Uniformly Accelerated Motion in Vertical DimentaionThe vertical motion of a projectile is non-constant, as it is thrown/fired upwards originally with an unbalanced force at an angle, but once it has left the throwers hand or the gun etc it no longer has a vertical force working on it, save for the possibility of some friction from air resistance which we are ignoring. However it has the forge of gravity working on it, pulling it back down towards the Earth. Thus the projectile will have a vertical velocity which decelerates, until it reaches its maximum point, in which case it begins to accelerate its velocity, but this time in the opposite (downwards) direction. The deceleration/acceleration is 9.8ms^-2 towards the Earth. however once it leaves the hand/gun etc it has no force acting upon it from this direction. assuming that there is no friction acting on the ball. Gravity has no effect on the horizontal velocity. resulting in the projectile continuing to move with the same horizontal motion. Uniformly Accelerated Motion in Horizonal Dimentaion The horizontal motion of a projectile is constant. the net force on the projectile is zero. No friction means that there is no force in the opposing direction. It is originally accelerated horizontally. As a result. . as it works perpindicularly to it. Using this we can rearrange the parabolic Velocity motion equation to find the range of the The horizontal velocity remains constant. in the vertical direction is just due to condition y=0 gravity. also known as free fall: . Parabolic Trajectory The initial velocity can be expressed as x We can use the displacement equations in components and y components: the x and y direction to obtain an equation Time of Flight for the parabolic form of a projectile motion: The time of flight of a projectile motion is Maximum Height the time from when the object is projected to The maximum height is reached when vy=0 the time it reaches the surface. . In this atom we will discuss the basic equations that go along with them in the special case in which the projectile initial positions are null (i. Projectile Motion at different angles Projectile motion is a form of motion where an object moves in a bilaterally symmetrical.e. Displacement At time. parabolic path. Projectile motion only occurs when there is one force applied at the beginning on the trajectory. In a previous atom we discussed what the various components of an object in projectile motion are. Using this we can rearrange the velocity Acceleration equation to find the time it will take for the In projectile motion. . the displacement components are: x=u⋅t⋅cosθy=u⋅t⋅sinθ−12gt2 The equation for the magnitude of the displacement is Δr=√ x2+y2 . motion: but the vertical velocity varies linearly. t. R=u2⋅sin2θg because the acceleration is constant. Range a The range of the motion is fixed by the . x0=0 and y0=0 Initial Velocity . there is no acceleration object to reach maximum height in the horizontal direction. after which the only interference is from gravity. The path that the object follows is called its trajectory. The acceleration. An equation can also be treated as a statement which describes qualitatively how one variable depends upon another. Thinking and reasoning proportionally about quantities allows you to predict how an alteration in one variable would effect another variable. Two quantities in an equation could be thought of as being either directly proportional or inversely proportional. Similarly. a two-fold or three-fold increase in the velocity (with the mass held constant) will result in a two-fold or a three-fold increase in the amount of momentum possessed by the object. Knowing the numerical values of all but one of the quantities in the equations allows one to calculate the final quantity in the equation. A two-fold or three-fold increase in the mass (with the velocity held constant) will result in a two-fold or a three-fold increase in the amount of momentum possessed by the object. Momentum is directly proportional to both mass and velocity. In equation form: p=m•v An equation such as the one above can be treated as a sort of recipe for problem-solving. The amount of momentum (p) possessed by the moving object is the product of mass (m) and velocity (v). . Momentum Momentum An object which is moving has momentum. the following equalities result. it could be said that the force times the time equals the mass times the change in velocity. a new equation results. Newton's second law (Fnet = m • a) stated that the acceleration of an object is directly proportional to the net force acting upon the object and inversely proportional to the mass of the object. it is important to understand its meaning in words. In physics. To truly understand the equation. And since the quantity m•v is the momentum. the quantity m•Δv must be the change in momentum. In words. The equation really says that the Impulse = Change in momentum . F • t = m • ∆v This equation represents one of two primary principles to be used in the analysis of collisions during this unit. Impulse These concepts are merely an outgrowth of Newton's second law as discussed in an earlier unit. F=m•a or F = m • ∆v / t If both sides of the above equation are multiplied by the quantity t. When combined with the definition of acceleration (a = change in velocity / time). the quantity Force • time is known as impulse. Click the button to check your answer. velocity-time graph. Collision Now consider a collision of a tennis ball with a wall. and ticker tape pattern). Support each answer. greatest acceleration. greatest momentum change. The diagrams below depict the changes in velocity of the same ball. Depending on the physical properties of the ball and wall. the speed at which the ball rebounds from the wall upon colliding with it will vary. and greatest impulse. indicate which case (A or B) has the greatest change in velocity. Vector Diagram . For each representation (vector diagram. The measurement of kinetic energy in an object is calculated based on the object's mass and velocity. and nuclear energy. The measurement of potential energy in an object is calculated based on the object's mass and its height or distance. . chemical. and vibration. It is stored energy that can become kinetic energy. It is measured in Joules. It is measured in Joules. It includes potential electrical. Mechanical energy ( Potential & Kinetic Energy) Kinetic energy is a form of energy that results from an object's motion. There are many types of motion that use kinetic energy: translation (moving from one place to another). rotation. Potential energy is a form of energy that results from an object's position or arrangement of parts. and they form new compounds with vastly different personalities. On an atomic scale. atoms move around during chemical reactions. a coiled spring. ELASTIC Elastic energy can be stored mechanically in a compressed gas or liquid. the stored energy is a temporary strain placed on the bonds between atoms. This stored energy is transformed when bonds are broken or formed through chemical reactions. or a stretched elastic band. meaning there’s no permanent change to the material. freeing lots of energy. . Forms Of Potential Energy GRAVITATIONAL Systems can increase gravitational energy as mass moves away from the center of Earth or other objects that are large enough to generate significant gravity (our sun. These bonds absorb energy as they are stressed. Like letters of the alphabet that can be rearranged to form new words with very different meanings. Hydrogen atoms in the sun experience nuclear fusion. and release that energy as they relax. CHEMICAL Chemical energy is stored in the bonds between the atoms in compounds. NUCLEAR Today’s nuclear power plants are fueled by fission. Uranium or plutonium atoms are broken apart. the planets and stars). combining to form helium and subsequently releasing large amounts of energy in the form of electromagnetic radiation and thermal energy. gamma rays. x-rays. and radio waves. Sound is the movement of energy through substances in longitudinal (compression/rarefaction) waves. The energy is transferred through the substance in a wave. which provides the fuel and warmth that make life on earth possible. The faster they move. the more energy is stored. Forms Of Potential Energy Radiant energy is electromagnetic energy that travels in transverse waves. . the energy in sound is smaller than in other forms of energy. Heat increases with increases in the speed that these particles move. Typically. It takes energy to get an object moving. Light is one type of radiant energy. Geothermal energy is the thermal energy in the earth. Wind is an example of motion energy. A dramatic example of motion energy is a car crash—a car comes to a total stop and releases all of its motion energy at once in an uncontrolled instant. Electrical energy is delivered by tiny charged particles called electrons. and energy is released when an object slows down. Lightning is an example of electrical energy in nature. Sunshine is radiant energy. typically moving through a wire. Sound is produced when a force causes an object or substance to vibrate. or heat. Radiant energy includes visible light. Thermal energy. Motion energy is energy stored in the movement of objects. is the energy that comes from the movement of atoms and molecules in a substance.
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