UNIVERSITY OF MANITOBA

Transcription

1 PAGE NO.: 1 of 6 + Formula Sheet Equal marks for all questions. No marks are subtracted for wrong answers. Record all answers on the computer score sheet provided. USE PENCIL ONLY! Black pen will look good but may not be read reliably by the scoring machine. Mark only one answer for each question! An answer should NOT be considered to be incorrect if the number of significant figures does not match the significant figures supplied in the question. A formula sheet is provided for your use; you may not use your own formula sheet. Be sure your name and student number are printed on the score sheet and the student number correctly coded in the box at the top right-hand side of the sheet. TABLE OF CONSTANTS G = x m 3 kg -1 s - Mass of the earth = 5.98 x 10 4 kg Radius of the earth = 6.38 x 10 3 km 1 Horsepower = W g = 9.80 m/s ρ water = 10 3 kg/m 3 Standard atmospheric pressure = Pa J = 1 Calorie 1. At a location where the acceleration due to gravity is m/s, the atmospheric pressure is Pa. A barometer at the same location is filled with an unknown liquid. What is the density of the unknown liquid if its height in the barometer is m? (a) 10 kg/m 3 (d) 867 kg/m 3 (b) 4336 kg/m 3 (e) 9688 kg/m 3 (c) 5317 kg/m 3. A small sculpture made of gold (ρ gold = 1980 kg/m 3 ) is believed to have a secret central cavity. The weight of the sculpture in air is 5.76 N. When it is submerged in water, the weight is 3.86 N. What is the volume of the secret cavity? (a) m 3 (d) m 3 (b) m 3 (e) m 3 (c) m 3

2 PAGE NO.: of 6 + Formula Sheet 3. A glass tube has several different cross-sectional areas with the values indicated in the figure. A piston at the left end of the tube exerts pressure so that the mercury within the tube flows from the right end with a speed of 8.0 m/s. Three points within the tube are labeled A, B, and C. NB: The drawing is not to scale. Atmospheric pressure is m/s ; and the density of mercury is kg/m 3. Determine the height h of mercury in the manometer with the evacuated upper end. (a) 136 mm (b) 69 mm (c) 76 mm (d) 366 mm (e) 371 mm 4. A.00-kg metal block slides on a rough, horizontal surface inside an insulated box. After sliding a distance of m, its temperature is increased by.00 C. Note: Assume that all of the heat generated by frictional heating goes into the metal block. For this metal, the specific heat capacity is cal/(g C ). What is the coefficient of sliding friction between the block and the surface? (a) zero (b) (c) (d) 0.56 (e) k 5. Which would cause a more serious burn: 30 g of steam or 30 g of liquid water, both at 100 C; and why is this so? (a) Water, because it is denser than steam. (b) Steam, because of its specific heat capacity. (c) Steam, because of its latent heat of vaporization. (d) Water, because its specific heat is greater than that of steam. (e) Either one would cause a burn of the same severity since they are both at the same temperature.

3 PAGE NO.: 3 of 6 + Formula Sheet 6. A slab of insulation is made of three layers, as Drawing I indicates. Each of the layers A, B, and C has the same thermal conductivity, and a different thickness. Heat flows through the slab, and the temperatures are as shown. What are the temperatures T 1 and T in Drawing II where the layers are arranged in a different order for the same amount of heat flow? (a) T 1 = 30 C and T = 170 C (b) T 1 = 00 C and T = 180 C (c) T 1 = 0 C and T = 160 C (d) T 1 = 180 C and T = 160 C (e) T 1 = 10 C and T = 190 C 7. A large cylindrical tank is sitting on the ground. It is filled with water and is open to the atmosphere at the top. There is a leak from a small hole located a distance h above the ground and a distance H below the water line. The water spurts out of the hole and lands on the ground a distance x from the base of the tank. If air resistance is neglected, the position where the water strikes the ground is given by: (a) x = 1 (b) x = hh hh (c) x = hh ( h) (d) (e) x = h H x = 1 H h 8. The instantaneous velocity of a certain simple harmonic oscillator is given by v = -11.3cos(3.60t), where v is in m/s. What is the amplitude of the simple harmonic motion? (a) 5.65 m (b) 0.87 m (c) 40.7 m (d) 1.80 m (e) 3.14 m 9. A box of mass m is at rest on a frictionless surface and is attached to an unstretched spring of force constant k. The box is struck by a hammer and given a speed v such as to compress the spring. The amplitude, A, of the resulting oscillations is: (a) A = m k v (c) k 1 m A = v (e) A = v m k m 1 k (b) A = v (d) A = v k π m

