second block.0 m apart on a frictionless table.21 out of a possible total of 157 points. Part A How far must you compress a spring with twice the spring constant to store the same amount of energy? Express your answer to two significant figures and include the appropriate units. April 4. 2014 You will receive no credit for items you complete after the assignment is due.5cm . ANSWER: ∆x = 1. Grading Policy Conceptual Question 10.3 Part A If a particle's speed increases by a factor of 5. by what factor does its kinetic energy change? ANSWER: K2 = 25 K1 Correct Conceptual Question 10.11 A spring is compressed 1.1 cm Correct .Assignment 8 Due: 11:59pm on Friday. 2 The lowest point in Death Valley is 85m below sea level. ANSWER: vc = 66. .Whitney? Express your answer to two significant figures and include the appropriate units.5 A boy reaches out of a window and tosses a ball straight up with a speed of 13m/s .3 Part A 4 At what speed does a 1800kg compact car have the same kinetic energy as a 1. The ball is 21m above the ground as he releases it.0km/hr ? Express your answer with the appropriate units. The summit of nearby Mt. ANSWER: ∆U = 3.Problem 10.80×10 kg truck going 21. Whitney has an elevation of 4420 m. Part A What is the change in potential energy of an energetic 80kg hiker who makes it from the floor of Death Valley to the top of Mt.4 km hr Correct Problem 10.5×106 J Correct Problem 10. ANSWER: v = 13 m s Correct Part C Use energy to find the speed of impact on the ground. ANSWER: Hmax = 30 m Correct Part B Use energy to find the ball's speed as it passes the window on its way down. ANSWER: v = 24 m s Correct .Part A Use energy to find the ball's maximum height above the ground. Express your answer to two significant figures and include the appropriate units. Express your answer to two significant figures and include the appropriate units. Express your answer to two significant figures and include the appropriate units. Part A .Problem 10.30m . Part A What speed does he need at the bottom? Express your answer with the appropriate units.8 A 59." a track that is one-quarter of a circle with a radius of 2.71 s Correct Problem 10.0kg skateboarder wants to just make it to the upper edge of a "quarter pipe. ANSWER: m 6.12 A 1500 kg car traveling at 12m/s suddenly runs out of gas while approaching the valley shown in the figure. The alert driver immediately puts the car in neutral so that it will roll. the total mechanical energy in a closed system is conserved. Since any two moments will work. technically. In this problem. let us consider an object launched vertically upward with an initial speed v. The law of conservation of energy for such cases implies that the sum of the object's kinetic energy and potential energy does not change with time. First. In the absence of nonconservative forces such as friction and air resistance. This is one particular case of the law of conservation of energy. The energy transformations that take place involve the object's kinetic energy K = (1/2)mv2 and its gravitational potential energy U = mgh. That choice. you will apply the law of conservation of energy to different objects launched from the earth. This idea can be expressed by the equation K i + Ui = K f + Uf .8 m s Correct Ups and Downs Learning Goal: To apply the law of conservation of energy to an object launched upward in the gravitational field of the earth. though. the choice of the moments to consider is. up to you. is usually suggested by the question posed in the problem.What will be the car’s speed as it coasts into the gas station on the other side of the valley? Express your answer to two significant figures and include the appropriate units. Neglect air resistance. what energy changes take place? ANSWER: . Part A As the projectile goes upward. ANSWER: v = 6. where "i" denotes the "initial" moment and "f" denotes the "final" moment. is associated with the interactions between the earth and the elevated object." it is useful to keep in mind that the energy. potential energy decreases. it is not the ball that possesses potential energy. Kinetic energy increases. Kinetic energy decreases. Kinetic energy is at a minimum. Kinetic energy is at a maximum. ANSWER: . Both kinetic and potential energy increase. it is the system "Earth-ball. potential energy is at a maximum. potential energy increases. Both kinetic and potential energy are at their minimum values." Although we will often talk about "the gravitational potential energy of an elevated object. in fact. Part C The potential energy of the object at the moment of launch __________. Correct Part B At the top point of the flight. Correct Strictly speaking. potential energy is at a minimum. rather. what can be said about the projectile's kinetic and potential energy? ANSWER: Both kinetic and potential energy are at their maximum values.Both kinetic and potential energy decrease. the zero level is chosen so as to make the relevant calculations simpler.5v? Express your answer in terms of ANSWER: h= 2 v 3 8g v and the magnitude of the acceleration of gravity g. Part E At what height h above the ground does the projectile have a speed of 0. it makes good sense to assume that only choice! Part D Using conservation of energy. the . U = 0 at the ground level--but this is not. v and the magnitude of the acceleration of gravity g. by any means. ANSWER: v2 hmax = 2g Correct You may remember this result from kinematics. In this case.is negative is positive is zero depends on the choice of the "zero level" of potential energy Correct Usually. find the maximum height Express your answer in terms of hmax to which the object will rise. It is comforting to know that our new approach yields the same answer. You need to determine the speed. the kinetic energy must be half of its original value (i.e. . You know that at the initial height (h 2 converted to potential energy when the projectile is at (1/2)hmax . ANSWER: u = 0. Using conservation of energy. (1/4)mv2 when h = (1/2)hmax). the best choice of "final" moment is the point at which the ball reaches its maximum height. as a multiple of v. the total energy is (1/2)mv . Express your answer in terms of v. Here.Correct Part F What is the speed u of the object at the height of Express your answer in terms of (1/2)hmax ? v and g. Use three significant figures in the numeric coefficient. the speed is v. Since the gravitational potential energy is proportional to h. and θ .707v Correct Let us now consider objects launched at an angle. g. At the maximum height. All of the energy is kinetic energy. find the maximum height hmax of the ball's flight. How to approach the problem = 0).. Thus. all of the energy is potential energy. since this is the point we are interested in. and so. Part G A ball is launched as a projectile with initial speed v at an angle θ above the horizontal. For such situations. Find the final kinetic energy Find the final kinetic energy K f of the ball. that corresponds to such a kinetic energy. Hint 1. Hint 1. half of the initial kinetic energy must have been You are being asked for the speed at half of the maximum height. using conservation of energy leads to a quicker solution than can be produced by kinematics. Using conservation of energy. m. and θ . find the maximum vertical height to which the ball will climb. hmax . Find the speed at the maximum height The speed of the ball at the maximum height is __________.5m(vcos(θ))2 ANSWER: 2 hmax = (vsin(θ)) 2g Correct Part H A ball is launched with initial speed v from ground level up a frictionless slope. Express your answer in terms of v. g. ANSWER: 0 v v cos θ v sin θ v tan θ ANSWER: K f = 0. The slope makes an angle θ with the horizontal. Hint 1. You may or may not use all of these quantities.Express your answer in terms of v. and θ . the equation K i + Ui = K f + Uf would have the same terms regardless of the steepness of the hill. The hill becomes steeper as the ball slides up. Part I A ball is launched with initial speed v from the ground level up a frictionless hill. however. the ball remains in contact with the hill at all times. the spring stretches to a length of 17cm . ANSWER: v2 hmax = 2g Correct The profile of the hill does not matter. the answer does not depend on θ . Express your answer in terms of v and g. Problem 10. When a 2.ANSWER: v2 hmax = 2g Correct Interestingly. Using conservation of energy.14 A 12-cm-long spring is attached to the ceiling.2kg mass is hung from it. find the maximum vertical height hmax to which the ball will climb. The difference between this situation and the projectile case is that the ball moving up a slope has no kinetic energy at the top of its trajectory whereas the projectile launched at an angle does. Part A What is the spring constant k? Express your answer to two significant figures and include the appropriate units. . you may want to review: Solving Algebraic Equations .ANSWER: N k = 430 m Correct Part B How long is the spring when a 3.0 kg mass is suspended from it? Express your answer to two significant figures and include the appropriate units.2kg mass hanging from a spring scale is slowly lowered onto a vertical spring. ANSWER: y ′ = 19 cm Correct Enhanced EOC: Problem 10. as shown in .257) . You may want to review ( pages 255 . For help with math skills.17 A 6. taking note of the directions from your picture. Hint 1. .7cm . How to approach the problem Draw a picture showing the forces acting on the mass before it touches the scale. What is the value of the spring constant for the lower spring? Express your answer to two significant figures and include the appropriate units. How to approach the problem Draw a picture showing the forces acting on the mass. What is the net force on the mass? What is the force on the mass due to gravity? What is the force on the mass due to the scale? Use these to determine the force on the mass by the spring.Part A What does the spring scale read just before the mass touches the lower spring? Express your answer to two significant figures and include the appropriate units. How is the spring constant ANSWER: N k = 1400 m k related to the force by the spring and the compression of the spring? Check your units. What is the net force on the mass? What is the force on the mass due to gravity? What is the force on the mass due to the scale? ANSWER: F = 61 N Correct Part B The scale reads 22N when the lower spring has been compressed by 2. Hint 1. 18 Part A How far must you stretch a spring with k = 800N/m to store 180J of energy? Express your answer to two significant figures and include the appropriate units. what is the force on the mass due to the scale? What is the gravitational force on the mass? What is the force on the mass by the spring? How is the compression length related to the force by the spring and the spring constant? Check your units. Hint 1.2 cm Correct Problem 10. When the scale reads zero. ANSWER: . How to approach the problem Draw a picture showing the forces on the mass. ANSWER: ∆y = 4.Correct Part C At what compression length will the scale read zero? Express your answer to two significant figures and include the appropriate units. 67 m Correct Problem 10. ANSWER: v = 2. The ball reaches a maximum height position of the spring. measured from the equilibrium . H . Part A What was the speed of the cart just before it hit the spring? Express your answer to two significant figures and include the appropriate units.22 A 15kg runaway grocery cart runs into a spring with spring constant 230N/m and compresses it by 57cm .∆s = 0.2 m s Correct Spring Gun A spring-loaded toy gun is used to shoot a ball straight up in the air. The spring was compressed half the distance. Potential energy of the ball At the highest point in the ball's trajectory. Assume that the spring is ideal and that the distance by which the spring is compressed is negligible compared to H . is traveling at speed vf . How far up does the ball go this time? Neglect friction. with the bullet in it. when launched. the block. Hint 2. has one quarter of the energy as in the first trial. Hint 1. The bullet hits the block and becomes completely embedded within it.Part A The same ball is shot straight up a second time from the same gun. Potential energy of the spring The potential energy of a spring is proportional to the square of the distance the spring is compressed. all of the spring's potential energy has been converted into gravitational potential energy of the ball. so the mass. After the bullet has come to rest within the block. ANSWER: height = H 4 Correct A Bullet Is Fired into a Wooden Block A bullet of mass mb is fired horizontally with speed vi at a wooden block of mass mw resting on a frictionless table. . but this time the spring is compressed only half as far before firing. ANSWER: perfectly elastic partially inelastic perfectly inelastic Correct Part B Which of the following quantities.Part A Which of the following best describes this collision? Hint 1. When is kinetic energy conserved? Kinetic energy is conserved only in perfectly elastic collisions. are conserved during this collision? Hint 1. you can infer what completely inelastic and elastic collisions are. ANSWER: . From this information. Types of collisions An inelastic collision is a collision in which kinetic energy is not conserved. but the objects colliding do not stick together. kinetic energy is lost. if any. In a partially inelastic collision. Find the momentum after the collision What is the total momentum ptotal of the block/bullet system after the collision? Express your answer in terms of vf and other given quantities. Use conservation of momentum The momentum of the block/bullet system is conserved. Therefore. the momentum before the collision is the same as the momentum after the collision. mw . ANSWER: ptotal = mb vi . Hint 1. and mb . this time expressed as the total momentum of the system before the collision. ANSWER: ptotal = (mw + mb )vf Hint 2.kinetic energy only momentum only kinetic energy and momentum neither momentum nor kinetic energy Correct Part C What is the speed of the block/bullet system after the collision? Express your answer in terms of vi . Express your answer in terms of vi and other given quantities. Find a second expression for ptotal. Part A What are the final velocities of each ball if the collision is perfectly elastic? Express your answer with the appropriate units.ANSWER: vf = m b m +vimw b Correct Problem 10.0m/s .82 m s Correct Part B Express your answer with the appropriate units. ANSWER: (vfx )2 = 9.18 m s Correct Part C . collides head on with ball 2. with a mass of 150g and traveling at 15.31 Ball 1. which has a mass of 340g and is initially at rest. ANSWER: (vfx )1 = -5. high.43 A package of mass m is released from rest at a warehouse loading dock and slides down the h = 2. you may want to review: Solving Algebraic Equations .2m . For help with math skills. Unfortunately. from the bottom of the chute. of mass 2m. ANSWER: (vfx )1 = 4.What are the final velocities of each ball if the collision is perfectly inelastic? Express your answer with the appropriate units.59 m s Correct Part D Express your answer with the appropriate units. the truck driver went on a break without having removed the previous package.59 m s Correct Enhanced EOC: Problem 10. ANSWER: (vfx )2 = 4. frictionless chute to a waiting truck.269) . You may want to review ( pages 265 . 2 m s Correct Part B Suppose the collision between the packages is perfectly elastic.Part A Suppose the packages stick together. How to approach the problem There are three parts to this problem: the block sliding down the incline. what are the kinetic and potential energies of the block at the top of the incline? What is the potential energy of the same block at the bottom just before the collision? What are the kinetic energy and velocity of block m just before the collision? What is conserved during the collision? What is the total momentum of the two blocks before the collision? What is the momentum of the two blocks stuck together after the collision? What is the velocity of the two blocks after the collision? ANSWER: v = 2. Hint 1. What conservation laws are valid in each part? . What conservation laws are valid in each part? In terms of m. How to approach the problem There are two parts to this problem: the block sliding down the frictionless incline and the collision. Hint 1. and mass m going back up the incline. What is their common speed after the collision? Express your answer to two significant figures and include the appropriate units. the collision. To what height does the package of mass m rebound? Express your answer to two significant figures and include the appropriate units. how are the initial and final velocities related when one of the masses is initially at rest? Using the velocity of m just before the collision from Part A.6 m s Correct Problem 10. ANSWER: vf = 81.What is an elastic collision? For an elastic collision.5m above a heavy-duty spring when the rope holding the safe breaks. what is the potential energy of mass m at its maximum height? What is the maximum ANSWER: h = 24 cm Correct Problem 10.0∘ angle fires a cannon ball at 79.0m -high fortress wall.0m/s from atop a 21. The safe hits the spring and compresses it 48cm .45 A 1000kg safe is 2.35 A cannon tilted up at a 35. what is the velocity of m just after the collision in this case? What are the kinetic and potential energies of mass What is the kinetic energy of mass height? m just after the collision? m at its maximum rebound height? Using conservation of energy. Part A What is the ball's impact speed on the ground below? Express your answer with the appropriate units. . ANSWER: v = 3.5×105 m Correct Problem 10.Part A What is the spring constant of the spring? Express your answer to two significant figures and include the appropriate units.2 m s Correct Part B What is the maximum compression of the spring? Express your answer to two significant figures and include the appropriate units.0m/s . Part A If the collision is perfectly elastic.49 A 100g block on a frictionless table is firmly attached to one end of a spring with k = 21N/m . The other end of the spring is anchored to the wall. ANSWER: . what is the ball's speed immediately after the collision? Express your answer to two significant figures and include the appropriate units. ANSWER: N k = 2. A 30g ball is thrown horizontally toward the block with a speed of 6. 4%. .4 m s Correct Part D Repeat part B for the case of a perfectly inelastic collision.∆x = 0. Express your answer to two significant figures and include the appropriate units. ANSWER: v = 1.11 m Correct Score Summary: Your score on this assignment is 99. ANSWER: ∆x = 0.28 out of a possible total of 121 points. You received 120. Express your answer to two significant figures and include the appropriate units.19 m Correct Part C Repeat part A for the case of a perfectly inelastic collision. 