2017 SEMESTER 1 - TEST 3 PREPARATION ASSIGNMENT 31. The following three point charges are placed on the x- axis: + 4 µC at x = 0, + 3 µC at x = 30 cm, and + 5 µC at x = 60 cm. Find the force on (a) the 5- µC charge and (b) the 3- µC charge. (2 N right, 0.3 N left) 2. Three point charges with values -3, + 4, and -6 µC are placed at x = 0, x = 40, and x = 120 cm, respectively. Find the force on (a) the – 3- µC charge and (b) the + 4- µC charge. (0.562 N right, 0.337 N left) 3. Two points charges are placed on the x-axis: a – 4- µC charge at x = 0 and a + 3- µC charge at x = 80 cm. At what point(s) in the vicinity of these two charges can a + 5- µC charge be placed to that it experiences no resultant force? ((5.176 m) 4. Two points charges are placed on the x-axis: a + 6- µC charge at x = 0 and a + 5- µC charge at x = 200 cm. At what point(s) in the vicinity of these two charges can a + 5- µC charge be placed to that it experiences no resultant force? (0.954 m) 5. Two points charges are placed on the x axis: - 5.0- µC charge at x = 0 and an + 8.0- µC charge at x = 90 cm. (a) At what point(s) in the vicinity of these two charges can a charge be placed to that it experiences no resultant force? (b) What is the electric field strength exactly in the centre of the two charges? (c) What is the absolute potential exactly in the centre of the two charges? (3.397 m, 577777.778 N/C) 6. Find the electric field strength due to a point charge q = -5.0 µC at a distance of 80 cm from the charge. Is the field directed radially outward or inward? (70312.5 N/C inward) 7. In the figure, the charge at A is +200 pC, while the charge at B is -100 pC. (a) Find the absolute potentials at points C and D. (b) How much work must be done to transfer a charge of +500 μC from point C to D? (VC = -2.25 V, VD = 7.875 V, VCD = -10.125 V, W CD = -5.063 mJ) A D C B 20 cm 60 cm 20 cm 8. Two charges are placed on the x-axis: a +6-µC charge at x = 80 cm and a –3-µC charge at x = 0. Find E at (a) x = 30 cm and (b) x=100 cm. (516 x 103 N/C left, 1.323 x 106 N/C right) 9. A tiny ball carrying a charge of -3.0 x 1012 C experiences an eastward force of 8.0 x 10-7 N due to its charge when it is suspended at a certain point in space. What are the magnitude and direction of E at that point? (3.75 x 10-6 N/C west) 10. The four point charges in the figure are each +3.0 µC. Find the magnitude and direction of the force on the bottom left charge, due to the other charges. Use a = 30 cm and b = 60 cm. (1.054 N, 68.52o below negative x-axis) b a 11. Four point charges are placed at the four corners of a square that is 30 cm on each side. Find the potential at the center of the square if (a) the four charges are each +2.0 and (b) two of the four charges are +2.0 µC and two are -2.0 µC. (3 396 22.642 V, 0 V) 12. (a) If the potential difference between A and B is 5 V, calculate the current and the voltage through each resistor. (b) If the current through the 60 Ω resistor is 2 A, calculate the voltage across each resistor and the voltage between A and B. (V10=1.67 V, V30 = V60 = 3.33 V, VAB = 5 V) 13. (a) If the potential between A and B is 9 V, what is the current through the 2.7 Ω resistor? (b) If the current through the 2.7 Ω resistor is 5 A, what is the potential difference between A and B? (IA = 0.731 A, VAB = 61.623 V) 14. An electron is released in a region where the electric fields is in the positive x direction and has a strength of 4000 N/C. Find the magnitude and direction of the electron’s acceleration. (Use me = 9.11 x 10-31 kg). (7.025 x 1014 m/s2 in negative x-direction) 15. (a) Calculate the current through the 30 Ω resistor. (b) What is the power dissipated in the 30 Ω resistor? (I30=0.133 A, P30 = 0.513 Watt) 16. Five resistors are connected as shown in the diagram. The potential difference between points A and B is 25 V. (a) What is the equivalent resistance between the points A and B? (b) What is the current through the 3.6 Ω resistor? (c) How