UNIVERSITY OF MANITOBA. Equal marks for all questions. No marks are subtracted for wrong answers.

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1 PAGE NO.: 1 of 5 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! If you disagree with all the answers for a given problem, blacken the space on the answer sheet that indicates "n.o.t.", i.e. "none of these answers". 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. Calculators of any type are allowed. 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 -2 Mass of the earth = 5.98 x kg Radius of the earth = 6.38 x 10 3 km 1 cal = J Specific heat of water = C w = 4190 J/kgEC Ideal gas law constant: R = 8.31 J/(mol@K) Avagadro s Number, N A = mol!1 g = 9.8 m/s 2 ρ water = 10 3 kg/m 3 Standard atmospheric pressure = Pa Speed of sound in air = 343 m/s 1. A woman whose eyes are 1.75 m above the ground is standing 32 m away from a building. Her line of sight to the top of the building makes an angle of 53.5E to the horizontal. How tall is the building? (a) 45.0 m (b) 43.3 m (c) 25.7 m (d) 27.5 m (e) 30.5 m 2. A fielder on a baseball field throws a ball back to the pitcher who catches it. The ball is caught at the same height above the ground, as it was when it left the fielder s hand. The horizontal distance between the fielder and the pitcher was 65 m and the ball reaches a maximum height of 5.0 m above its starting point. What was the magnitude of the initial velocity of the ball? (a) 9.90 m/s (b) 32.2 m/s (c) 64.4 m/s (d) 65.2 m/s (e) 33.7 m/s 3. A professor, carrying a briefcase of mass m is in an elevator that accelerates either up or down with a magnitude of acceleration a. What is the ratio of force that he needs to apply to carry a briefcase when the elevator is accelerating upward to the force required when the elevator is accelerating downwards? (g&a) (a%g) g (g%a) a (a) (b) (c) (d) (e) (g%a) (a&g) a (g&a) g 4. During a landslide a 350 kg boulder slides down a 45E slope with an acceleration of 2.00 m/s 2. What is the coefficient of kinetic friction between the ground and the boulder? (a) (b) (c) (d) (e) 0.796

2 PAGE NO.: 2 of 5 5. The world s largest Ferris wheel with a radius of 50.0 m is located in Yokohama City, Japan. Each of the sixty gondolas on the wheel takes 1.00 minute to complete one revolution when it is running at full speed. What is the centripetal acceleration of the gondola when the Ferris wheel is running at full speed? (a) m/s 2 (b) 6.91 m/s 2 (c) 2.21 m/s 2 (d) m/s 2 (e) 6.28 m/s 2 6. Callisto and Io are two of Jupiter s moons. The distance from Callisto to the center of Jupiter is approximately 4.5 times as far as that of Io. How does Callisto s orbital period, T C, compare to that of Io, T I? (a) T C ' 4.5 T I (b) T C ' 21 T I (c) T C ' 9.5 T I (d) T C ' 0.2 T I (e) T C ' 2.7 T I 7. A block of mass m is released from rest at a height R above a horizontal surface. The acceleration due to gravity is g. The block slides along the inside of a frictionless circular hoop of radius R. What is the magnitude of the normal force exerted on the block by the hoop when the block has reached the bottom? (a) zero (b) mg 2 /R (c) mg (d) 2 mg (e) 3 mg 8. A 51-kg woman runs up a flight of stairs in 5.0 s. Her net upward displacement is 5.0 m. Approximately, what average power did the woman exert while she was running? (a) 5.0 kw (b) 1.0 kw (c) 0.75 kw (d) 0.50 kw (e) 0.25 kw 9. 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 1/4 the original kinetic energy of the sled. (b) It is 1/2 the original kinetic energy of the sled. (c) It is 3/4 the original kinetic energy of the sled. (d) It is the same as the original kinetic energy of the sled. (e) It is twice the original kinetic energy of the sled.

3 PAGE NO.: 3 of A comet fragment of mass kg is moving at m/s when it crashes into Callisto, a moon of Jupiter. The mass of Callisto is kg. The collision is completely inelastic. Assuming for this calculation that Callisto s initial momentum is zero, what is the recoil speed of Callisto immediately after the collision? (a) !18 m/s (c) !12 m/s (e) !5 m/s (b) !14 m/s (d) !7 m/s 11. What is the angular speed in rad/s of the second hand of a watch? (a) !3 rad/s (b) 0.10 rad/s (c) 0.02 rad/s (d) 6.28 rad/s (e) 60 rad/s 12. Three objects are situated on the x axis. Their weights and positions are: 43.0 N at x = m, 18.0 N at x =!0.600 m, and 36.7 N at x =!1.40 m. Where on the x axis is the center of gravity? (a) m (b) 0.33 m (c) m (d) 1.23 m (e) n.o.t. 13. A 3.0-kg block is placed between two horizontal springs. Neither spring is strained when the block is located at the position labeled x = 0 in the drawing. The block is then displaced a distance of m from the position where x = 0 and released from rest. What is the speed of the block when it passes back through the x = 0 position? (a) 1.91 m/s (b) 1.34 m/s (c) 2.68 m/s (d) 0.91 m/s (e) n.o.t. 14. A gold prospector finds a solid rock that is composed solely of quartz and gold. The rock has a mass of 24.0 kg and a volume of !3 m 3. What mass of gold is contained in the rock? The densities of gold and quartz are 19,300 kg/m 3 and 2,660 kg/m 3, respectively. (a) 3.13 kg (b) 1.57 kg (c) 6.26 kg (d) 10.3 kg (e) n.o.t. 15. The Mariana trench is located in the Pacific Ocean at a depth of about 11,000 m below the surface of the water. The density of seawater is 1025 kg/m 3. If an underwater vehicle were to explore such a depth, what force would the water exert on the vehicle s observation window (radius = 0.10 m)? (a) N (b) N (c) N (d) N (e) n.o.t. 16. A constant-volume gas thermometer has a pressure of Pa when the gas temperature is 0.00EC. What is the temperature (inec) when the pressure is Pa? (a) 82.0 EC (b) 109 EC (c) 146 EC (d) 123 EC (e) n.o.t.