2014 You will receive no credit for items you complete after the assignment is due. ANSWER: A⃗ ⋅ B⃗ = -15 Correct Part B Evaluate the dot product A⃗ ⋅ B⃗ if A⃗ = −5^i + 9^j and B⃗ = 5^i + 6^j. Grading Policy Problem 11. Express your answer using two significant figures. April 11.Assignment 9 Due: 11:59pm on Friday. ANSWER: A⃗ ⋅ B⃗ = 29 Correct Problem 11.2 Part A Evaluate the dot product A⃗ ⋅ B⃗ if A⃗ = 5^i − 6^j and B⃗ = −9^i − 5^j.4 . Express your answer using two significant figures. the work done by the force can be calculated as W = F ⃗ ⋅ s ⃗ = ∣∣F ∣∣⃗ ∣s ∣⃗ cos θ.Part A What is the angle θ between vectors A⃗ and B⃗ if A⃗ = 2 ^ı + 5 ^ȷ and B⃗ = −2 ^ı − 4 ^ȷ? Express your answer as an integer and include the appropriate units. it is said that work is being done on the object. If the object is moving in a straight line and the displacement and the force are known. where W is the work done by force F ⃗ on the object that undergoes displacement s ⃗ directed at angle θ relative to F . ANSWER: θ = 175 ∘ Correct Part B What is the angle θ between vectors A⃗ and B⃗ if A⃗ = −6 ^ı + 2 ^ȷ and B⃗ = − ^ı − 3 ^ȷ? Express your answer as an integer and include the appropriate units. ANSWER: θ = 90 ∘ Correct ± All Work and No Play Learning Goal: To be able to calculate work done by a constant force directed at different angles relative to displacement If an object undergoes displacement while being acted upon by a force (or several forces).⃗ . Note that depending on the value of cos θ, the work done can be positive, negative, or zero. In this problem, you will practice calculating work done on an object moving in a straight line. The first series of questions is related to the accompanying figure. Part A What can be said about the sign of the work done by the force F 1⃗ ? ANSWER: It is positive. It is negative. It is zero. There is not enough information to answer the question. Correct When θ Part B = 90∘ , the cosine of θ is zero, and therefore the work done is zero. What can be said about the work done by force F 2⃗ ? ANSWER: It is positive. It is negative. It is zero. Correct When 0∘ < θ < 90∘ , cos θ is positive, and so the work done is positive. Part C The work done by force F 3⃗ is ANSWER: positive negative zero Correct When 90∘ < θ < 180∘ , cos θ is negative, and so the work done is negative. Part D The work done by force F 4⃗ is ANSWER: positive negative zero Correct Part E The work done by force F 5⃗ is ANSWER: positive negative zero Correct Part F The work done by force F 6⃗ is ANSWER: positive negative zero Correct Part G The work done by force F 7⃗ is ANSWER: positive negative zero Correct In the next series of questions, you will use the formula W = F ⃗ ⋅ s ⃗ = ∣∣F ∣∣⃗ ∣s ∣⃗ cos θ to calculate the work done by various forces on an object that moves 160 meters to the right. Part H Find the work W done by the 18-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: W = 2900 J Correct Part I Find the work W done by the 30-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: W = 4200 J Correct Part J Find the work W done by the 12-newton force. Use two significant figures in your answer. Express your answer in joules. Express your answer in joules. The first part of this problem contains short-answer questions that review the work-energy theorem. and K i and K f are the initial and final kinetic energies. ANSWER: W = -1800 J Correct Introduction to Potential Energy Learning Goal: Understand that conservative forces can be removed from the work integral by incorporating them into a new form of energy called potential energy that must be added to the kinetic energy to get the total mechanical energy. respectively. But for now. where Wall is the work done by all forces that act on the object. Use two significant figures in your answer. In the second part we introduce the concept of potential energy.ANSWER: W = -1900 J Correct Part K Find the work W done by the 15-newton force. please answer in terms of the work-energy theorem. . Work-Energy Theorem The work-energy theorem states K f = K i + Wall. Part A The work-energy theorem states that a force acting on a particle as it moves over a ______ changes the ______ energy of the particle if the force has a component parallel to the motion. Using the work-energy concept. but since the string's force is always perpendicular to the motion it does no work and cannot change the kinetic energy of the ball. Part B To calculate the change in energy. you must know the force as a function of _______. resulting in an increase of the ______ energy of the stone. the string does apply a force to the ball. For example. if a ball is attached to a string and whirled in uniform circular motion. consider the case of a stone falling from xi to xf under the influence of gravity. Choose the best answer to fill in the blank above: ANSWER: acceleration work distance potential energy Correct Part C To illustrate the work-energy concept. we say that work is done by the gravitational _____. Choose the best answer to fill in the blanks above: . The work done by the force causes the energy change.Choose the best answer to fill in the blanks above: ANSWER: distance / potential distance / kinetic vertical displacement / potential none of the above Correct It is important that the force have a component acting in the direction of motion. i where Uf and Ui are the final and initial potential energies. we will revisit the falling stone example using the concept of potential energy. The key aspect that allows for potential energy is the existence of conservative forces. we now (when using potential energy rather than work-energy) say that the increased kinetic energy comes from the ______ of the _______ energy. only the initial and final positions of the object. which now changes the total energy: K f + Uf = Ef = Wnc + Ei = Wnc + K i + U. only nonconservative forces contribute to the work. forces for which the work done on an object does not depend on the path of the object. Then only the work due to nonconservative forces needs to be calculated. it replaces the work done by the associated conservative force.ANSWER: force / kinetic potential energy / potential force / potential potential energy / kinetic Correct Potential Energy You should read about potential energy in your text before answering the following questions. when using the concept of potential energy. the frictional force is not. and Wnc is the work due only to nonconservative forces. When potential energy is used. The change in potential energy is the negative of the work done by conservative forces. Hence considering the initial and final potential energies is equivalent to calculating the work done by the conservative forces. Part D Rather than ascribing the increased kinetic energy of the stone to the work of gravity. enlarging the concept of energy in the most physically useful way. In summary. Choose the best answer to fill in the blanks above: ANSWER: . Now. The gravitational force is conservative. Potential energy is a concept that builds on the work-energy theorem. work / potential force / kinetic change / potential Correct Part E This process happens in such a way that total mechanical energy.6 ^j ) N on a particle that moves through displacement ∆r ⃗ = 3.2 ^i + 6. is _______. equal to the ______ of the kinetic and potential energies.7 Part A How much work is done by the force F ⃗ = (− 2. ANSWER: .9 ^i m Express your answer to two significant figures and include the appropriate units. Choose the best answer to fill in the blanks above: ANSWER: sum / conserved sum / zero sum / not conserved difference / conserved Correct Problem 11. 27m above the floor.W = -8.10 A 1. You pick it up and place it on a bookshelf 2.80-m-high table. ANSWER: Wg = -26 J Correct Part B .6 ^j ) N on a particle that moves through displacement ∆r ⃗ = 3. Part A How much work does gravity do on the book? Express your answer to two significant figures and include the appropriate units.8kg book is lying on a 0.2 ^i + 6.9 ^j m? Express your answer to two significant figures and include the appropriate units. ANSWER: W = 26 J Correct Problem 11.6 J Correct Part B How much work is done by the force F ⃗ = (− 2. W2 . Part A How much work is done by each of the three forces? Express your answers using two significant figures. ANSWER: W1 .-2.12 The three ropes shown in the bird's-eye view of the figure are used to drag a crate 3. ANSWER: WH = 26 J Correct Problem 11. W3 = 1.9.3m across the floor.1.1 kJ . Enter your answers numerically separated by commas.2.How much work does your hand do on the book? Express your answer to two significant figures and include the appropriate units. pages 286 . How to approach the problem What is the work–kinetic energy theorem? What is the kinetic energy at x = 0 m? How is the work done in going from x = 0 m to x = 2 m related to force shown in the graph? Using the work–kinetic energy theorem.16 A 1.287) . For help with math skills. you may want to review: The Definite Integral Part A What is its velocity at x = 2 m? Express your answer to two significant figures and include the appropriate units.6m/s at You may want to review ( x = 0 m.Correct Enhanced EOC: Problem 11. Hint 1.2kg particle moving along the x-axis experiences the force shown in the figure. what is the kinetic energy at ANSWER: x = 2 m? What is the velocity at x = 2 m? . The particle's velocity is 4. 6 m s Correct Work on a Sliding Block A block of weight w sits on a frictionless inclined plane. applied parallel to the incline.2 m s Correct Part B What is its velocity at x = 4 m? Express your answer to two significant figures and include the appropriate units. How to approach the problem What is the work–kinetic energy theorem? What is the kinetic energy at x = 0 m? How is the work done in going from x = 0 m to x = 4 m related to force shown in the graph? Can the work be negative? Using the work–kinetic energy theorem. as shown.v = 6. Hint 1. A force of magnitude F . . which makes an angle θ with respect to the horizontal. pulls the block up the plane at constant speed. what is the kinetic energy at x = 4 m? What is the velocity at x = 4 m? ANSWER: v = 4. The block does not stop after moving this distance but continues to move with constant speed.Part A The block moves a distance L up the incline. Find the change in kinetic energy What is the change in the kinetic energy of the block.) Express your answer in terms of given quantities. Hint 1. from the moment it starts moving until it has been pulled a distance L? Remember that the block is pulled at constant speed. ANSWER: Kf − Ki = 0 ANSWER: Wtot = 0 . use the work-energy theorem: Wtot = K f − K i. its kinetic energy cannot change. What physical principle to use To find the total work done on the block. Hint 2. not the work needed to start the block moving from rest. What is the total work Wtot done on the block by all forces? (Include only the work done after the block has started moving. Consider kinetic energy If the block's speed does not change. Hint 1. the work done on the block by the force of gravity as the block moves a distance L up the incline? Express the work done by gravity in terms of the weight w and any other quantities given in the problem introduction. Hint 1. Force of gravity component What is the component of the force of gravity in the direction of the block's displacement (along the inclined plane)? Express your answer in terms of w and θ . Relative direction of the force and the motion Remember that the force of gravity acts down the plane. Force diagram Hint 2.Correct Part B What is Wg . Hint 1. whereas the block's displacement is directed up the plane. ANSWER: . ANSWER: WF = FL Correct Part D What is Wnormal .Fg|| = −wsin(θ) ANSWER: Wg = −wLsin(θ) Correct Part C What is WF . the work done on the block by the applied force F as the block moves a distance L up the incline? Express your answer in terms of F and other given quantities. over the path followed by the object. the work done on the block by the normal force as the block moves a distance L up the inclined plane? Express your answer in terms of given quantities. Hint 1. Hint 1. the dot product becomes simple multiplication. since the force is constant and the path is a straight segment of length L up the inclined plane. In this case. How to find the work done by a constant force Remember that the work done on an object by a particular force is the integral of the dot product of the force and the instantaneous displacement of the object. First step in computing the work . The normal force and the block's displacement vector are perpendicular. Therefore. ANSWER: Fy = 0 N Correct Part B What is the y-component of the force on the particle at y = 1 m? Express your answer to two significant figures and include the appropriate units. where y is in m. Part A What is the y-component of the force on the particle at y = 0 m? Express your answer to two significant figures and include the appropriate units. .20 A particle moving along the y -axis has the potential energy U = 3.The work done by the normal force is equal to the dot product of the force vector and the block's displacement vector. what is their dot product? ANSWER: N ⃗ ⋅ L⃗ = 0 ANSWER: Wnormal = 0 Correct Problem 11.2y 3 J. 6 N Correct Part C What is the y-component of the force on the particle at y = 2 m? Express your answer to two significant figures and include the appropriate units. ANSWER: vf = 8.28 A cable with 25.40m ? Solve this problem using work and energy. Part A What is the block's speed after being lifted 2.08kg block that is initially at rest. ANSWER: Fy = -38 N Correct Problem 11. Express your answer with the appropriate units.00 m s Correct .ANSWER: Fy = -9.0N of tension pulls straight up on a 1. 23×104 W Correct Problem 11.62×106 J Correct Part B How much power must the motor supply to do this in 50s at constant speed? Express your answer with the appropriate units.0min and a 11.0hr ? Part A Hair dryer: Express your answer with the appropriate units.29 Part A How much work does an elevator motor do to lift a 1500kg elevator a height of 110m ? Express your answer with the appropriate units. .Problem 11.0W night light left on for 16.32 How many energy is consumed by a 1. ANSWER: Wext = 1.20kW hair dryer used for 10. ANSWER: P = 3. 20m/s2 for 10.45×105 J Correct .42 A 2500kg elevator accelerates upward at 1.20×105 J Correct Part B Night light: Express your answer with the appropriate units.34×105 J Correct Problem 11.ANSWER: W = 7. starting from rest. Part A How much work does gravity do on the elevator? Express your answer with the appropriate units. ANSWER: W = 6.0m . ANSWER: −2. 00×104 J Correct Part D What is the speed of the elevator as it reaches 10. ANSWER: 3.75×105 J Correct Part C Use the work-kinetic energy theorem to find the kinetic energy of the elevator as it reaches 10. ANSWER: m 4. ANSWER: 2. Express your answer with the appropriate units.Part B How much work does the tension in the elevator cable do on the elevator? Express your answer with the appropriate units.0m ? Express your answer with the appropriate units.0m .90 s Correct . Express your answer to two significant figures and include the appropriate units. After the box travels some distance.4kg box across a frictionless. The coefficient of kinetic friction of the box on the surface is 0. Part A Use work and energy to find the length of a ramp that will stop a 15.45.49 Truck brakes can fail if they get too hot. ANSWER: l = 53 cm Correct Problem 11.15.0∘ and the coefficient of rolling friction is 0. horizontal surface.Problem 11.000 kg truck that enters the ramp at 30m/s . In some mountainous areas. ramps of loose gravel are constructed to stop runaway trucks that have lost their brakes. Part A Use work and energy to find how far the box slides across the rough surface before stopping. Suppose a gravel ramp slopes upward at 6. the surface becomes rough. ANSWER: l = 83 m Correct .47 A horizontal spring with spring constant 130N/m is compressed 17cm and used to launch a 2. Express your answer to two significant figures and include the appropriate units. The combination of a slight upward slope and a large coefficient of rolling friction as the truck tires sink into the gravel brings the truck safely to a halt. Express your answer in terms of the variables M .Problem 11. m. and free fall acceleration g. µk .51 Use work and energy to find an expression for the speed of the block in the following figure just before it hits the floor. . h. Part A Find an expression for the speed of the block if the coefficient of kinetic friction for the block on the table is Express your answer in terms of the variables M . ANSWER: m. µk . and free fall acceleration g. ANSWER: v= Part B Find an expression for the speed of the block if the table is frictionless. h. The track is frictionless until it starts up the incline. ANSWER: . Part A What is the student's speed just after losing contact with the spring? Express your answer to two significant figures and include the appropriate units.v= Problem 11. ANSWER: v = 17 m s Correct Part B How far up the incline does the student go? Express your answer to two significant figures and include the appropriate units.57 The spring shown in the figure is compressed 60cm and used to launch a 100 kg physics student. The student's coefficient of kinetic friction on the 30∘ incline is 0.12 . You received 112. .37 out of a possible total of 120 points.6%.∆s = 41 m Correct Score Summary: Your score on this assignment is 93. their rotational kinetic energies to .. all of equal mass.3 Part A The figure shows three rotating disks. from largest to smallest.masteringphysics. April 18. Rank in order. To rank items as equivalent. Assignment 10 Due: 11:59pm on Friday. overlap them.Assignment 10 1 of 21 http://session. Rank from largest to smallest.. ANSWER: 4/11/2014 1:13 PM . 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 12.com/myct/assignmentPrintView?displayM. Part A By what factor does the moment of inertia of sphere 2 exceed the moment of inertia of sphere 1? ANSWER: = 32 Correct Problem 12. Try Again Conceptual Question 12.masteringphysics.Assignment 10 2 of 21 http://session.. Incorrect. Sphere 2 has twice the radius of sphere 1. ANSWER: = Constant Angular Acceleration in the Kitchen 4/11/2014 1:13 PM .59 ? Express your answer to two significant figures and include the appropriate units.59 ..com/myct/assignmentPrintView?displayM. ANSWER: = Part B Through how many revolutions does it turn during this first 0. Part A What is the drill's angular acceleration? Express your answer to two significant figures and include the appropriate units.2 A high-speed drill reaches 2500 in 0.6 You have two steel solid spheres. 0 times in 5. Assume that the spinner slows down with constant angular acceleration.. and its angular velocity decreases uniformly from 540 interval of length 4.masteringphysics.Assignment 10 3 of 21 http://session. a prep cook at an Italian restaurant. The salad spinner rotates 6.00 seconds and then stops spinning it.00 more times before it comes to rest. Dario. Part A What is the angular acceleration of the salad spinner as it slows down? Express your answer numerically in degrees per second per second.com/myct/assignmentPrintView?displayM. You did not open hints for this part. ± A Spinning Electric Fan An electric fan is turned off.. ANSWER: = Part B Find the number of revolutions made by the fan blades during the time that they are slowing down in Part A. to 250 in a time Part A Find the angular acceleration in revolutions per second per second. ANSWER: = Part B This question will be shown after you complete previous question(s). You did not open hints for this part. 4/11/2014 1:13 PM . spins a salad spinner and observes that it rotates 20.40 . 