much energy is dissipated in the 1.8 Ω resistor in 4.0 seconds? (d) What is the potential drop across the 3.5 Ω resistor? (7.488 Ω, 3.339 A, 54.867 J, 2.022 V) 17. In the figure, the electric field causes the ball of mass m=20 g and the magnitude of the charge q =2.0 µC to hang at the angle shown. (a) Find E. (b) Is the charge positive or negative? (T=0.392 N, FE=0.34 N, E = 169.74 N/C, negative) 30o E 18. The three point charges in the rectangle in the figure are each 7.0 µC. (a) Find the magnitude and direction of the force on top right charge due to the other charges. (b) What is the resultant electric field strength at the empty corner P? (c) What is the absolute potential at the empty corner P? Use a = 50 cm. (2.021 N, 79.1o above positive x-axis, 278713.647 N/C 65.6o above negative x-axis, 261748.68 V)) P a 30o Learning unit 16 1. A solid sphere made of a certain material has a radius of 2.00 cm and a mass of 81.0 g. What is the density of the material? (2.417 g/cm3) 2. How much force does the atmosphere exert on a person’s back? Assume that Pa = 100 kPa and that the back has an area of 300 cm2. Why doesn’t this enormous force crush the person? (3000 N) 3. Hydraulic stamping machines exert tremendous forces on a sheet of metal to form into the desired shape. Suppose the input force is 800 N on a piston that has a diameter of 1.40 cm. The output force is exerted on a piston that has a diameter of 35 cm. How large a force does the press exert on the sheet being formed? (500 kN) 4. A beaker has a 2.0-cm-thick layer of oil (ρoil = 843 kg/m3) floating on 3.0 cm of water. What is the combined pressure due to the liquids at the bottom of the beaker? (459.2 Pa) 5. A 1200-kg automobile has its tires inflated to a gauge pressure of 180 kPa. How large an area of each tire is in contact with the pavement? Assume the wheels share the load equally. (0.01633 m2) 6. A glass tube is bent into a U shape. Water is poured into the tube until it stands 10 cm high in each side. Benzene is added slowly to one side until the water on the other side rises 4 cm. Density of Benzene 0.8786 g/cm³. What length is the benzene column? (9.1 cm) 7. Oil flows through a 4.0 cm i.d. pipe at an average speed of 2.5 m/s. Find the flow in m 3/s and cm3/s. (3.142 x 10-3 m3.s-1,3141.593 m3/s) 8. Compute the average speed of water in a pipe having an i.d. of 5.0 cm and delivering 2.5 m 3 of water per hour. (0.354 m/s) 9. A pipe of varying inner diameter carries water. At point 1 the diameter is 30 cm and the pressures is 150 kPa. At point 2, which is 3.0 m lower than point 1, the diameter is 20 cm. If the flow is 0.090 m 3/s, what is the pressure at the second point? (176 kPa) 10. A large open tank of non-viscous liquid springs a leak 4.5 m below the top of the liquid. What is the theoretical velocity of outflow from the hole? If the area of the hole is 0.25 cm 2, how much liquid would escape in exactly 1 minute? 11. Water flows steadily through a horizontal pipe of varying cross section. At one place the pressure is 130 kPa and the speed is 0.60 m/s. Determine the pressure at another place in the same pipe where the speed is 9.0 m/s. (89.68 kPa) 12. A pipe of varying inner diameter carries water. At point 1 the diameter is 20 cm and the pressures is 130 kPa. At point 2, which is 4.0 m higher than point 1, the diameter is 30 cm. If the flow is 0.080 m 3/s, what is the pressure at the second point? (93.4 kPa) 13. Fuel oil of density 820 kg/m3 flows through a venture meter having a throat diameter of 4.0 cm an and entrance diameter of 8.0 cm. The pressure drop between entrance and throat is 16 cm of mercury. Find the flow. The density of mercury is 13 600 kg/m 3. 