4 PAGE NO.: 4 of 6 + Formula Sheet 10. A football is kicked with a speed of 18 m/s at an angle of 65 to the horizontal. How long is the football in the air? Neglect air resistance. (a) 1.6 s (b).0 s (c) 4.0 s (d) 3.3 s (e) 1.1 s 11. The rate at which the acceleration of an object changes with time is called the jerk. What is the dimension of the jerk? [L] (a) 3 [T ] (b) [L] [T] (c) [L] [T ] 3 (d) [L ] [T ] [L] (e) [T ] 1. A tennis ball is shot vertically upward from the surface of an atmosphere-free planet with an initial speed of 0.0 m/s. One second later, the ball has an instantaneous velocity in the upward direction of 15.0 m/s. How long does it take the ball to reach its maximum height? (a) 4.6 s (b).0 s (c) 8.0 s (d) 4.0 s (e).3 s 13. A.00-kg projectile is fired at an angle of 0.0. What is the magnitude of the force exerted on the projectile when it is at the highest position in its trajectory? (a) 19.6 N (b) 9.80 N (c) 14.7 N (d) 0 N (e) 4.90 N 14. A block of mass M is held motionless on a frictionless inclined plane by means of a string attached to a vertical wall as shown in the drawing. If the string breaks, what is the magnitude of the acceleration of the block as it slides down the inclined plane? (a) g tan θ (c) g cos θ (e) zero m/s (b) g (d) g sin θ 15. A block is pulled along a rough level surface at constant speed by the force P. The figure shows the free-body diagram for the block. FN represents the normal force on the block; and f represents the force of kinetic friction. What is the magnitude of FN? (a) mg

5 PAGE NO.: 5 of 6 + Formula Sheet (b) This cannot be determined from the information given. (c) mg (d) f (e) P 16. A 1500-kg car travels at a constant speed of m/s around a circular track that has a radius of 85 m. Determine the magnitude of the net force that acts on the car. (a) N (b) N (c) zero newtons (d) 390 N (e) 1800 N 17. A tennis ball is thrown from ground level with velocity vo directed 30 above the horizontal. If it takes the ball 1.0 s to reach the top of its trajectory, what is the magnitude of the initial velocity? (a) 19.6 m/s (b) 34.4 m/s (c) 11.3 m/s (d) 4.9 m/s (e) 9.8 m/s 18. A 0.5-kg ball attached to a string is rotating in a horizontal circle of radius 0.5 m. If the ball revolves twice every second, what is the tension in the string? (a) 0 N (b) 5 N (c) N (d) 10 N (e) 7 N 19. Sara puts a box into the trunk of her car. Later, she drives around an unbanked curve that has a radius of 48 m. She finds that if the speed of the car on the curve is greater than16 m/s, the box just begins to move relative to the floor of the trunk. Determine the coefficient of static friction for the box on the floor of the trunk. (a) This cannot be determined without (c) 0.17 knowing the mass of the box. (d) 0.54 (b) 0.4 (e) 0.33