10 A thin.0 disk with a diameter of 9.8 A 100 ball and a 230 ball are connected by a 34mass at 130 .com/myct/assignmentPrintView?displayM.200 of kinetic energy. ANSWER: Part C How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in Part A? You did not open hints for this part. 60. -long.Assignment 10 4 of 21 http://session. massless. Part A What is the speed of a point on the rim? 4/11/2014 1:13 PM . ANSWER: Problem 12.. rigid rod. ANSWER: = Problem 12. You did not open hints for this part.masteringphysics. The balls rotate about their center of Part A What is the speed of the 100 ball? Express your answer to two significant figures and include the appropriate units..00 rotates about an axis through its center with 0. 4/11/2014 1:13 PM . and the cord's weight can be ignored. Express your answer with the appropriate units..Assignment 10 5 of 21 http://session.masteringphysics. while the mass of the pulley is equal to the mass of block A.12 A drum major twirls a 95- -long. ANSWER: = Net Torque on a Pulley The figure below shows two blocks suspended by a cord over a pulley. The blocks are let free to move and the cord moves on the pulley without slipping or stretching.com/myct/assignmentPrintView?displayM. The mass of block B is twice the mass of block A. Part A What is the baton's rotational kinetic energy? Express your answer to two significant figures and include the appropriate units. ANSWER: Problem 12. 470 baton about its center of mass at 150 . There is no friction in the pulley axle. Part A Which of the following statements correctly describes the system shown in the figure? Check all that apply.. . You did not open hints for this part. what is the magnitude of net torque about the axle? Express your answer to two significant figures and include the appropriate units.. ANSWER: = Part B What is the direction of net torque about the axle? ANSWER: 4/11/2014 1:13 PM .masteringphysics. Part B This question will be shown after you complete previous question(s). The net torque on the pulley is zero.Assignment 10 6 of 21 http://session. The angular acceleration of the pulley is nonzero. ANSWER: The acceleration of the blocks is zero. Problem 12.18 Part A In the figure .com/myct/assignmentPrintView?displayM. 22 An athlete at the gym holds a 3.5 steel ball in his hand.6 . long and has a mass of 3. to . Clockwise Counterclockwise Problem 12. His arm is 78 center of mass of the arm is at the geometrical center of the arm. 4/11/2014 1:13 PM . the moment of inertia of the rod with respect to a parallel axis through one end of the rod.masteringphysics.. The mathematical statement of the theorem is through point p.com/myct/assignmentPrintView?displayM.Assignment 10 7 of 21 http://session. Part A Suppose a uniform slender rod has length and mass . parallel to the floor? Express your answer to two significant figures and include the appropriate units.. where is the perpendicular distance from the center of mass to the axis that passes is the mass of the object. and . the moment of inertia of the same object about a parallel axis passing through point p. Use fractions rather than decimal numbers in your answer. Assume the Part A What is the magnitude of the torque about his shoulder if he holds his arm straight out to his side. ANSWER: = Part B What is the magnitude of the torque about his shoulder if he holds his arm straight. Express in terms of and . the moment of inertia of an object about an axis passing through its center of mass. Find . The moment of inertia of the rod about about an axis that is perpendicular to the rod and that passes through its center of mass is given by . but below horizontal? Express your answer to two significant figures and include the appropriate units. ANSWER: = Parallel Axis Theorem The parallel axis theorem relates . ANSWER: = Problem 12. ANSWER: = Part B Now consider a cube of mass with edges of length . Part A How much torque is applied to the disk? Express your answer to two significant figures and include the appropriate units..9 to reach its operating angular velocity of 2000 Assume that the angular acceleration is constant. Use fractions rather than decimal numbers in your answer.26 Starting from rest.Assignment 10 8 of 21 http://session.masteringphysics. Find . You did not open hints for this part. . a 12-diameter compact disk takes 2. 4/11/2014 1:13 PM . the moment of inertia about an axis p through one of the edges of the cube Express in terms of and .com/myct/assignmentPrintView?displayM. You did not open hints for this part. The moment of inertia its center of mass and perpendicular to one of its faces is given by of the cube about an axis through . The disk's moment of inertia is .. 1 cat and a 2. ANSWER: = Part B How many revolutions does it make before reaching full speed? Express your answer using two significant figures.5 bowl of tuna fish are at opposite ends of the 4.70 .com/myct/assignmentPrintView?displayM..31 A 5.Assignment 10 9 of 21 http://session. Part A What is the total torque on the object? ANSWER: Problem 12. 4/11/2014 1:13 PM . ANSWER: = rev Problem 12. Its angular velocity is increasing at the rate of 3.masteringphysics.0- -long seesaw.20 .23 An object's moment of inertia is 2.. . length and its center of mass is a distance from the scapula. (For this problem ignore the rest of the arm. Use throughout the problem.) The deltoid muscle attaches to the humerus a distance from the scapula. Assume the humerus bone has a mass . to the nearest integer. Part A Find the tension in the deltoid muscle.Assignment 10 10 of 21 http://session.. Express the tension in newtons. as shown. Part A How far to the left of the pivot must a 3.masteringphysics.com/myct/assignmentPrintView?displayM. ANSWER: = Static Equilibrium of the Arm You are able to hold out your arm in an outstretched horizontal position because of the action of the deltoid muscle. You did not open hints for this part.8 cat stand to keep the seesaw balanced? Express your answer to two significant figures and include the appropriate units. The deltoid muscle makes an angle of with the horizontal. ANSWER: 4/11/2014 1:13 PM . .. 4/11/2014 1:13 PM . Express your answer in newtons. ANSWER: = ± Moments around a Rod A rod is bent into an L shape and attached at one point to a pivot. Express your answer in newtons. The rod sits on a frictionless table and the diagram is a view from above. find the magnitude of the vertical component of the force exerted by the scapula on the humerus (where the humerus attaches to the rest of the body). and . meters. ANSWER: = Part C Now find the magnitude of the horizontal component of the force exerted by the scapula on the humerus. You did not open hints for this part.masteringphysics. . There are three forces that are applied to the rod at different points and angles: . to the nearest integer. seconds). although the answers are requested in SI units (kilograms. to the nearest integer.com/myct/assignmentPrintView?displayM.Assignment 10 11 of 21 http://session. This means that gravity can be ignored for this problem. = N Part B Using the conditions for static equilibrium. Note that the dimensions of the bent rod are in centimeters in the figure. ANSWER: = N Part B If the L-shaped rod has a moment of inertia time . without trigonometric functions. What does and . in newtons. You did not open hints for this part. Express the time in seconds to two significant figures. You did not open hints for this part. would it take for the object to move through ( . but now a force with nonzero magnitude is acting on have to be to obtain equilibrium? Give a numerical answer. ANSWER: = N 4/11/2014 1:13 PM . to two significant figures. Part A If and .. ANSWER: = s Part C Now consider the situation in which the rod.masteringphysics..com/myct/assignmentPrintView?displayM. and again . . You did not open hints for this part. each force moves with the object so as to retain its initial angle relative to the object.Assignment 10 12 of 21 http://session. what does the magnitude of have to be for there to be rotational equilibrium? Answer numerically in newtons to two significant figures. how long a /4 radians)? Assume that as the object starts to move. ANSWER: Part B What is the speed of a point at the top edge of the tire? Express your answer to three significant figures and include the appropriate units.30 .. in rpm? Express your answer to three significant figures and include the appropriate units. Part A What is the tire's rotation frequency.masteringphysics.0 in diameter. ANSWER: Problem 12. Part A What is the can's kinetic energy? Express your answer with the appropriate units. 8.00-cm-diameter solid cylinder rolls across the floor at 1.com/myct/assignmentPrintView?displayM. ANSWER: Part C What is the speed of a point at the bottom edge of the tire? Express your answer as an integer and include the appropriate units.32 A car tire is 55.0 .Assignment 10 13 of 21 http://session. Problem 12. The car is traveling at a speed of 24.33 A 460 . 4/11/2014 1:13 PM .. .Assignment 10 14 of 21 http://session.46 4/11/2014 1:13 PM .com/myct/assignmentPrintView?displayM.masteringphysics.45 Part A What is the magnitude of the angular momentum of the 780 rotating bar in the figure ? ANSWER: Part B What is the direction of the angular momentum of the bar ? ANSWER: into the page out of the page Problem 12. ANSWER: Problem 12.. com/myct/assignmentPrintView?displayM.60 A 3. Part A What is the magnitude of the angular momentum of the 2. The coefficient of static friction between the ladder and the floor is 0.46. 4..20 .masteringphysics.0..-long ladder. leans against a frictionless wall. as shown in the following figure. 4/11/2014 1:13 PM .Assignment 10 15 of 21 http://session.60-cm-diameter rotating disk in the figure ? ANSWER: Part B What is its direction? ANSWER: x direction -x direction y direction -y direction z direction -z direction Problem 12. rigid beam in the following figure is supported at each end.Assignment 10 16 of 21 http://session.0 from Part A How much upward force does the support 1 exert on the beam? Express your answer to two significant figures and include the appropriate units. ANSWER: = Problem 12..61 The 3.-long.masteringphysics.. 90 support 1. An 70 student stands 2. Part A What is the minimum angle the ladder can make with the floor without slipping? Express your answer to two significant figures and include the appropriate units.com/myct/assignmentPrintView?displayM.0. ANSWER: 4/11/2014 1:13 PM . masteringphysics.5the beam. but not attached to. A 22 You may want to review ( boy starts walking along pages 330 ..com/myct/assignmentPrintView?displayM. 5.. For help with math skills. the two posts in the figure . -long beam is supported. You did not open hints for this part. ANSWER: 4/11/2014 1:13 PM . = Part B How much upward force does the support 2 exert on the beam? Express your answer to two significant figures and include the appropriate units.334) .63 A 44 . ANSWER: = Enhanced EOC: Problem 12. you may want to review: The Vector Cross Product Part A How close can he get to the right end of the beam without it falling over? Express your answer to two significant figures and include the appropriate units.Assignment 10 17 of 21 http://session. then the wheel's energy can be released quickly to accomplish a task that demands high power. = Problem 12. Part A A motor spins up the flywheel with a constant torque of 54 speed? .6 diameter and a mass of 270 . An industrial flywheel has a 1.Assignment 10 18 of 21 http://session.68 Flywheels are large.com/myct/assignmentPrintView?displayM. massive wheels used to store energy. Its maximum angular velocity is 1500 .. Half the energy stored in the flywheel is delivered in 2. How long does it take the flywheel to reach top Express your answer to two significant figures and include the appropriate units.masteringphysics. ANSWER: = Part C The flywheel is disconnected from the motor and connected to a machine to which it will deliver energy.. What is the average power delivered to the machine? Express your answer to two significant figures and include the appropriate units. ANSWER: = Part B How much energy is stored in the flywheel? Express your answer to two significant figures and include the appropriate units. ANSWER: = 4/11/2014 1:13 PM . They can be spun up slowly.2 . 4/11/2014 1:13 PM . 40. The axle is parallel to the floor.71 The 3.com/myct/assignmentPrintView?displayM.0 . Part D How much torque does the flywheel exert on the machine? Express your answer to two significant figures and include the appropriate units. then released. .. ANSWER: = Problem 12. The cylinder is held with the center of mass at the same height as the axle.30 350 ..74 A 5.Assignment 10 19 of 21 http://session.masteringphysics. 60-diameter cylinder rotates on an axle passing through one edge.0-cm-diameter disk in the figure is spinning at Part A How much friction force must the brake apply to the rim to bring the disk to a halt in 2. ANSWER: Problem 12.10 ? Express your answer with the appropriate units. Assignment 10 20 of 21 http://session.82 A 45 figure skater is spinning on the toes of her skates at 0..com/myct/assignmentPrintView?displayM. 200-tall cylinder. ANSWER: = Problem 12. 20 average diameter. 20-diameter. ANSWER: = Part B What is the magnitude of the cylinder's angular velocity when it is directly below the axle? Express your answer to two significant figures and include the appropriate units. in revolutions per second? Express your answer to two significant figures and include the appropriate units. ANSWER: 4/11/2014 1:13 PM . 67 long) attached to the outside of the torso.masteringphysics. the skater can be modeled as a cylindrical torso (40 . 160 tall) plus two rod-like arms (2.5 each. In this orientation. where she appears to be a 45 . Part A What is the magnitude of the cylinder's initial angular acceleration? Express your answer to two significant figures and include the appropriate units.90 .. Part A What is her new rotation frequency. Her arms are outstretched as far as they will go. The skater then raises her arms straight above her head. 4/11/2014 1:13 PM .84 out of a possible total of 198 points. You received 7.masteringphysics.com/myct/assignmentPrintView?displayM..Assignment 10 21 of 21 http://session.. = Score Summary: Your score on this assignment is 4.0%. 035. It can be written in terms of the momentum p and mass m as 2 KE = P . Find the x.P. –/2 points SerCP9 1. A point is located in a polar coordinate system by the coordinates r = 3. A small turtle moves at a speed of 459 furlongs per fortnight. p. Note that 1 furlong = 220 yards and 1 fortnight = 14 days. 2 2 Kinetic energy KE has dimensions kg · m /s ..webassign.0 m and θ = 30°.0 10 -7 3 kg and density 1054 kg/m that spreads out into a circle of radius 41.HW #1 1 of 3 http://www. Your instructor may ask you to turn in this work.and y-coordinates of this point. Summer 1 2013 Instructor: Shawn Slavin WebAssign Physics 220 . –/2 points SerCP9 1. You can obtain a rough estimate of the size of a molecule by the following simple experiment. (Do this on paper. aalromia::app-6@purdue Summer-2013-PHYS-22000-01-XLST. x= m y= m Show My Work (Optional) 19-05-2013 13:42 . –/2 points SerCP9 1.P.016. what is the order of magnitude of the diameter of an oil molecule? 10 −5 10 −7 10 −9 10 −11 10 −14 Show My Work (Optional) 3. Let a droplet of oil spread out on a smooth surface of water. Find the speed of the turtle in centimeters per second.P. write a simple equation relating a constant force F exerted on an object.Physics 220 .8 cm on the water surface.FB. Given the units of force. an interval of time t during which the force is applied. The resulting oil slick will be approximately one molecule thick. 2m (a) Determine the proper units for momentum using dimensional analysis. assuming that the two coordinate systems have the same origin.502. 2 kg · m/s kg · m/s 2 kg · m /s 2 kg · m/s 2 (b) Force has the SI units kg · m/s .XP. –/2 points SerCP9 1.006. cm/s Show My Work (Optional) 4.MI.) Show My Work (Optional) 2.net/web/Student/Assignment-Responses/last?d.HW #1 (Homework) Current Score : – / 20 Due : Wednesday.P. May 22 2013 11:59 PM EDT 1. Given an oil droplet of mass 6.. and the resulting momentum of the object. P. 5.028. In 1865.webassign..) 2 m/s 2 Compare your answer with the free-fall acceleration.e.0 m/s. –/2 points SerCP9 1. In the figure below. g Show My Work (Optional) 7.P. –/2 points SerCP9 2.045. (a) How high does it rise? m (b) How long does it take to reach its highest point? s (c) How long does the ball take to hit the ground after it reaches its highest point? s (d) What is its velocity when it returns to the level from which it started? m/s Show My Work (Optional) 19-05-2013 13:42 .net/web/Student/Assignment-Responses/last?d. Jules Verne proposed sending men to the Moon by firing a space capsule from a 220-m-long cannon with final speed of 10. 9.P. (a) the side opposite θ (b) the side adjacent to (c) cos θ (d) sin (e) tan Show My Work (Optional) 6. how many times stronger than gravity is this force?). find each of the following. –/2 points SerCP9 2.HW #1 2 of 3 http://www.. A ball is thrown vertically upward with a speed of 18.97 km/s.045.Physics 220 .80 m/s (i.WI. What would have been the unrealistically large acceleration experienced by the space travelers during their launch? (A human can stand an acceleration of 15g for a short time. which can jump to a height of 3.P. –/2 points SerCP9 3.P.webassign.025.P.010.. Vector A has a magnitude of 25 units and points in the positive y-direction.7 m when leaving the ground at an angle of 45°.WI.0° north of east for 2.–/2 points SerCP9 3. When vector B is added to A. The best leaper in the animal kingdom is the puma.70 km. With what speed must the animal leave the ground to reach that height? m/s Show My Work (Optional) 19-05-2013 13:42 . A person walks 17. the resultant vector A + B points in the negative y-direction with a magnitude of 14 units. 8.Physics 220 .001. Find the magnitude and direction of B? magnitude unit(s) direction Show My Work (Optional) 9.net/web/Student/Assignment-Responses/last?d..HW #1 3 of 3 http://www. –/2 points SerCP9 3. How far due north and how far due east would she have to walk to arrive at the same location? north km east km Show My Work (Optional) 10. aalsadah::app-6@purdue Summer-2013-PHYS-22000-01-XLST.502. –/2 points SerCP9 1. A small turtle moves at a speed of 219 furlongs per fortnight.HW #1 1 of 3 http://www.0 10 -6 3 kg and density 882 kg/m that spreads out into a circle of radius 41. 