14. Find the flow in liter/s of a non-viscous liquid through an opening 0.50 cm 2 in area and 2.5 m below the level of the liquid in an open tank. (0.34 l/s) 15. Calculate the theoretical velocity of efflux of water from an aperture that is 8.0 m below the surface of water in a large tank, if an added pressure of 140 kPa is applied to the surface of the water. (20.9 m/s) Learning unit 17 1. A heat-resistant glass flask is calibrated to hold exactly 100 cm 3 at 20ºC. How much more will it hold at 30ºC? Hint: The hollow flask expands as though it were a solid volume. (0.023 cm3) 2. A certain straight roadway is made of concrete slabs, each 25 m long. How large an expansion gap should be left between slabs at 20ºC if they are to just touch at 45ºC? (15 mm) 3. A salad-dressing jar has an aluminium screw-type lid. At 20ºC, the lid fits so tightly that it does not screw off. By what factor will the lid’s diameter expand if it is heated to 70ºC? Why should you not heat the lid any longer than necessary? (1.15 x 10-3) 4. A meter stick made from aluminium is heated from 20ºC to 35ºC. What is its fractional change in length? (3.45 x 10-4) 5. Determine the temperature Tf that results when 150 g of ice at 0ºC is mixed with 300 g of water at 50ºC. (6.66 oC) 6. Calculate the heat of fusion from the following data for ice at 0 oC added to water. Mass of calorimeter 60 g Mass of calorimeter plus water 460 g Mass of calorimeter plus water and ice 618 g Initial temperature of water 38.0 ºC Final temperature of mixture 5.0 ºC Specific heat of calorimeter 400 J/kg.ºC (333799.114 J/kg) 7. A 55-g copper calorimeter (c = 387 J/(kg.ºC)) contains 250 g of water at 18.0ºC. When 75 g of an alloy at 100ºC is dropped into the calorimeter, the resulting temperature is 20.4ºC. What is the specific heat of the alloy? (429.26 J.kg-1.oC-1) 8. Determine the temperature that results when 1.0 kg of ice at 0ºC is mixed with 9.0 kg of water at 50ºC. (37 oC) 9. How much heat is required to change 10 g of ice at exactly 0ºC to steam at 100ºC? (30136 J) 10. Calculate how much steam will condense when 100 g of steam at 100ºC is passed into 200 g of water and 20 g of ice at exactly 0ºC in a calorimeter, which behaves thermally as if it were equivalent to 30 g of water. Tip: First decide what the final temperature of the mixture is. (49.27 g) 11. Calculate how much ice will melt when 10 g of steam at 100ºC is passed into 400 g of water and 100 g of ice at exactly 0ºC in a calorimeter, which behaves thermally as if it were equivalent to 10 g of water. (80 g) 12. A steel gas tank of volume 0.070 m 3 is filled to the top with gasoline at 20 °C. The tank is placed inside a chamber with an interior temperature of 50 °C. The coefficient of volume expansion for gasoline is 9.50 x 10 -4 oC-1, and the coefficient of linear expansion of steel is 12.0 x 10-6 oC-1. After the tank and its contents reach thermal equilibrium with the interior of the chamber, how much gasoline has spilled? (0.0019194 m3) 13. A 55-g copper calorimeter (c = 387 J/(kg.ºC)) (c = 930 J. kg -1.oC-1) contains 250 g of water (c=4186 J. kg -1.oC-1) and 10 g ice (L=3.35 x 105 J.kg -1) at 0ºC. When 75 g of an alloy at 100ºC is dropped into the calorimeter, the resulting temperature is 20.4ºC. What is the specific heat of the alloy? (4352.89 J/(kg.ºC)) Learning unit 19 1. Iodine 131 is used to treat thyroid disorders because, when ingested, it localizes in the thyroid gland. Its half-life is 8.1 days. What is the activity of 0.70 μg of 131-I. (3.19 x 109 Bq) 2. Compute the binding energy per nucleon of the 20-Ne nucleus. Its atomic mass is 19.9211 u. (227.0997 MeV/nucleon) 3. A sample gives 820 counts per minute at one time; 36 h later; it has a count rate of 102 counts/min. What is its half-life? (11.97 hour) 4. A sample that contains 4.2 x 1011 atoms has a half-life of 0.8 yr. (a) What is its decay constant? (b) How many nuclei in it undergo decay in 30 s? (c) How many disintegrations occur each second? (d) How long will it take to disintegrate to a ½ of its original number? (e) How long will it take to disintegrate to a ¼ of its original number? (2.7474441 x 10-8 s-1, 346177.814, 11539.265 Bq, 0.8 year, 1.6 year)
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