4 PAGE NO.: 4 of Liquid nitrogen boils at a chilly!195.8 EC when the pressure is one atmosphere. A silver coin of mass !2 kg and temperature 25.0 EC is dropped into the liquid. What mass of nitrogen boils off as the coin cools to!195.8 EC? The specific heat capacity of silver is C = 235 J/(kg CE), the latent heat of vaporisation of liquid nitrogen is L v = J/kg. (a) !3 kg (b) 6.5 g (c) 4.2 g (d) !3 kg (e) n.o.t. 18. An arrow is shot vertically upwards. After 15.0 seconds have passed, it has a velocity of 55.0 m/s downwards. What was is the magnitude of its original velocity? (a) 73.5 m/s (b) 147 m/s (c) 92.0 m/s (d) 129 m/s (e) 202 m/s 19. Astronauts on a distant planet set up a simple pendulum of length 1.2 m. The pendulum executes simple harmonic motion and makes 100 complete vibrations in 300 s. What is the acceleration due to gravity? (a) 6.00 m/s 2 (b) 5.26 m/s 2 (c) 3.18 m/s 2 (d) 4.38 m/s 2 (e) n.o.t. 20. An airplane wing is designed so that the speed of air across the top of the wing is 251 m/s when the speed of the air below the wing is 225 m/s. The density of the air is 1.29 kg/m 3. What is the lifting force on a wing of area 36.0 m 2? (a) N (b) N (c) N (d) N (e) n.o.t. 21. A lead sphere has a diameter that is 0.050% larger than the inner diameter of a steel ring when each has a temperature of 60.0 EC. Thus, the ring will not slip over the sphere. At what common temperature will the ring just slip over the sphere? The linear thermal expansion coefficients of lead and steel are 29 10!6 (CE)!1 and 12 10!6 (CE)!1, respectively. (a) 31EC (b) 29EC (c) 12EC (d) 70EC (e) n.o.t. 22. How many molecules of H 2 O are there in 250 g of pure water? (a) (b) (c) (d) (e) n.o.t. 23. Compared to an echo on a cold day, an echo on a hot day will return (Assume other atmospheric conditions are the same on the two days.): (a) in less time (b) in more time (c) in the same time (d) in more or less time depending on the sound intensity level (e) in more or less time depending on the pitch of the sound

5 PAGE NO.: 5 of The speed of a transverse wave on a string is 450 m/s, while the wavelength is 0.18 m. The amplitude of the wave is 2.0 mm. How much time is required for a particle of the string to move through a total distance of 1.0 km? (a) 200 s (b) 50 s (c) 100 s (d) 2.22 s (e) n.o.t. 25. Two identical rifles are shot at the same time, and the sound intensity level is 80 db. What is the sound intensity level if only one of the rifles is shot? (a) 40 db (b) 70 db (c) 77 db (d) 79 db (e) 80 db 26. Two whistles produce sounds of wavelength 3.4 and 3.3 m. What is the beat frequency produced? (a) 0.1 Hz (b) 1.0 Hz (c) 2.0 Hz (d) 3.0 Hz (e) 4.0 Hz 27. Two loudspeakers are vibrating in phase. A listener is 51.4 m from the left speaker and 30.0 m from the right speaker. What are the two lowest frequencies in the audible range (20 Hz to 20 khz) that are louder because of constructive interference? (a) 22.6 Hz and 34.0 Hz (c) 32.0 Hz and 48.0 Hz (e) 20.0 Hz and 26.7 Hz (b) 22.6 Hz and 45.2 Hz (d) 32.0 Hz and 64.0 Hz 28. A rock of mass m with a density twice that of water is sitting on the bottom of an aquarium tank filled with water. The normal force exerted by the bottom of the tank on the rock is (a) 2mg (b) mg (c) mg/2 (d) zero (e) it depends on the depth of the water 29. In pure simple harmonic motion, the period of the motion (a) always increases with increasing amplitude (b) always decreases with increasing amplitude (c) may increase or decrease with increasing amplitude depending on the mass (d) is independent of the amplitude (e) None of these is correct. 30. A uniform plank with a mass of 50 kg is supported by a single pivot 50 cm from one end. How far from the pivot should the centre of a 50 kg mass be placed to balance the plank? (a) 25 cm (b) 0 cm (at the pivot) (c) 50 cm (at the end) (d) 15 cm (e) The plank cannot be balanced with a 50 kg mass. THE END