2 kg · m/s kg · m/s 2 kg · m /s 2 kg · m/s 2 (b) Force has the SI units kg · m/s .webassign.net/web/Student/Assignment-Responses/last?d. May 22 2013 11:59 PM EDT 1.P.6 m and θ = 22°.HW #1 (Homework) Current Score : – / 20 Due : Wednesday. write a simple equation relating a constant force F exerted on an object.P. cm/s Show My Work (Optional) 4. Given an oil droplet of mass 1.MI. Find the x. p. –/2 points SerCP9 1. an interval of time t during which the force is applied. You can obtain a rough estimate of the size of a molecule by the following simple experiment. assuming that the two coordinate systems have the same origin.006.Physics 220 .8 cm on the water surface.and y-coordinates of this point. Summer 1 2013 Instructor: Shawn Slavin WebAssign Physics 220 . A point is located in a polar coordinate system by the coordinates r = 5.P. (Do this on paper.) Show My Work (Optional) 2. The resulting oil slick will be approximately one molecule thick. Your instructor may ask you to turn in this work. –/2 points SerCP9 1. what is the order of magnitude of the diameter of an oil molecule? 10 −5 10 −7 10 −9 10 −11 10 −14 Show My Work (Optional) 3. It can be written in terms of the momentum p and mass m as 2 KE = P . Find the speed of the turtle in centimeters per second. and the resulting momentum of the object.XP.035. x= m y= m Show My Work (Optional) 19-05-2013 20:37 .. Note that 1 furlong = 220 yards and 1 fortnight = 14 days.016. 2m (a) Determine the proper units for momentum using dimensional analysis..FB. 2 2 Kinetic energy KE has dimensions kg · m /s . Let a droplet of oil spread out on a smooth surface of water. Given the units of force.P. –/2 points SerCP9 1. WI. –/2 points SerCP9 2. 9.045. In the figure below. Jules Verne proposed sending men to the Moon by firing a space capsule from a 220-m-long cannon with final speed of 10.0 m/s.P. –/2 points SerCP9 1. –/2 points SerCP9 2.80 m/s (i.028. In 1865. What would have been the unrealistically large acceleration experienced by the space travelers during their launch? (A human can stand an acceleration of 15g for a short time.045..webassign.P..) 2 m/s 2 Compare your answer with the free-fall acceleration.net/web/Student/Assignment-Responses/last?d. how many times stronger than gravity is this force?). (a) the side opposite θ (b) the side adjacent to (c) cos θ (d) sin (e) tan Show My Work (Optional) 6. g Show My Work (Optional) 7.97 km/s. find each of the following. 5.e.P.HW #1 2 of 3 http://www. A ball is thrown vertically upward with a speed of 11. (a) How high does it rise? m (b) How long does it take to reach its highest point? s (c) How long does the ball take to hit the ground after it reaches its highest point? s (d) What is its velocity when it returns to the level from which it started? m/s Show My Work (Optional) 19-05-2013 20:37 .Physics 220 . 0° north of east for 2.025.001. Find the magnitude and direction of B? magnitude unit(s) direction Show My Work (Optional) 9.20 km.WI.HW #1 3 of 3 http://www.7 m when leaving the ground at an angle of 45°. How far due north and how far due east would she have to walk to arrive at the same location? north km east km Show My Work (Optional) 10.webassign.P.. When vector B is added to A. A person walks 27..Physics 220 . –/2 points SerCP9 3. which can jump to a height of 3. the resultant vector A + B points in the negative y-direction with a magnitude of 12 units. –/2 points SerCP9 3.–/2 points SerCP9 3.P.P.net/web/Student/Assignment-Responses/last?d. With what speed must the animal leave the ground to reach that height? m/s Show My Work (Optional) 19-05-2013 20:37 . The best leaper in the animal kingdom is the puma. 8.010. Vector A has a magnitude of 29 units and points in the positive y-direction. 2m (a) Determine the proper units for momentum using dimensional analysis.HW #1 1 of 3 http://www.P. –/2 points SerCP9 1. Find the x. Given the units of force.HW #1 (Homework) Current Score : – / 20 Due : Wednesday. 2 2 Kinetic energy KE has dimensions kg · m /s . Your instructor may ask you to turn in this work. Let a droplet of oil spread out on a smooth surface of water. Note that 1 furlong = 220 yards and 1 fortnight = 14 days.P.6 m and θ = 34°. cm/s Show My Work (Optional) 4.502. The resulting oil slick will be approximately one molecule thick. x= m y= m Show My Work (Optional) 19-05-2013 13:21 . assuming that the two coordinate systems have the same origin.Physics 220 . an interval of time t during which the force is applied. 2 kg · m/s kg · m/s 2 kg · m /s 2 kg · m/s 2 (b) Force has the SI units kg · m/s . –/2 points SerCP9 1. Given an oil droplet of mass 8. A point is located in a polar coordinate system by the coordinates r = 5. akalajmi::app-6@purdue Summer-2013-PHYS-22000-01-XLST.0 10 -7 3 kg and density 1122 kg/m that spreads out into a circle of radius 41. You can obtain a rough estimate of the size of a molecule by the following simple experiment.FB.) Show My Work (Optional) 2.8 cm on the water surface. Find the speed of the turtle in centimeters per second.P. –/2 points SerCP9 1.webassign..006. and the resulting momentum of the object. Summer 1 2013 Instructor: Shawn Slavin WebAssign Physics 220 . –/2 points SerCP9 1.MI.016.P. (Do this on paper.XP. write a simple equation relating a constant force F exerted on an object.035.net/web/Student/Assignment-Responses/last?d..and y-coordinates of this point. p. It can be written in terms of the momentum p and mass m as 2 KE = P . A small turtle moves at a speed of 213 furlongs per fortnight. what is the order of magnitude of the diameter of an oil molecule? 10 −5 10 −7 10 −9 10 −11 10 −14 Show My Work (Optional) 3. May 22 2013 11:59 PM EDT 1. 045. (a) How high does it rise? m (b) How long does it take to reach its highest point? s (c) How long does the ball take to hit the ground after it reaches its highest point? s (d) What is its velocity when it returns to the level from which it started? m/s Show My Work (Optional) 19-05-2013 13:21 .P. –/2 points SerCP9 2... (a) the side opposite θ (b) the side adjacent to (c) cos θ (d) sin (e) tan Show My Work (Optional) 6. What would have been the unrealistically large acceleration experienced by the space travelers during their launch? (A human can stand an acceleration of 15g for a short time.webassign.e.) 2 m/s 2 Compare your answer with the free-fall acceleration. 9.P. find each of the following.net/web/Student/Assignment-Responses/last?d.0 m/s.P.97 km/s. –/2 points SerCP9 2. how many times stronger than gravity is this force?). In the figure below. g Show My Work (Optional) 7.028.WI. In 1865. A ball is thrown vertically upward with a speed of 11. Jules Verne proposed sending men to the Moon by firing a space capsule from a 220-m-long cannon with final speed of 10.045.HW #1 2 of 3 http://www. 5.80 m/s (i.Physics 220 . –/2 points SerCP9 1. webassign. A person walks 27. which can jump to a height of 3. the resultant vector A + B points in the negative y-direction with a magnitude of 15 units. With what speed must the animal leave the ground to reach that height? m/s Show My Work (Optional) 19-05-2013 13:21 . When vector B is added to A. Find the magnitude and direction of B? magnitude unit(s) direction Show My Work (Optional) 9. Vector A has a magnitude of 29 units and points in the positive y-direction. –/2 points SerCP9 3. –/2 points SerCP9 3.0° north of east for 2.–/2 points SerCP9 3..WI. How far due north and how far due east would she have to walk to arrive at the same location? north km east km Show My Work (Optional) 10.P.HW #1 3 of 3 http://www.net/web/Student/Assignment-Responses/last?d.P. The best leaper in the animal kingdom is the puma.001.Physics 220 ..010.90 km.025.P.7 m when leaving the ground at an angle of 45°. 8. ANSWER: Negative Positive Correct .Assignment 1 Due: 11:59pm on Wednesday. Grading Policy Conceptual Question 1. ANSWER: Positive Negative Correct Part B Determine the sign (positive or negative) of the velocity for the particle in the figure. February 5. 2014 You will receive no credit for items you complete after the assignment is due.6 Part A Determine the sign (positive or negative) of the position for the particle in the figure. ANSWER: .Part C Determine the sign (positive or negative) of the acceleration for the particle in the figure.7 Part A Determine the sign (positive or negative) of the position for the particle in the figure. ANSWER: Positive Negative Correct Conceptual Question 1. Positive Negative Correct Part B Determine the sign (positive or negative) of the velocity for the particle in the figure. ANSWER: Positive Negative Correct Part C Determine the sign (positive or negative) of the acceleration for the particle in the figure. ANSWER: Negative Positive Correct Enhanced EOC: Problem 1. . The camera took one frame every 2 s.18 The figure shows the motion diagram of a drag racer. 1 in the book/e-text. what two observables are associated with each point? Which position or point of the drag racer occurs first? Which position occurs last? If you label the first point as happening at t = 0 s.You may want to review ( pages 16 . Hint 1. at what time does the next point occur? At what time does the last position point occur? What is the position of a point halfway in between x ANSWER: = 0 m and x = 200 m? Can you think of a way to estimate the positions of the points using a ruler? .19) . How to approach the problem Based on Table 1. For help with math skills. you may want to review: Plotting Points on a Graph Part A Make a position-versus-time graph for the drag racer. Two toy rockets are traveling in the same direction (taken to be the x axis). A diagram is shown of a time-exposure image where a stroboscope has illuminated the rockets at the uniform time intervals indicated.Correct Motion of Two Rockets Learning Goal: To learn to use images of an object in motion to determine velocity and acceleration. . t2 ] = x(t2 )−x(t1 ) . You can't find instantaneous velocity from this diagram.Part A At what time(s) do the rockets have the same velocity? Hint 1. you will need to estimate these based on the distance between successive positions of the rockets. t2 −t1 Note that no position values are given in the diagram. but you can determine the average velocity between two times t1 and t2 : vavg[t1 . How to determine the velocity The diagram shows position. not velocity. ANSWER: = 1 only at time t = 4 only at times t = 1 and t = 4 at time t at some instant in time between t at no time shown in the figure Correct = 1 and t = 4 . Part B At what time(s) do the rockets have the same x position? ANSWER: = 1 only at time t = 4 only at times t = 1 and t = 4 at time t at some instant in time between t = 1 and t = 4 at no time shown in the figure Correct Part C At what time(s) do the two rockets have the same acceleration? Hint 1. How to determine the acceleration The velocity is related to the spacing between images in a stroboscopic diagram. Since acceleration is the rate at which velocity changes, the acceleration is related to the how much this spacing changes from one interval to the next. ANSWER: = 1 only at time t = 4 only at times t = 1 and t = 4 at time t at some instant in time between t at no time shown in the figure = 1 and t = 4 Correct Part D The motion of the rocket labeled A is an example of motion with uniform (i.e., constant) __________. ANSWER: and nonzero acceleration velocity displacement time Correct Part E The motion of the rocket labeled B is an example of motion with uniform (i.e., constant) __________. ANSWER: and nonzero acceleration velocity displacement time Correct Part F At what time(s) is rocket A ahead of rocket B? Hint 1. Use the diagram You can answer this question by looking at the diagram and identifying the time(s) when rocket A is to the right of rocket B. ANSWER: = 1 only after t = 4 only before t = 1 and after t = 4 between t = 1 and t = 4 before t at no time(s) shown in the figure Correct Dimensions of Physical Quantities Learning Goal: To introduce the idea of physical dimensions and to learn how to find them. Physical quantities are generally not purely numerical: They have a particular dimension or combination of dimensions associated with them. Thus, your height is not 74, but rather 74 inches, often expressed as 6 feet 2 inches. Although feet and inches are different units they have the same dimension--length. Part A In classical mechanics there are three base dimensions. Length is one of them. What are the other two? Hint 1. MKS system The current system of units is called the International System (abbreviated SI from the French Système International). In the past this system was called the mks system for its base units: meter, kilogram, and second. What are the dimensions of these quantities? ANSWER: acceleration and mass acceleration and time acceleration and charge mass and time mass and charge time and charge Correct There are three dimensions used in mechanics: length ( l), mass ( m), and time ( t). A combination of these three dimensions suffices to express any physical quantity, because when a new physical quantity is needed (e.g., velocity), it always obeys an equation that permits it to be expressed in terms of the units used for these three dimensions. One then derives a unit to measure the new physical quantity from that equation, and often its unit is given a special name. Such new dimensions are called derived dimensions and the units they are measured in are called derived units. [A] = l2. (Note that "dimensions of variable x" is symbolized as [x].) You can find these dimensions by looking at the formula for the area of a square A = s 2 , where s is the length of a side of the square. Clearly [s] = l. Plugging this into the equation gives [A] = [s]2 = l2. For example, area A has derived dimensions Part B Find the dimensions [V ] of volume. Express your answer as powers of length ( l), mass ( m), and time ( t). Hint 1. Equation for volume You have likely learned many formulas for the volume of various shapes in geometry. Any of these equations will give you the dimensions for volume. You can find the dimensions most easily from the volume of a cube V = e3, where e is the length of the edge of the cube. ANSWER: [V ] = l3 Correct Part C Find the dimensions [v] of speed. Express your answer as powers of length ( l), mass ( m), and time ( t). Hint 1. Equation for speed Speed v is defined in terms of distance d and time t as v= Therefore, d . t [v] = [d]/[t]. Hint 2. Familiar units for speed You are probably accustomed to hearing speeds in miles per hour (or possibly kilometers per hour). Think about the dimensions for miles and hours. If you divide the dimensions for miles by the dimensions for hours, you will have the dimensions for speed. ANSWER: [v] = lt−1 Correct The dimensions of a quantity are not changed by addition or subtraction of another quantity with the same dimensions. This means that dimensions as speed. ∆v, which comes from subtracting two speeds, has the same It does not make physical sense to add or subtract two quanitites that have different dimensions, like length plus time. You can add quantities that have different units, like miles per hour and kilometers per hour, as long as you convert both quantities to the same set of units before you actually compute the sum. You can use this rule to check your answers to any physics problem you work. If the answer involves the sum or difference of two quantities with different dimensions, then it must be incorrect. This rule also ensures that the dimensions of any physical quantity will never involve sums or differences of the base dimensions. (As in the preceeding example, l + t is not a valid dimension for a In SI units. Part A Gravity causes objects to be attracted to one another. and time ( t). This attraction keeps our feet firmly planted on the ground and causes the moon to orbit the earth.physical quantitiy. we start with the equation . Time is measured in seconds. and G is the gravitational constant. mass ( m). r2 m1 and m2 are the masses of the bodies. Part D Find the dimensions [a] of acceleration. Hint 1. Equation for acceleration In physics. the units of mass are kg. r is the distance between them. For this equation to have consistent units. the units of force are kg ⋅ m/s . and mass is measured in kilograms. every physical quantity is measured with respect to a unit. The force of gravitational attraction is represented by the equation F= where F is the magnitude of the gravitational attraction on either body." ANSWER: [a] = lt−2 Correct Consistency of Units In physics. m2/3 l2 t−2 ). The ∆ is a symbol that means "the change in. length is measured in meters.g. Express your answer as powers of length ( l). How to approach the problem To solve this problem. the units of G must be which of the following? 2 Hint 1. Gm1 m2 .) A valid dimension will only involve the product or ratio of powers of the base dimensions (e. Knowing the units of physical quantities will help you solve problems in physics. acceleration a is defined as the change in velocity in a certain time. This is shown by the equation a = ∆v/∆t. and the units of distance are m. In SI units. we start with the equation E = mc2 . the units of E must be which of the following? Hint 1. we replace m1 with kg. For example. For example. We now solve this equation for ANSWER: E. r2 For each symbol whose units we know. ANSWER: kg3 m⋅s 2 kg⋅s2 m3 m3 kg⋅s2 m kg⋅s2 Correct Part B One consequence of Einstein's theory of special relativity is that mass is a form of energy.F= Gm1 m2 . How to approach the problem To solve this problem. We now solve this equation for G. we replace the symbol with those units. c is the speed of the light. we replace the symbol with those units. For the preceding equation to have consistent units (the same units on both sides of the equation). we replace m with kg. This mass-energy relationship is perhaps the most famous of all physics equations: E = mc2 . For each symbol whose units we know. the units of speed are m/s. and E is the energy. . where m is mass. We now solve this equation for the units of the unknown variable.24 Convert the following to SI units: Part A 5.kg⋅m s kg⋅m2 s2 kg⋅s2 m2 kg⋅m2 s Correct To solve the types of problems typified by these examples.13 m Correct Part B 54ft/s Express your answer to two significant figures and include the appropriate units. we replace the symbol with those units. .0in Express your answer to two significant figures and include the appropriate units. Problem 1. we replace m with kg. ANSWER: 0. For example. we start with the given equation. For each symbol whose units we know. 55 The figure shows a motion diagram of a car traveling down a street. The camera took one frame every 10 s. .ANSWER: m 16 s Correct Part C 72mph Express your answer to two significant figures and include the appropriate units.1×10−2 m2 Correct Problem 1. ANSWER: 1. ANSWER: m 32 s Correct Part D 17in2 Express your answer to two significant figures and include the appropriate units. A distance scale is provided. Hint 1. Try Again ± Moving at the Speed of Light Part A How many nanoseconds does it take light to travel a distance of 4.Part A Make a position-versus-time graph for the car. it is often recommended.40km in vacuum? Express your answer numerically in nanoseconds. ANSWER: Incorrect. How to approach the problem Light travels at a constant speed. Before performing any calculations. you can use the formula for the distance traveled in a certain amount of time by an object moving at constant speed. although it is not strictly necessary. . therefore. to convert all quantities to their fundamental units rather than to multiples of the fundamental unit. The speed of an object The equation that relates the distance s traveled by an object with constant speed v in a time t is s = vt.00 × 108 m/s. Find how many seconds it takes light to travel the given distance Given that the speed of light in vacuum is 3.Hint 2.40km ? Express your answer numerically in seconds. Hint 1. Find the time it takes light to travel a certain distance How long does it take light to travel a distance r? Let c be the speed of light. Convert the given distance to meters Convert d = 4. Hint 1. Conversion of kilometers to meters Recall that 1 km = 103 m. how many seconds does it take light to travel a distance of 4. Hint 1. Express your answer numerically in meters.40km to meters. ANSWER: r⋅c r c c r Correct Hint 2. . Recall that ANSWER: 1.7%.ANSWER: 4. 