6 PAGE NO.: 6 of 6 + Formula Sheet 0. A football is kicked with a speed of m/s at an angle of 60.0 to the positive x direction. At that instant, an observer rides past the football in a car that moves with a constant speed of 11 m/s in the positive x direction. Complete the following statement: According to the observer in the car, the ball will (a) follow a straight line that is angled (less than 90 ) with respect to the x direction. (b) follow a path that is straight up and down in the y direction. (c) follow a path that is straight across in the +x direction. (d) follow a parabolic path. (e) follow a hyperbolic path. 1. Two boxes are connected to each other as shown. The system is released from rest and the 1.00-kg box falls through a distance of 1.00 m. The surface of the table is frictionless. What is the kinetic energy of box B just before it reaches the floor? A) 39. J B) 4.90 J C) 9.4 J D) 9.80 J E).45 J. A constant force of 5 N is applied as shown to a block which undergoes a displacement of 7.5 m to the right along a frictionless surface while the force acts. What is the work done by the force? A) +94 J B) zero joules C) 160 J D) +160 J E) 94 J 3. An escalator is 30.0 meters long and slants at 30.0 relative to the horizontal. If it moves at 1.00 m/s, at what rate does it do work in lifting a 50.0 kg man from the bottom to the top of the escalator? A) 45 W B) 9 W C) 495 W D) 49.3 W E) 98.0 W 4. A motorist driving a 1000-kg car wishes to increase her speed from 0 m/s to 30 m/s in 5 s. Determine the horsepower required to accomplish this increase. Neglect friction. A) 30 hp B) 80 hp C) 90 hp D) 70 hp E) 0 hp

7 PAGE NO.: 7 of 6 + Formula Sheet 5. The head of a hammer (m = 1.5 kg) moving at 4.5 m/s strikes a nail and bounces back with the same speed after an elastic collision lasting s. What is the magnitude of the average force the hammer exerts on the nail? A) 90 N B) 180 N C) 40 N D) 60 N E) 6.8 N 6. In the game of billiards, all the balls have approximately the same mass, about 0.17 kg. In the figure, the cue ball strikes another ball such that it follows the path shown. The other ball has a speed of 1.5 m/s immediately after the collision. What is the speed of the cue ball after the collision? A) 1.8 m/s B) 1.5 m/s C) 5. m/s D).6 m/s E) 4.3 m/s 7. A sled of mass m is coasting on the icy surface of a frozen river. While it is passing under a bridge, a package of equal mass m is dropped straight down and lands on the sled (without causing any damage). The sled plus the added load then continue along the original line of motion. How does the kinetic energy of the sled + load compare with the original kinetic energy of the sled? A) It is twice the original kinetic energy of the sled. B) It is 1/ the original kinetic energy of the sled. C) It is the same as the original kinetic energy of the sled. D) It is 1/4 the original kinetic energy of the sled. E) It is 3/4 the original kinetic energy of the sled. 8. An 80-kg astronaut carrying a 0-kg tool kit is initially drifting toward a stationary space shuttle at a speed of m/s. If she throws the tool kit toward the shuttle with a speed of 6 m/s as seen from the shuttle, her final speed is A) 6 m/s away from the shuttle. D) 4 m/s toward the shuttle. B) 1 m/s away from the shuttle. E) 1 m/s toward the shuttle. C) m/s toward the shuttle. 9. What is the angular speed in rad/s of the second hand of a watch? A) rad/s B) 60 rad/s C) 0.10 rad/s D) 6.8 rad/s E) 0.0 rad/s 30. A sign of mass m is suspended from a wall by a cable and a hinge as shown. What is the tension in the supporting cable?

8 PAGE NO.: 8 of 6 + Formula Sheet a) b) c) d) e) mg cosθ mg sinθ mg sinθ mg sinθ mg cosθ Hinge θ EAT AT JOE S.00 m The End

9 PAGE NO.: 9 of 6 + Formula Sheet Answer Key -- Final exam for D. E 3. C 4. D 5. C 6. C 7. B 8. E 9. A 10. D 11. A 1. D 13. A 14. D 15. A 16. B 17. A 18. A 19. D 0. B 1. E. C 3. A 4. D 5. B 6. D 7. B 8. E 9. C 30. C