1 ns = 10−9 s.40km = 4400 m Correct ANSWER: −5 1. You received 50.47×104 ns Correct Score Summary: Your score on this assignment is 84.47×10 s Correct Now convert the time into nanoseconds.84 out of a possible total of 60 points. . 2014 You will receive no credit for items you complete after the assignment is due. February 12.6 Part A The figure shows the position-versus-time graph for a moving object. ANSWER: .Assignment 2 Due: 11:59pm on Wednesday. At which lettered point or points: Is the object moving the slowest? Is the object moving the fastest? Is the object at rest? Drag the appropriate items to their respective bins. Grading Policy Conceptual Question 2. Correct Part B At which lettered point or points is the object moving to the negative direction? ANSWER: . At which lettered point or points: Part A Is the object moving the fastest? ANSWER: .7 The figure shows the position-versus-time graph for a moving object.A B C D E Correct Conceptual Question 2. A B C D E F Correct Part B Is the object speeding up? ANSWER: A B C D E F Correct Part C Is the object moving to the left and turning around? ANSWER: . speed. position B.Correct Kinematic Vocabulary One of the difficulties in studying mechanics is that many common words are used with highly specific technical meanings. displacement . and displacement. among them velocity. position. The series of questions in this problem is designed to get you to try to think of these quantities like a physicist. direction C. acceleration. Answer the questions in this problem using words from the following list: A. Enter the letter from the list given in the problem introduction that best completes the sentence. I. G.D. K. coordinates velocity acceleration distance magnitude vector scalar components Part A Velocity differs from speed in that velocity indicates a particle's __________ of motion. H. Enter the letter from the list given in the problem introduction that best completes the sentence. both __________ and direction. E. ANSWER: Correct Part C A vector has. J. Enter the letter from the list given in the problem introduction that best completes the sentence. . velocity is a __________ quantity. by definition. ANSWER: Correct Part B Unlike speed. F. Hint 1.g. ANSWER: Correct . Enter the letter from the list given in the problem introduction that best completes the sentence. Enter the letter from the list given in the problem introduction that best completes the sentence. you can express a two-dimensional vector using a pair of quantities known collectively as __________.. ANSWER: Correct Part E Speed differs from velocity in the same way that __________ differs from displacement. Definition of displacement Displacement is the vector that indicates the difference of two positions (e. it is independent of the coordinate system used to describe it (although its vector components depend on the coordinate system). the final position from the initial position). Being a vector.ANSWER: Correct Part D Once you have selected a coordinate system. There is more than one correct answer. For example. but there are several other quantities that are independent of the choice of origin for a coordinate system: in particular. you can usually choose the coordinate system origin to be wherever is most convenient or intuitive. Separate the letters with commas. = r B⃗ − r A . but the __________ from A to B is/are the same as expressed in both coordinate systems. The __________ of the particle at point A differ(s) as expressed in one coordinate system compared to the other. ANSWER: Correct The coordinates of a point will depend on the coordinate system that is chosen.J. ANSWER: ⃗ . In working physics problems. distance. Type the letters from the list given in the problem introduction that best complete the sentence. but you should only enter one pair of comma-separated letters. This process is described from two coordinate systems that are identical except that they have different origins. and velocity. direction. enter I. if the words "vector" and "scalar" fit best in the blanks. unless you are interested in the position of an object or event relative to a specific origin.Part F Consider a physical situation in which a particle moves from point A to point B. ⃗ Note that the vector indicating a displacement from A to B is usually represented as r BA Part G Identify the following physical quantities as scalars or vectors. displacement. 4 The figure is the position-versus-time graph of a jogger.Correct Problem 2. . 0 m s . ANSWER: v = -5.Part A What is the jogger’s velocity at t = 10 s? Express your answer to two significant figures and include the appropriate units. ANSWER: v = 1. ANSWER: v= 0 m s Correct Part C What is the jogger’s velocity at t = 35 s? Express your answer to two significant figures and include the appropriate units.3 m s Answer Requested Part B What is the jogger’s velocity at t = 25 s? Express your answer to two significant figures and include the appropriate units. Part A At which of the times do the two cars pass each other? Hint 1. The cars’ motions are represented by the position versus time graph shown in the figure.Correct Analyzing Position versus Time Graphs: Conceptual Question Two cars travel on the parallel lanes of a two-lane road. ANSWER: . Answer the questions using the times from the graph indicated by letters. Two cars passing Two objects can pass each other only if they have the same position at the same time. Thus. In physics. if any. Determining velocity from a position versus time graph The slope on a position versus time graph is the "rise" (change in position) over the "run" (change in time). the slope on a position versus time graph is the velocity of the object being graphed. the ratio of change in position over change in time is defined as the velocity. does car #1 momentarily stop? Hint 1. ANSWER: .A B C D E None Cannot be determined Correct Part B Are the two cars traveling in the same direction when they pass each other? ANSWER: yes no Correct Part C At which of the lettered times. the slope on a position versus time graph is the velocity of the object being graphed. if any. Thus. In physics. ANSWER: A B C D E none cannot be determined . does car #2 momentarily stop? Hint 1. the ratio of change in position over change in time is defined as the velocity.A B C D E none cannot be determined Correct Part D At which of the lettered times. Determining velocity from a position versus time graph The slope on a position versus time graph is the "rise" (change in position) over the "run" (change in time). the ratio of change in position over change in time is defined as the velocity. Determining Velocity from a Position versus Time Graph The slope on a position versus time graph is the “rise” (change in position) over the “run” (change in time). . ANSWER: A B C D E None Cannot be determined Correct Problem 2. the slope on a position versus time graph is the velocity of the object being graphed. Thus.6 A particle starts from 10m at t0 = 0 and moves with the velocity graph shown in the figure. In physics.Correct Part E At which of the lettered times are the cars moving with nearly identical velocity? Hint 1. at what time? Express your answer using two significant figures and include the appropriate units.Part A Does this particle have a turning point? ANSWER: Yes No Correct Part B If so. ANSWER: t = 1. 4 s ? .0 s Correct Part C What is the object's position at t = 2. 3. vB. Part A How long after Car B started the race will Car B catch up with Car A? Express the time in terms of given quantities. and thus Car B travels at a constant speed vB . and t for time. Car B starts at the starting line but has a better engine than Car A. What is the acceleration of Car A? The acceleration of Car A is zero. DA. Consider the kinematics relation Write an expression for the displacement of Car A from the starting line at a time t after Car B starts.Express your answers using two significant figures separated by commas. ANSWER: xA (t) = DA + vA t Hint 2. x4 = 10. Hint 1.26 m Correct Overcoming a Head Start Cars A and B are racing each other along the same straight road in the following manner: Car A has a head start and is a distance DA beyond the starting line at t = 0. The starting line is at Car A travels at a constant speed vA . so the general formula x(t) = x0 + v0 t + (1/2)at2 has at least one term equal to zero. What is the relation between the positions of the two cars? = 0.) x = 0. (Note that we are taking this time to be t Answer in terms of vA . which is greater than vA . Hint 1. and take x = 0 at the starting line. ANSWER: x2 . x3 . .16. . ANSWER: xB (t) = vB t ANSWER: D tcatch = v −Av B A Correct Part B How far from Car B's starting line will the cars be when Car B passes Car A? Express your answer in terms of known quantities.) Hint 1. Give your answer in terms of any variables needed (use t for time). Consider Car B's position as a function of time Write down an expression for the position of Car B at time t after starting. (You may use tcatch as well. and substitute in the correct value for tcatch (found in the previous part). Which expression should you use? Just use your expression for the position of either car after time t ANSWER: dpass = vvB−DvA B A Correct = 0. Hint 3.The positions of the two cars are equal at time tcatch. Problem 2.0 m s = 2 m at t0 = 0 . ANSWER: vx = 4. and (c) acceleration? Part A Express your answer to two significant figures and include the appropriate units. Its initial position is x0 particle's (a) position. what are the . ANSWER: x = 6.11 The figure shows the velocity graph of a particle moving along the x-axis. (b) velocity.0 m Correct Part B Express your answer to two significant figures and include the appropriate units. At t = 2s . assuming it to be a constant acceleration? Express your answer to two significant figures and include the appropriate units.54) . . After traveling 3.13 A jet plane is cruising at 300m/s when suddenly the pilot turns the engines up to full throttle. ANSWER: m a = 9.0 s 2 Correct Enhanced EOC: Problem 2. m deep. it falls into a hole 10 You may want to review ( pages 51 .20 A rock is tossed straight up with a velocity of 22 m/s When it returns.Correct Part C Express your answer to two significant figures and include the appropriate units.9km .0 s 2 Correct Problem 2. ANSWER: m ax = 2. Part A What is the jet's acceleration. the jet is moving with a speed of 400 m/s. Hint 1. .1 m s Correct Part B How long is the rock in the air. Choose a coordinate system. you may want to review: Quadratic Equations For general problem-solving tips and strategies for this topic. Part A What is the rock's velocity as it hits the bottom of the hole? Express your answer with the appropriate units. The quadratic equation has two solutions for the time. what is the sign of the initial velocity and the sign of the acceleration? Calling the launch time t = 0. you may want to view a Video Tutor Solution of Time in the air for a tossed ball. initial direction. Where is y = 0 m? What is the positive y direction? What is the position of the launch point and the bottom of the hole? In this coordinate system.For help with math skills. and indicate it on your picture. Which solution makes sense physically in terms of the picture that you drew at the beginning? Keeping the same coordinate system. what is the equation for y as a function of time? What is the y position at the bottom of the hole? This will lead to a quadratic equation for the time t when the rock hits the bottom of the hole. Not all mathematical solutions make sense physically. How to approach the problem Start by drawing a picture of the path of the rock. including its launch point. and end point in the hole. what is the velocity in the y direction as a function of time? What is the y velocity when the rock hits the bottom of the hole? ANSWER: v = -26. from the instant it is released until it hits the bottom of the hole? Express your answer with the appropriate units. 00. what are the particle's (a) position.23 A particle moving along the x-axis has its position described by the function x acceleration? You may want to review ( pages 38 .Hint 1. and (c) . How to approach the problem How is the time the rock was in the air related to the time at which the rock hit the ground in Part A? ANSWER: t = 4. you may want to review: Differentiation of Polynomial Functions = ( 2.42) .00 ) m. For help with math skills.00 t3 − 5. (b) velocity. where t is in s.90 s Correct Enhanced EOC: Problem 2.00 t + 5. At t= 4. from the position. ANSWER: 113 m Correct Part B Express your answer with the appropriate units. . how do you determine v at a particular time? ANSWER: m 91. How to approach the problem Evaluate the position at time t= 4.0 s Correct Part C Express your answer with the appropriate units. v(t).Part A Express your answer with the appropriate units. How to approach the problem How do you determine the velocity as a function of time. Hint 1. Hint 1. x(t)? What calculus operation do you have to perform? Once you have v(t).00 s. Part A Where is the particle when vx = 4.00 t + 6.26 A particle's position on the x-axis is given by the function x = (t2 − 6.Hint 1. v(t)? What calculus operation do you have to perform? Once you have a(t). . where t is in s. from the velocity. how do you determine the acceleration at a particular time? ANSWER: 48.30 A particle's velocity is described by the function vx = t2 − 7t + 7 m/s. where t is in s.00m/s ? Express your answer with the appropriate units. a(t). ANSWER: 1.00 ) m. How to approach the problem How do you determine the acceleration as a function of time.00 m Correct Problem 2.0 m s2 Correct Problem 2. ANSWER: 2 Correct Part B At what times does the particle reach its turning points? Express your answers using two significant figures separated by a comma. ANSWER: t1 .6 m/s2 Correct .2 s Correct Part C What is the particle's acceleration at each of the turning points? Express your answers using two significant figures separated by a comma.Part A How many turning points does the particle reach. ANSWER: a1 .8.1. a2 = 4. Express your answer as an integer. t2 = 5.-4.6. Part A What is the rocket's maximum altitude? Express your answer to two significant figures and include the appropriate units. It accelerates upward at 35m/s2 for 30s . ANSWER: h = 72 km Correct Part B How long is the rocket in the air? Express your answer to two significant figures and include the appropriate units. Part A How far does the elevator move while accelerating to full speed from rest? . ANSWER: t = 260 s Answer Requested Problem 2. Its acceleration and deceleration both have a magnitude of 1.49 A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up.52 A hotel elevator ascends 200 m with maximum speed of 5 m/s .0 m/s2 .Problem 2. then runs out of fuel. Ignore any air resistance effects. labeled A ⃗ through D⃗ . This problem will ask you various questions about these vectors.5 m Correct Part B How long does it take to make the complete trip from bottom to top? Express your answer with the appropriate units. All answers should be in decimal notation. ANSWER: 45. The grid runs from -5 to 5 on both axes.Express your answer with the appropriate units. ANSWER: 12. with coordinate axes x and y . unless otherwise specified.0 s Answer Requested Components of Vectors Shown is a 10 by 10 grid. . Drawn on this grid are four vectors. Part A What is the x component of A?⃗ Express your answer to two significant figures. ANSWER: Ax = 2. the axes being specfied in advance. ANSWER: Ay = 3 Correct A⃗ that lies along A⃗ down to the x axis. the x component is the x coordinate at which the perpendicular from the head of the vector hits . which is horizontal in this problem. You are asked for the component of the x axis. The length of the x A.5 Correct Part B What is the y component of A?⃗ Express your answer to the nearest integer.⃗ In this problem. How to derive the component A component of a vector is its length (but with appropriate sign) along a particular coordinate axis. Imagine two lines perpendicular to the x axis running from the head (end with the arrow) and tail of axis between the points where these lines intersect is the x component of the origin (because the tail of the vector is at the origin). Hint 1. but it might be easier to visualize. Another way is to imagine bringing the tail of C ⃗ to the origin. Therefore. The starting point of the vector is of no consequence to its definition. How to find the start and end points of the vector components A vector is defined only by its magnitude and direction. This is equivalent to the previous method. .⃗ and another to the tail. You can run two perpendiculars to the x axis. with the x component being the difference between x coordinates of head and tail (negative if the tail is to the right of the head). you need to somehow eliminate the starting point from C.Part C What is the y component of B⃗ ? Express your answer to the nearest integer. ANSWER: By = -3 Correct Part D What is the x component of C ?⃗ Express your answer to the nearest integer. one from the head (end with the arrow) of to find the components of ANSWER: Cx = -2 A⃗ and B⃗ . and then using the same procedure you used before your answer. Consider the direction Don't forget the sign. Hint 1. Hint 1. . Express your answers to the nearest integer.5. Part E In ordered pair notation. The answers below are all integers.Correct The following questions will ask you to give both components of vectors using the ordered pairs method. For example. and then the y component. Express your answers to the nearest integer. Dy = 2. so estimate the components to the nearest whole number. write down the components of vector D⃗ . followed by a comma. the components of A⃗ would be written 2.-3 Correct Part G What is true about B⃗ and D⃗ ? Choose from the pulldown list below.-3 Correct Part F In ordered pair notation. write down the components of vector B⃗ .3 in ordered pair notation. By = 2. In this method. ANSWER: Bx. ANSWER: Dx . the x component is written first. 6 Find x. ANSWER: . They are the same vectors.-370 m Correct Part B v ⃗ = (610m/s. ry = 210. They have the same components but are not the same vectors. Correct Problem 3. 60∘ below positive x − axis) Express your answers using two significant figures.ANSWER: They have different components and are not the same vectors. Enter your answers numerically separated by a comma. ANSWER: rx. 23∘ above positive x − axis) Express your answers using two significant figures. Part A r ⃗ = (430m. Enter your answers numerically separated by a comma.and y-components of the following vectors. ANSWER: . ay = 0. Draw the vector with its tail at the origin.3 m/s2 Correct Problem 3. Enter your answers numerically separated by a comma.3m/s2 .-7. vy = 560.10 Part A Draw B⃗ = −4 ^ı + 4^ȷ. ANSWER: ax .240 m/s Correct Part C a⃗ = (7. negative y − direction) Express your answers using two significant figures.vx . Correct Part B Find the magnitude of B⃗ . Express your answer using two significant figures.7 Correct . ANSWER: B = 5. 0^ȷ ) cm. ANSWER: . Draw the vector with its tail at the origin.0 ^ı − 1. Express your answer using two significant figures. ANSWER: θ B = 45 ∘ above the negative x-axis Correct Part D Draw r ⃗ = (−2.Part C Find the direction of B⃗ . 2 cm Correct . ANSWER: r = 2.Correct Part E Find the magnitude of r .⃗ Express your answer using two significant figures. ⃗ ANSWER: θ r = 26.Part F Find the direction of r . Draw the vector with its tail at the origin. ANSWER: .6 ∘ below the negative x-axis Correct Part G Draw v ⃗ = (−10 ^ı − 100^ȷ ) m/s. Correct Part H Find the magnitude of v. ANSWER: v = 100.⃗ Express your answer using four significant figures.5 m/s Correct . Part I Find the direction of v. ANSWER: .⃗ ANSWER: θ v = 84. Draw the vector with it's tail at the origin.3 ∘ below the negative x-axis Correct Part J Draw a⃗ = (20 ^ı + 10^ȷ ) m/s2. ⃗ ANSWER: a = 22.4 m/s2 Correct Part L .Correct Part K Find the magnitude of a. and D⃗ = A⃗ − B.14 Let A⃗ = 5 ^ı − 2^ȷ.6 ∘ above the positive x-axis Correct Problem 3.Find the direction of a.⃗ Part A What is the component form of vector ANSWER: D⃗ = 7 ^ı − 8^ȷ D⃗ = −7 ^ı − 5^ȷ D⃗ = 7 ^ı + 8^ȷ D⃗ = 4 ^ı + 5^ȷ Correct Part B What is the magnitude of vector ANSWER: D⃗ ? D⃗ ? . B⃗ = −2 ^ı + 6^ȷ.⃗ ANSWER: θ a = 26. ANSWER: E⃗ = 10 ^ı + 2^ȷ E⃗ = ^ı + 10^ȷ E⃗ = −10^ȷ E⃗ = 10 ^ı − 2^ȷ . ANSWER: θ = 49 ∘ below positive x-axis Correct Problem 3.15 Let A⃗ = 4 ^ı − 2^ȷ.6 Correct Part C What is the direction of vector D⃗ ? Express your answer using two significant figures.⃗ Part A Write vector E⃗ in component form.D = 10. and E⃗ = 4A⃗ + 2B. B⃗ = −3 ^ı + 5^ȷ. Correct Part B Draw vectors A.⃗ B⃗ . ANSWER: Correct Part C .⃗ Draw the vectors with their tails at the origin. and E. . ANSWER: θ = 11 ∘ counterclockwise from positive direction of x-axis Correct Problem 3.0 Correct Part D What is the direction of vector E?⃗ Express your answer using two significant figures.What is the magnitude of vector E?⃗ Express your answer using two significant figures. ANSWER: E = 10.24 Part A What is the angle ϕ between vectors E⃗ and F ⃗ in the figure? Express your answer with the appropriate units. 0 ∘ Correct Score Summary: Your score on this assignment is 91.6 ∘ Correct Part B Use components to determine the magnitude of G⃗ = E⃗ + F .3%. . ANSWER: θ = 90.00 Correct Part C Use components to determine the direction of G⃗ = E⃗ + F .ANSWER: ϕ = 71.⃗ Express your answer with the appropriate units.⃗ ANSWER: G = 3. You received 129. .62 out of a possible total of 142 points. m ahead has just turned red.Assignment 3 Due: 11:59pm on Friday. Superman is headed straight down with a speed of 36. It so happens that Superman flies by at the instant you release the watermelon.71 s .0 s Correct Problem 2.63 A motorist is driving at 20 m/s when she sees that a traffic light 200 again.0 s to step on the brakes and begin slowing. Part A How fast is the watermelon going when it passes Superman? Express your answer with the appropriate units. 2014 You will receive no credit for items you complete after the assignment is due. 320 m above the sidewalk. you drop a watermelon off the top of the Empire State Building. February 14. It takes her 1.68 As a science project. and she wants to reach the light just as it turns green Part A What is her speed as she reaches the light at the instant it turns green? Express your answer with the appropriate units. ANSWER: m 5. Grading Policy Problem 2. ANSWER: m 72.0m/s . She knows that this light stays red for 15 s . Correct Conceptual Question 4.1 Part A At this instant. slowing down. is the particle in the figurespeeding up. curving to the left. or traveling at constant speed? ANSWER: Speeding up Slowing down Traveling at constant speed Correct Part B Is this particle curving to the right. or traveling straight? . slowing down. or traveling at constant speed? ANSWER: .ANSWER: Curving to the right Curving to the left Traveling straight Correct Conceptual Question 4.2 Part A At this instant. is the particle in the following figure speeding up. The particle is curving downward.8 A particle's trajectory is described by x = ( 12 t3 Part A What is the particle's speed at ANSWER: v = 2 m/s t = 0s? − 2t2 ) m and y = ( 12 t2 − 2t) m . curving downward. Correct Part B Is this particle curving upward. . The particle is traveling at constant speed. or traveling straight? ANSWER: The particle is curving upward. The particle is slowing down. where t is in s. Correct Problem 4. The particle is traveling straight.The particle is speeding up. at Express your answer using two significant figures. ANSWER: θ = 9.0s ? Express your answer using two significant figures.Correct Part B What is the particle's speed at t = 5. at t= 0 s? Express your answer using two significant figures. measured as an angle from the x-axis. measured as an angle from the x-axis.0s ? . ANSWER: v = 18 m/s Correct Part C What is the particle's direction of motion. t = 5. ANSWER: θ = -90 ∘ counterclockwise from the +x axis. Correct Part D What is the particle's direction of motion.7 ∘ counterclockwise from the +x axis. Part A In which direction is the puck moving at t = 3s ? Give your answer as an angle from the x-axis.9 A rocket-powered hockey puck moves on a horizontal frictionless table.and y-components of the puck’s velocity.Correct Problem 4. Express your answer using two significant figures. the x. respectively. The puck starts at the origin. ANSWER: θ = 51 ∘ Correct Part B above the x-axis . The figure shows the graph of vx and the figure shows the graph of vy . 0m away. Choose an x-y coordinate system. Label the distances given in the problem. making sure to label the origin. You can assume that the gun was held parallel to the ground.How far from the origin is the puck at 5s ? Express your answer to two significant figures and include the appropriate units. you may want to review: Quadratic Equations Part A What was the bullet's flight time? Express your answer with the appropriate units.50cm below the aim point. The bullet hits the target 1. Hint 1. What is the y coordinate when the bullet leaves the gun? What is the y coordinate when it hits the target? What is the initial velocity in the y direction? What is the acceleration in the y direction? What is the equation y(t) that describes the motion in the vertical y direction as a function of time? Can you use the equation for necessary to include the motion in the x direction? y(t) to determine the time of flight? Why was it not . For help with math skills. How to approach the problem Start by drawing a picture of the bullet's trajectory. including where it leaves the gun and where it hits the target.13 A rifle is aimed horizontally at a target 51. It is conventional to have x in the horizontal direction and y in the vertical direction. You may want to review ( pages 91 . ANSWER: s = 180 cm Correct Enhanced EOC: Problem 4.95) . However. . To make a problem more managable.ANSWER: −2 5. Projectile motion may seem rather complex at first. How to approach the problem In the coordinate system introduced in Part A. a particle has some initial velocity v.⃗ In general. it is common to break up such a quantity into its x component vx and its y component vy . you will find that it is really no different than the one-dimensional motions that you have already studied.53×10 s Correct Part B What was the bullet's speed as it left the barrel? Express your answer with the appropriate units. For instance. by breaking it down into components. One of the most often used techniques in physics is to divide two. in projectile motion.and three-dimensional quantities into components. this velocity can point in any direction on the xy plane and can have any magnitude. what are the x coordinates when the bullet leaves the gun and when it hits the target? Is there any acceleration in the x direction? What is the equation x(t) that describes the motion in the horizontal x direction as a function of time? Can you use the equation for x(t) to determine the initial velocity? ANSWER: m 922 s Correct Introduction to Projectile Motion Learning Goal: To understand the basic concepts of projectile motion. Hint 1. but for now you will only be looking at problems where they do not. then the x component of the velocity will change.Consider a particle with initial velocity v ⃗ that has magnitude 12. ANSWER: vx = -6. Part C Look at this applet.0 m/s and is directed 60. Eventually.4 m/s Correct Breaking up the velocities into components is particularly useful when the components do not affect each other. Part A ⃗ What is the x component vx of v? Express your answer in meters per second. ANSWER: vy = 10. if you shined a spotlight to the left and recorded the particle's shadow. The x-component motion diagram is what you would get if you shined a spotlight down on the particle as it moved and recorded the motion of its shadow. How would you describe the two motion diagrams for the components? ANSWER: . Similarly.00 m/s Correct Part B ⃗ What is the y component vy of v? Express your answer in meters per second. but the y component of the velocity will not. as are the motion diagrams for each component. The motion diagram for a projectile is displayed. you will learn about situations in which the components of velocity do affect one another. if there is acceleration in the x direction but not in the y direction. So.0 degrees above the negative x axis. you would get the motion diagram for its y component. Both the vertical and horizontal components exhibit motion with constant nonzero acceleration. The vertical component exhibits motion with constant nonzero acceleration, whereas the horizontal component exhibits constant-velocity motion. The vertical component exhibits constant-velocity motion, whereas the horizontal component exhibits motion with constant nonzero acceleration. Both the vertical and horizontal components exhibit motion with constant velocity. Correct As you can see, the two components of the motion obey their own independent kinematic laws. For the vertical component, there is an acceleration downward with magnitude g Thus, you can calculate the vertical position of the particle at any time using the standard kinematic equation y direction, so the horizontal position of the particle is given by the standard kinematic equation x = 10 m/s2 . = y0 + v0 t + (1/2)at2. Similarly, there is no acceleration in the horizontal = x0 + v0 t. Now, consider this applet. Two balls are simultaneously dropped from a height of 5.0 m. Part D How long tg does it take for the balls to reach the ground? Use 10 m/s2 for the magnitude of the acceleration due to gravity. Express your answer in seconds to two significant figures. Hint 1. How to approach the problem The balls are released from rest at a height of 5.0 m at time t ground. = 0 s. Using these numbers and basic kinematics, you can determine the amount of time it takes for the balls to reach the ANSWER: tg = 1.0 s Correct This situation, which you have dealt with before (motion under the constant acceleration of gravity), is actually a special case of projectile motion. Think of this as projectile motion where the horizontal component of the initial velocity is zero. Part E Imagine the ball on the left is given a nonzero initial speed in the horizontal direction, while the ball on the right continues to fall with zero initial velocity. What horizontal speed vx must the ball on the left start with so that it hits the ground at the same position as the ball on the right? Remember that the two balls are released, starting a horizontal distance of 3.0 m apart. Express your answer in meters per second to two significant figures. Hint 1. How to approach the problem Recall from Part B that the horizontal component of velocity does not change during projectile motion. Therefore, you need to find the horizontal component of velocity vx such that, in a time tg = 1.0 s, the ball will move horizontally 3.0 m. You can assume that its initial x coordinate is x0 = 0.0 m. ANSWER: vx = 3.0 m/s Correct You can adjust the horizontal speeds in this applet. Notice that regardless of what horizontal speeds you give to the balls, they continue to move vertically in the same way (i.e., they are at the same y coordinate at the same time). Problem 4.12 A ball thrown horizontally at 27m/s travels a horizontal distance of 49m before hitting the ground. Part A From what height was the ball thrown? Express your answer using two significant figures with the appropriate units. ANSWER: h = 16 m Correct Enhanced EOC: Problem 4.20 The figure shows the angular-velocity-versus-time graph for a particle moving in a circle. You may want to review ( page ) . For help with math skills, you may want to review: The Definite Integral Part A How many revolutions does the object make during the first 3.5s ? Express your answer using two significant figures. You did not open hints for this part. ANSWER: n= Incorrect; Try Again Problem 4.26 To withstand "g-forces" of up to 10 g's, caused by suddenly pulling out of a steep dive, fighter jet pilots train on a "human centrifuge." 10 g's is an acceleration of 98 m/s2 . Part A If the length of the centrifuge arm is 10.0m , at what speed is the rider moving when she experiences 10 g's? Express your answer with the appropriate units. ANSWER: m 31.3 s Correct Problem 4.28 Your roommate is working on his bicycle and has the bike upside down. He spins the 60.0cm -diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. Part A What is the pebble's speed? Express your answer with the appropriate units. ANSWER: m 5.65 s Correct Part B What is the pebble's acceleration? Express your answer with the appropriate units. ANSWER: 107 m s2 Correct Enhanced EOC: Problem 4.43 On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a 6 iron. The acceleration due to gravity on the moon is 1/6 of its value on earth. Suppose he hits the ball with a speed of 13m/s at an angle 50∘ above the horizontal. You may want to review ( pages 90 - 95) . For help with math skills, you may want to review: Quadratic Equations Part A How much farther did the ball travel on the moon than it would have on earth? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Start by drawing a picture of the path of the golf ball, showing its starting and ending points. Choose a coordinate system, and label the origin. It is conventional to let x be the horizontal direction and y the vertical direction. What is the initial velocity in the x and y directions? What is the acceleration in the x and y directions on the moon and on the earth? What are the equations for x and y as a function of time, x(t) and y(t), respectively? What is the y coordinate when the golf ball hits the ground? Can you use this information to determine the time of flight on the moon and on the earth? How to approach the problem What is the equation x(t) describing x as a function of time? What is the initial x component of the ball's velocity? How are the initial x component of the ball's velocity and the distance traveled related to the time of flight? What is the difference between the time of flight on the moon and on earth? ANSWER: t = 10 s Correct Problem 4. ANSWER: L = 85 m Correct Part B For how much more time was the ball in flight? Express your answer to two significant figures and include the appropriate units. how can you use the x(t) equation to determine the total distance traveled? Compare the distance traveled on the moon to the distance traveled on the earth .Once you have the time of flight. The shot leaves her hand at a height of 1.42 In the Olympic shotput event. an athlete throws the shot with an initial speed of 12 m/s at a 40.8 m above the ground.0∘ angle from the horizontal. Hint 1. . 0∘ ) = 16.5∘ ) = 16.36 m Correct Part B Repeat the calculation of part (a) for angles of 42.5 ∘ .Part A How far does the shot travel? Express your answer to four significant figures and include the appropriate units.0 ∘ .31 m Correct Part D . ANSWER: x = 16.5 ∘ . ANSWER: x(45. 45. Express your answer to four significant figures and include the appropriate units. and 47. ANSWER: x(42.39 m Correct Part C Express your answer to four significant figures and include the appropriate units. 5∘ Correct Problem 4.5∘ 45.0∘ 47. ANSWER: x(47.44 A ball is thrown toward a cliff of height h with a speed of 32m/s and an angle of 60∘ above horizontal.0∘ 42. Part A How high is the cliff? Express your answer to two significant figures and include the appropriate units.5∘ ) = 16.2s later.13 m Correct Part E At what angle of release does she throw the farthest? ANSWER: 40. ANSWER: h = 39 m . It lands on the edge of the cliff 3.Express your answer to four significant figures and include the appropriate units. Answer Requested Part B What was the maximum height of the ball? Express your answer to two significant figures and include the appropriate units. Test tubes have to be placed into a centrifuge very carefully because of the very large accelerations. Part A What is the acceleration at the end of a test tube that is 10 cm from the axis of rotation? Express your answer with the appropriate units. . ANSWER: hmax = 39 m Correct Part C What is the ball's impact speed? Express your answer to two significant figures and include the appropriate units.58 A typical laboratory centrifuge rotates at 3600rpm . ANSWER: v = 16 m s Correct Problem 4. 37 × 106 m. Part A What is the speed of a satellite in a geosynchronous orbit? Express your answer with the appropriate units. and the altitude of a geosynchronous orbit is 3.0 m and stopped in a 1.7-ms-long encounter with a hard floor? Express your answer with the appropriate units. The radius of the earth is 6. ANSWER: m a = 2610 s 2 Correct Problem 4.ANSWER: m a = 1. what is the magnitude of the acceleration a test tube would experience if dropped from a height of 1.58 × 107 m( ≈22000 miles).42×104 s 2 Correct Part B For comparison. ANSWER: v = 3070 m s Correct .62 Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. Part B What is the magnitude of the acceleration of a satellite in a geosynchronous orbit? Express your answer with the appropriate units.82 out of a possible total of 116 points.5%.223 s2 Correct Score Summary: Your score on this assignment is 89. . ANSWER: m a = 0. You received 103. Thus. The x and y components of A⃗ are.0∘ above the negative x axis in the second quadrant. Express your answer in newtons. F 1⃗ and F 2⃗ . Grading Policy ± Two Forces Acting at a Point Two forces. 2014 You will receive no credit for items you complete after the assignment is due. where A is the magnitude of the vector.20N and is Part A What is the x component of the resultant force? Express your answer in newtons.1∘ below the negative x axis in the third quadrant. Hint 1. Ax = A cos θ and Ay = A sin θ. its x component is the sum of the x components of the forces.80N and is directed at an angle of 56. Find the x component of F 1⃗ Find the x component of F 1⃗ . F 2⃗ has a magnitude of 5. February 26. act at a point. Ax < 0 and Ay < 0 if π < θ< 3π . Note that Ax < 0 and Ay > 0 if π2 < θ < π. Components of a vector Consider a vector A⃗ that forms an angle θ with the positive x axis. How to approach the problem The resultant force is defined as the vector sum of all forces. F 1⃗ has a magnitude of 9. 2 .Assignment 4 Due: 11:59pm on Wednesday. Hint 2. and its y component is the sum of the y components of the forces. directed at an angle of 54. Hint 1. respectively. Hint 1. Note that Ax < 0 and Ay > 0 if π2 Typesetting math: 100% < θ < π. When you calculate the components of F 1⃗ . where A is the magnitude of the vector.48 N Hint 3. . Find the x component of F 2⃗ Find the x component of F 2⃗ . What is the angle that F 1⃗ forms with the positive x axis? Select an answer from the following list. Ax = A cos θ and Ay = A sin θ. Components of a vector Consider a vector A⃗ that forms an angle θ with the positive x axis.0∘ above the x axis in the second quadrant.0∘ . however. ANSWER: θ 180∘ − θ 180∘ + θ 90∘ + θ ANSWER: -5.Hint 2. The x and y components of A⃗ are. respectively. Express your answer in newtons. Find the direction of F 1⃗ F 1⃗ is directed at an angle of 56. where θ = 56. the direction of the force is commonly expressed in terms of the angle that the vector representing the force forms with the positive x axis. 2 Hint 2. Typesetting math: 100% .1∘ below the x axis in the third quadrant.Ax < 0 and Ay < if π <θ< 3π . where θ = 54. ANSWER: θ 180∘ − θ θ − 180∘ −90∘ − θ ANSWER: -3. When you calculate the components of F 2⃗ . What is the angle that F 2⃗ forms with the positive x axis? Select an answer from the following list.05 N ANSWER: -8.53 N Correct Part B What is the y component of the resultant force? Express your answer in newtons. the direction of the force is commonly expressed in terms of the angle that the vector representing the force forms with the positive x axis. however. Find the direction of F 2⃗ F 2⃗ is directed at an angle of 54.1∘ . though now calculate the y components of the two forces. Ax = A cos θ and Ay = A sin θ.Hint 1. respectively. Find the y component of F 1⃗ Find the y component of F 1⃗ . Express your answer in newtons. Ax < 0 and Ay < 0 if π < ANSWER: 8. where A is the magnitude of the vector. How to approach the problem Follow the same procedure that you used in Part A to find the x component of the resultant force. 2 .12 N Hint 3. Hint 1. Components of a vector Typesetting math: 100% θ< 3π . Hint 1. Components of a vector Consider a vector A⃗ that forms an angle θ with the positive x axis. The x and y components of A⃗ are. Hint 2. Find the y component of F 2⃗ Find the y component of F 2⃗ . Note that Ax < 0 and Ay > 0 if π2 < θ < π. Express your answer in newtons. Typesetting math: 100% θ< 3π . Ax < 0 and Ay < 0 if π < ANSWER: -4.⃗ whose components are Ax and Ay. where A is the magnitude of the vector.21 N ANSWER: 3. Ax = A cos θ and Ay = A sin θ. Hint 1. respectively. 2 .91 N Correct Part C What is the magnitude of the resultant force? Express your answer in newtons. The magnitude of A⃗ is −−−−−−− A = √A2x + A2y . Magnitude of a vector Consider a vector A. The x and y components of A⃗ are.Consider a vector A⃗ that forms an angle θ with the positive x axis. Note that Ax < 0 and Ay > 0 if π2 < θ < π. For help with math skills. you may want to review: Finding the Slope of a Line from a Graph Part A m1 What is the mass ratio m ? 2 Express your answer using two significant figures.38 N Correct Enhanced EOC: Problem 5.ANSWER: 9. Typesetting math: 100% .130) .9 The figure shows acceleration-versus-force graphs for two objects pulled by rubber bands. You may want to review ( pages 127 . if a net external force Fnet acts on a body. and the net force is equal to the mass the body: Fnet = ma. what two points are easy to measure accurately to determine the slope of line? How is the slope determined from the x and y coordinates of the two points you chose for each line? ANSWER: m1 m2 = 0. Part A How much horizontal force F must a sprinter of mass 54kg exert on the starting blocks to produce this acceleration? Express your answer in newtons using two significant figures.36 Correct A World-Class Sprinter World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude 15 m/s2 .Hint 1. How to approach the problem How are the acceleration and the force on an object related to its mass? How is the slope of each line in the figure related to each object's mass? For each line. Newton's 2nd law of motion According to Newton's 2nd law of motion. ANSWER: F = 810 N Typesetting math: 100% m of the body times the acceleration a of . Hint 1. the body accelerates. sprinters push backward on the starting blocks with their feet. but opposite in direction. As a reaction.Correct Part B Which body exerts the force that propels the sprinter. ANSWER: the blocks the sprinter Correct To start moving forward. the blocks push forward on their feet with a force of the same magnitude. Problem 5. the blocks or the sprinter? Hint 1. Newton's 3rd law tells you that the blocks exert a force on the sprinter of the same magnitude. This external force accelerates the sprinter forward. How to approach the question To start moving forward. sprinters push backward on the starting blocks with their feet. Typesetting math: 100% .12 The figure shows an acceleration-versus-force graph for a 600g object. always start with a free-body diagram. ANSWER: m a2 = 3. Typesettingyou math: 100% . ANSWER: m a1 = 1.33 s2 Correct Free-Body Diagrams Learning Goal: To gain practice drawing free-body diagrams Whenever face a problem involving forces.67 s2 Correct Part B What must a2 equal in order for the graph to be correct? Express your answer with the appropriate units.Part A What must a1 equal in order for the graph to be correct? Express your answer with the appropriate units. In this problem you will only draw the free-body diagram. and apply Newton's first or second law. Also. that are not forces. Part A Determine the object of interest for the situation described in the problem introduction. ANSWER: Typesetting math: 100% . The piano can slide across the floor without friction. do not include quantities. In most problems. 2. Suppose that you are asked to solve the following problem: Chadwick is pushing a piano across a level floor (see the figure). Isolate the object of interest.To draw a free-body diagram use the following steps: 1. Always make the object of interest the origin of your coordinate system. after you have drawn the free-body diagrams. sum the x and y forces. Do not include forces acting on other objects in the problem. what is the piano's acceleration? To solve this problem you should start by drawing a free-body diagram. 3. you will explicitly label your coordinate axes and directions. When possible. Then you will need to divide the forces into x and y components. such as velocities and accelerations. the length of the force vectors you draw should represent the relative magnitudes of the forces acting on the object. How to approach the problem You should first think about the question you are trying to answer: What is the acceleration of the piano? The object of interest in this situation will be the object whose acceleration you are asked to find. Identify all the forces acting on the object and their directions. It is customary to represent the object of interest as a point in your diagram. Hint 1. If Chadwick applies a horizontal force to the piano. Draw the vectors for each force acting on your object of interest. but you don't need to worry about the exact scale. To maximize your learning. Part C Typesetting math: 100% . Correct Part B Identify the forces acting on the object of interest. the piano. select the forces that act on the piano. Check all that apply. you should draw the diagram yourself before looking at the choices in the next part. From the list below. ANSWER: acceleration of the piano gravitational force acting on the piano (piano's weight) speed of the piano gravitational force acting on Chadwick (Chadwick's weight) force of the floor on the piano (normal force) force of the piano on the floor force of Chadwick on the piano force of the piano pushing on Chadwick Correct Now that you have identified the forces acting on the piano. Draw the length of your vectors to represent the relative magnitudes of the forces. you should draw the free-body diagram. You are on your honor to do so. You won't have the exact value of all of the forces until you finish solving the problem.the floor. For this situation you should draw a free-body diagram for Chadwick. Determine the directions and relative magnitudes of the forces Which of the following statements best describes the correct directions and relative magnitudes of the forces involved? ANSWER: The normal force and weight are both upward and the pushing force is horizontal. ANSWER: Typesetting math: 100% .Select the choice that best matches the free-body diagram you have drawn for the piano. The normal force and weight are both downward and the pushing force is horizontal. and the pushing force is horizontal. The normal force has a greater magnitude than the weight. The normal force and weight have the same magnitude. the weight is downward. The normal force is upward. The normal force is upward. the weight is downward. and the pushing force is horizontal. The normal force is upward. and the pushing force is horizontal. Hint 1. The normal force has a smaller magnitude than the weight. the weight is downward. Typesetting math: 100% . at left. Is Chadwick strong enough to push the piano up the ramp alone or must he get help? To solve this problem you should start by drawing a free-body diagram. Choose the position of the piano as the origin. you should draw a free-body diagram for Chadwick. For this situation.Correct If you were actually going to solve this problem rather than just draw the free-body diagram. you would need to define the coordinate system. Again draw your diagram before you look at the choices Typesetting math: 100% . in the direction of the acceleration. Chadwick now needs to push the piano up a ramp and into a moving van. Correct Now draw the free-body diagram of the piano in this new situation. the piano. The ramp is frictionless. ANSWER: the ramp. In this case it is simplest to let the y axis point vertically upward and the x axis point horizontally to the right. Part D Determine the object of interest for this situation. Follow the same sequence of steps that you followed for the first situation. below. Part E Which diagram accurately represents the free-body diagram for the piano? ANSWER: Typesetting math: 100% . Typesetting math: 100% . Instead.18 The figure shows two of the three forces acting on an object in equilibrium. showing all three forces. Problem 5. Part A Redraw the diagram. The length of the vector will not be graded. it is most often easiest to select a coordinate system that is not vertical and horizontal. Draw the force vector starting at the black dot. ANSWER: Typesetting math: 100% . Label the third force F 3⃗ . choose the x axis so that it is parallel to the incline and choose the y axis so that it is perpendicular to the incline.Correct In working problems like this one that involve an incline. The location and orientation of the vector will be graded. Correct Problem 5.25 An ice hockey puck glides across frictionless ice. Part A Identify all forces acting on the object. ANSWER: Typesetting math: 100% . The orientation of your vectors will be graded.Normal force n⃗ . Draw the force vectors with their tails at the dot. Gravity → ⃗ . Gravity ⃗ FG Normal force n⃗ . ANSWER: Typesetting math: 100% . The exact length of your vectors will not be graded but the relative length of one to the other will be graded.⃗ Weight Thrust w⃗ → ⃗ Fthrust. Gravity F G Correct Part B Draw a free-body diagram of the ice hockey puck. Kinetic friction f FG k Tension T . 26 Your physics textbook is sliding to the right across the table. Part A Identify all forces acting on the object. ANSWER: Typesetting math: 100% .Correct Problem 5. → w;⃗ Kinetic friction fk → → Thrust Fthrust; Kinetic friction fk Weight → w⃗; Kinetic friction fk → Normal force n⃗ ; Weight w⃗; Static friction fs Normal force n⃗ ; Weight Correct Part B Draw a free-body diagram of the object. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: Typesetting math: 100% Correct Enhanced EOC: Problem 5.35 A constant force is applied to an object, causing the object to accelerate at 13m/s2 . You may want to review ( pages 127 - 130) . For help with math skills, you may want to review: Proportions I Proportions II Typesetting math: 100% Part A What will the acceleration be if the force is halved? Express your answer with the appropriate units. Hint 1. How to approach the problem How is the acceleration of an object related to its mass and the force applied? Expressing the acceleration in terms of the force and mass, what happens to the acceleration if the force is halved but the mass remains the same? ANSWER: m a = 6.50 s 2 Correct Part B What will the acceleration be if the object's mass is halved? Express your answer with the appropriate units. Hint 1. How to approach the problem How is the acceleration of an object related to its mass and the force applied? Expressing the acceleration in terms of the force and mass, what happens to the acceleration if the mass is halved but the force remains the same? ANSWER: m a = 26.0 s 2 Correct Part C Typesetting math: 100% What will the acceleration be if the force and the object's mass are both halved? Express your answer with the appropriate units. Hint 1. How to approach the problem How is the acceleration of an object related to its mass and the force applied? Expressing the acceleration in terms of the force and mass, what happens to the acceleration if both the force and mass are reduced by a factor of two? ANSWER: m a = 13.0 s 2 Correct Part D What will the acceleration be if the force is halved and the object's mass is doubled? Express your answer with the appropriate units. Hint 1. How to approach the problem How is the acceleration of an object related to its mass and the force applied? Expressing the acceleration in terms of the force and mass, what happens to the acceleration if the force is decreased by a factor of two and the mass is increased by a factor of two? Check your answer by choosing numerical values of the force and mass, and then halve the force and double the mass. ANSWER: m a = 3.25 s 2 Correct Typesetting math: 100% Problem 5.44 A rocket is being launched straight up. Air resistance is not negligible. Part A Which of the following is the correct motion diagram for the situation described above? Enter the letter that corresponds with the best answer. ANSWER: Correct Part B Draw a free-body diagram. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: Typesetting math: 100% 82 out of a possible total of 64 points. You received 63.7%.Correct Score Summary: Your score on this assignment is 99. Typesetting math: 100% . smaller than.Assignment 5 Due: 11:59pm on Wednesday. March 5. or equal to mg? ANSWER: Equal to mg Larger than mg Smaller than mg Correct . 2014 You will receive no credit for items you complete after the assignment is due.13 A hand presses down on the book in the figure. Part A Is the normal force of the table on the book larger than. Grading Policy Conceptual Question 6. ANSWER: T3 = 94 N Correct Part B What is the direction of the tension T 3⃗ in the third rope? Express your answer using two significant figures. Part A What is the magnitude of the tension T 3⃗ in the third rope? Express your answer using two significant figures.2 The three ropes in the figure are tied to a small. Typesetting math: 100% . Two of these ropes are anchored to walls at right angles with the tensions shown in the figure.Problem 6. very light ring. Which statement about the magnitude of the normal force n acting on the suitcase is true during the time that the man pulls upward on the suitcase? Hint 1. he is unable to lift the suitcase from the floor. there is always a force perpendicular to the surface. Identify the correct free-body diagram Which of the figures represents the free-body diagram of the suitcase while the man is pulling on the handle with a force of magnitude fpull? Typesetting math: 100% . Part A A man attempts to pick up his suitcase of weight ws by pulling straight up on the handle. However. Hint 2. The two questions to the right will explore the normal force.ANSWER: θ = 58 ∘ below horizontal Correct The Normal Force When an object rests on a surface. to examine how the forces acting on the suitcase relate to each other. identify the forces that act on the suitcase and draw a free-body diagram. Then use the fact that the suitcase is in equilibrium. ∑ F ⃗ = 0. denoted by n⃗ . we call this the normal force. How to approach this problem First. ANSWER: A B C D ANSWER: The magnitude of the normal force is equal to the magnitude of the weight of the suitcase. The magnitude of the normal force is equal to the magnitude of the weight of the suitcase minus the magnitude of the force of the pull. Correct Part B Typesetting math: 100% . The magnitude of the normal force is equal to the sum of the magnitude of the force of the pull and the magnitude of the suitcase's weight. The magnitude of the normal force is greater than the magnitude of the weight of the suitcase. ANSWER: Typesetting math: 100% . Identify the correct free-body diagram.Now assume that the man of weight wm is tired and decides to sit on his suitcase. Which statement about the magnitude of the normal force n acting on the suitcase is true during the time that the man is sitting on the suitcase? Hint 1. Which of the figures represents the free-body diagram while the man is sitting atop the suitcase? Here the vector labeled wm is a force that has the same magnitude as the man's weight. This is an important point to understand. Correct Recognize that the normal force acting on an object is not always equal to the weight of that object. Part A What is the magnitude of the normal force of the roof on the worker? Express your answer to two significant figures and include the appropriate units.5 A construction worker with a weight of 880N stands on a roof that is sloped at 18∘ . Problem 6. The magnitude of the normal force is less than the magnitude of the suitcase's weight.A B C D ANSWER: The magnitude of the normal force is equal to the magnitude of the suitcase's weight. The magnitude of the normal force is equal to the sum of the magnitude of the man's weight and the magnitude of the suitcase's weight. The magnitude of the normal force is equal to the magnitude of the suitcase's weight minus the magnitude of the man's weight. ANSWER: n = 840 N Correct Typesetting math: 100% . Express your answer to two significant figures and include the appropriate units.67 s 2 Correct Part B For diagram the part A. the x-component of the acceleration. find the value of ay .0kg object. ANSWER: Typesetting math: 100% . the y-component of the acceleration. Express your answer to two significant figures and include the appropriate units.Problem 6.6 In each of the two free-body diagrams. find the value of ax . Part A For diagram . ANSWER: m ax = -0. the forces are acting on a 3. ay = 0 m s2 Correct Part C For diagram . Express your answer to two significant figures and include the appropriate units. ANSWER: m ax = 0. find the value of ax . find the value of ay .67 s2 Correct Part D For diagram the part C. the x-component of the acceleration. Express your answer to two significant figures and include the appropriate units. the y-component of the acceleration. ANSWER: Typesetting math: 100% . 7 In each of the two free-body diagrams.ay = 0 m s2 Correct Problem 6. the x component of the acceleration in diagram (a). ANSWER: m ax = 0. Part A Find the value of ax . Express your answer to two significant figures and include the appropriate units. the forces are acting on a 3.99 s2 Correct Typesetting math: 100% .0kg object. ANSWER: ay = 0 m s2 Correct Typesetting math: 100% . ANSWER: m ax = -0. the y component of the acceleration in diagram (b).18 s 2 Correct Part D Find the value of ay . Express your answer to two significant figures and include the appropriate units. the y component of the acceleration in diagram (a). Express your answer to two significant figures and include the appropriate units. ANSWER: ay = 0 m s2 Correct Part C Find the value of ax . the x component of the acceleration in diagram (b).Part B Find the value of ay . Express your answer to two significant figures and include the appropriate units. ANSWER: Typesetting math: 100% . ANSWER: T = 0N Correct Part B The box moves at a steady vx = 4.0kg box on frictionless ice.80m/s and ax = 4. What is the tension in the rope if: Part A The box is at rest? Express your answer as an integer and include the appropriate units.Problem 6.10 A horizontal rope is tied to a 53.60m/s2 ? Express your answer to three significant figures and include the appropriate units.80m/s ? Express your answer as an integer and include the appropriate units. ANSWER: T = 0N Correct Part C The box vx = 4. ANSWER: w = 590 N Correct Part B What is the passenger's weight while the elevator is speeding up? Express your answer to two significant figures and include the appropriate units.14 It takes the elevator in a skyscraper 4.5s to reach its cruising speed of 11m/s .T = 244 N Correct Problem 6. ANSWER: w = 730 N Correct Part C Typesetting 100% What is math: the passenger's weight after the elevator reaches its cruising speed? . A 60kg passenger gets aboard on the ground floor. Part A What is the passenger's weight before the elevator starts moving? Express your answer to two significant figures and include the appropriate units. with the x axis along the plane. and F f⃗ . the normal force. Three forces act upon the block: large enough to prevent the block from sliding . The coefficient of friction is Part A Consider coordinate system a. ANSWER: w = 590 N Correct Block on an Incline A block lies on a plane raised an angle θ from the horizontal. Which forces lie along the axes? ANSWER: Typesetting math: 100% . F w⃗ . the force of friction. the force of gravity. F n⃗ .Express your answer to two significant figures and include the appropriate units. F f⃗ only F n⃗ only F w⃗ only F f⃗ and F n⃗ F f⃗ and F w⃗ F n⃗ and F w⃗ F f⃗ and F n⃗ and F w⃗ Correct Part B Which forces lie along the axes of the coordinate system b. in which the y axis is vertical? ANSWER: F f⃗ only F n⃗ only F w⃗ only F f⃗ and F n⃗ F f⃗ and F w⃗ F n⃗ and F w⃗ F f⃗ and F n⃗ and F w⃗ Correct Typesetting math: 100% . the y component of the force F n⃗ . Ff . each multiplied by a trigonometric function. Find the y component of F n⃗ Write an expression for Fny . Some geometry help . and θ . using coordinate system b. as shown in the figure. In these coordinates you will find the magnitude Fn appearing in both the x and y Part C Because the block is not moving. Hint 1. Fw . You will find the normal force. then you are better off choosing the coordinate system with the most vectors along the coordinate axes.Usually the best advice is to choose coordinate system so that the acceleration of the system is directly along one of the coordinate axes. F n⃗ . Express your answer in terms of Fn and θ . If the system isn't accelerating. Find an expression for the sum of the y components of the forces acting on the block. Express your answer in terms of some or all of the variables Fn . equations. ANSWER: Typesetting math: 100% . But now you are going to ignore that advice. using vertical coordinate system b. the sum of the y components of the forces acting on the block must be zero. using coordinate system b. Hint 1.a useful angle The smaller angle between F n⃗ and the y-axis is also θ . Express your answer in terms of Ff and θ . Find the y component of F f⃗ Write an expression for Ffy .Fny = Fn cos(θ) Hint 2. the y component of the force F f⃗ .a useful angle The smaller angle between F f⃗ and the x-axis is also θ . Hint 1. using coordinate system b. as shown in the figure. Some geometry help . ANSWER: Ffy = Ff sin(θ) ANSWER: ∑ Fy = 0 = Fn cos(θ) + Ff sin(θ) − Fw Typesetting math: 100% . Hint 1. and θ . ANSWER: Fnx = −Fn sin(θ) ANSWER: ∑ Fx = 0 = −Fn sin(θ) + Ff cos(θ) Correct Part E To find the magnitude of the normal force. Combine these equations to eliminate Ff . using coordinate system b. Express your answer in terms of Fn and θ . the sum of the x components of the forces acting on the block must be zero. Express your answer in terms of some or all of the variables Fn . Find the x component of F n⃗ Write an expression for Fnx . Ff . The key is to multiply the . the x component of the force F n⃗ .Correct Part D Because the block is not moving. Find an expression for the sum of the x components of the forces acting on the block. How to approach the problem Frommath: your100% answers to the previous two parts you should have two force equations (∑ Fy Typesetting = 0 and ∑ Fx = 0). Hint 1. find an expression for Fn involving Fw and θ but not Ff . you must express Fn in terms of Fw since Ff is an unknown. Using the equations you found in the two previous parts. using coordinate system b. Fw . equation for the y components by cos θ and the equation for the x components by sin θ . Two solid objects cannot occupy the same space at the same time. Indeed. the y-coordinate equation is immediately to the result obtained here for ∑ Fy = Fn − FW cos(θ) = 0. and acceleration of. they exert repulsive normal forces on each other. An alternative motivation for the algebra is to eliminate the trig functions in front of is simple to solve for Fn by using the trig identity sin2 (θ) + cos2 (θ) = 1. Now realize that in coordinate system a. As two surfaces are pushed together these forces increase exponentially over an atomic distance scale. easily becoming strong enough to distort the bulk material in the objects if they approach too close. we can conclude the following: The magnitude of contact forces is determined by ∑ F ⃗ = µn (although they can be smaller than this or even zero). which leads Fn . then add or subtract the two equations to eliminate the term Ff cos(θ) sin(θ) . or something similar) respectively. contact forces are limited by the deformation or acceleration of the objects. CONCLUSION: A thoughtful examination of which coordinate system to choose can save a lot of algebra. except for friction forces under certain circumstances. In everyday experience. these forces must be determined from: net Force = ma. ANSWER: Fn = Fw cos(θ) Correct Congratulations on working this through. rather than by the fundamental interatomic forces. At the very least this would result in an equation that Fn . Kinetic friction when surfaces slide Typesetting math: 100% n and f (or Ffric . These contact forces arise from a complex interplay between the electrostatic forces between the electrons and ions in the objects and the laws of quantum mechanics. the contacting bodies. as well as frictional forces that resist their slipping relative to each other. which is aligned with the plane. by the other forces on. the normal and frictional forces. Contact Forces Introduced Learning Goal: To introduce contact forces (normal and friction forces) and to understand that. Hence. These are the . when the objects touch. ma.⃗ that is. usually designated by components of the overall contact force: n perpendicular to and f parallel to the plane of contact. The only exception is that the frictional forces cannot exceed Normal and friction forces Two types of contact forces operate in typical mechanics problems. in agreement with the observation that when a force is large enough that something breaks loose and starts to slide.When one surface is sliding past the other. it often accelerates. As long as the sliding continues. Static friction when surfaces don't slide When there is no relative motion of the surfaces. The frictional force is always less than µk n. fk is proportional to the normal force. The frictional force is determined by other forces on the objects so it can be either equal to or less than µk n. Invariably. and 3. the frictional force is then fk = µk n (valid when the surfaces slide by each other). often designated µ k . The equation fs = µs n is valid only when the surfaces are on the verge of sliding. experiments show three things about the friction force (denoted fk ): 1. Part A When two objects slide by one another. The constant of proportionality is called the coefficient of kinetic friction. 2. Correct Part B Typesetting math: 100% . The actual magnitude and direction of the static friction force are such that it (together with other forces on the object) causes the object to remain motionless with respect to the contacting surface as long as the static friction force required does not exceed µs n. The frictional force opposes the relative motion at the point of contact. the frictional force can assume any value from zero up to a maximum µs n. µs is larger than µk . the ratio of the magnitude of the frictional force to that of the normal force is fairly constant over a wide range of speeds. The frictional force for surfaces with no relative motion is therefore fs ≤ µ s n (valid when the contacting surfaces have no relative motion). which of the following statements about the force of friction between them. is true? ANSWER: The frictional force is always equal to µk n. where µs is the coefficient of static friction. will cause the object to have the observed acceleration. which in turn reduces the friction. is true? ANSWER: The frictional force is always equal to µs n. Fg is larger than the force of maximum static friction. Once the box is moving. or equal to µs n depends on the magnitude of the other forces (if any) as well as the acceleration of the object through ∑ F ⃗ = ma. the actual magnitude and direction of the friction force are such that it. together with any other forces present. when determining at what point an object will just begin to slip). Whether the actual magnitude of the friction force is 0. The magnitude of the force cannot exceed µs n.⃗ Part C When a board with a box on it is slowly tilted to larger and larger angle. Fg is smaller than the force of maximum static friction but larger than the force of kinetic friction. the sliding reduces the normal force. When the box is stationary. If the magnitude of static friction needed to keep acceleration equal to zero exceeds µs n. Typesetting math: 100% Fg equals the force of static friction.e. then the object will slide subject to the resistance of kinetic friction. The frictional force is always less than µs n. .When two objects are in contact with no relative motion. The box begins to slide once the component of gravity acting parallel to the board Fg just begins to exceeds the maximum force of static friction. less than µs n. which of the following statements about the frictional force between them. Correct For static friction.. Once the box is moving. Do not automatically assume that fs = µs n unless you are considering a situation in which the magnitude of the static friction force is as large as possible (i. common experience shows that the box will at some point "break loose" and start to accelerate down the board. Which of the following is the most general explanation for why the box accelerates down the board? ANSWER: The force of kinetic friction is smaller than that of maximum static friction. but Fg remains the same. The frictional force is determined by other forces on the objects so it can be either equal to or less than µs n. but once the box starts moving. ) For the box to then accelerate. there must be a net force on the box along the board. The normal force Select the best answer. or the car is going around a banked turn). the car is sliding down an icy incline. Therefore the force of kinetic friction µ k n must be less than the force of static friction µs n which implies µ k < µ s . as expected. on the box has just reached a magnitude such that the force of static friction. the acceleration is unknown)." you know that the component of the box's weight that is parallel to the board just exceeds µs n (i.17 Bonnie and Clyde are sliding a 323kg bank safe across the floor to their getaway car. Each of the answer options is valid under some conditions (θ = 0. Do not memorize values for the normal force valid in different problems--you must determine n⃗ from ∑ F ⃗ = ma. there is not enough information given to determine the normal force (e. Thus. ANSWER: n = Mg n = Mg cos(θ) n= Mg cos(θ) is found using ∑ F ⃗ = M a⃗ Correct The key point is that contact forces must be determined from Newton's equation.. In the problem described above.g. the component of the box's weight parallel to the board must be greater than the force of kinetic friction. The safe slides with a constant speed if Clyde pushes from behind with 375N of force while Bonnie pulls forward onTypesetting a rope with 335 N of force. this component of gravitational force µs n .⃗ Problem 6.e. but in fact none is likely to be correct if there are other forces on the car or if the car is accelerating.. can no longer oppose it.Correct At the point when the box finally does "break loose. math: 100% . which has a maximum value of Part D Consider a problem in which a car of mass M is on a road tilted at an angle θ . The orientation of your vectors will be graded. Part A Draw a free-body diagram showing all the forces on the crate if the conveyer belt runs at constant speed.19 A 10 kg crate is placed on a horizontal conveyor belt. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. Draw the force vectors with their tails at the dot.Part A What is the safe's coefficient of kinetic friction on the bank floor? ANSWER: 0.224 Correct Problem 6. ANSWER: Typesetting math: 100% .3. The materials are such that µs = 0.5 and µ k = 0. The exact length of your vectors will not be graded but the relative length of one to the other will be graded.Correct Part B Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up. ANSWER: Typesetting math: 100% . The orientation of your vectors will be graded. Draw the force vectors with their tails at the dot. Correct Part C What is the maximum acceleration the belt can have without the crate slipping? Express your answer to two significant figures and include the appropriate units.9 s 2 Correct Typesetting math: 100% . ANSWER: m amax = 4. ANSWER: Typesetting math: 100% . Part A What is the tension in rope 1? Express your answer to two significant figures and include the appropriate units.28 A 1100kg steel beam is supported by two ropes.Problem 6. ANSWER: T1 = 7000 N Correct Part B What is the tension in rope 2? Express your answer to two significant figures and include the appropriate units. 35 The position of a 1.4kg mass is given by x = (2t3 − 3t2 ) m.4 N Correct Part B What is the net horizontal force on the mass at t = 1 s? Express your answer to two significant figures and include the appropriate units. ANSWER: F = 8.4 N Correct Problem 6.39 Typesetting math: 100% . ANSWER: F = -8.T2 = 4800 N Correct Problem 6. where t is in seconds. Part A What is the net horizontal force on the mass at t = 0 s? Express your answer to two significant figures and include the appropriate units. 5. you decide to give the box a push and have it slide down to him. who is at the edge of the roof directly below you. ANSWER: fk = 5800 N Correct Part B How long does it take the bullet to come to rest after entering the wood? Express your answer to two significant figures and include the appropriate units.A rifle with a barrel length of 61cm fires a 8g bullet with a horizontal speed of 400m/s . Part A What resistive force (assumed to be constant) does the wood exert on the bullet? Express your answer to two significant figures and include the appropriate units. asks you for the box of nails.0m away. Typesetting math: 100% .45 You and your friend Peter are putting new shingles on a roof pitched at 21∘ . Rather than carry the 2. Part A If the coefficient of kinetic friction between the box and the roof is 0. with what speed should you push the box to have it gently come to rest right at the edge of the roof? Express your answer to two significant figures and include the appropriate units.5×10−4 s Correct Problem 6.0kg box of nails down to Peter. ANSWER: t = 5. You're sitting on the very top of the roof when Peter. The bullet strikes a block of wood and penetrates to a depth of 11cm .55. 0 kg wood box in the figure slides down a vertical wood wall while you push on it at a 45 ∘ angle. ANSWER: F = 23 N Correct Typesetting math: 100% . Part A What magnitude of force should you apply to cause the box to slide down at a constant speed? Express your answer to two significant figures and include the appropriate units.ANSWER: v = 3.9 m s Correct Problem 6.54 The 2. Score Summary: Your score on this assignment is 98.8%.57 out of a possible total of 116 points. You received 114. Typesetting math: 100% .