Physics 23 Exam 3 April 2, 2009

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1 1. A string is tied to a doorknob 0.79 m from the hinge as shown in the figure. At the instant shown, the force applied to the string is 5.0 N. What is the torque on the door? A) 3.3 N m B) 2.2 N m C) 1.1 N m D) 0.84 N m 2. A meter stick is pivoted at the 0.50-m mark. A 3.0-kg object is hung from the 0.10-m mark. Where should a 5.0-kg object be hung to achieve equilibrium? A) 0.06-m B) 0.24-m C) 0.56-m D) 0.81-m 3. A 20 N m torque acts on a wheel of moment of inertia 50 kg m 2. If the wheel starts from rest, how long will it take the wheel to travel through 20 radians? A) 0.50 s B) 2.00 s C) 6.00s D) s Page 1

2 4. A string is wrapped around a pulley of radius 0.05 m and moment of inertia 0.2 kg m 2. If the string is pulled with a force F, the resulting angular acceleration of the pulley is 2 rad/s 2. Determine the magnitude of the force F. A) 0.4 N B) 2 N C) 8 N D) 16 N 5. A 6.0-kg solid cylinder of radius 0.5 m rotates at a rate of 40 rad/s about its cylindrical axis. What power is required to bring the cylinder to rest in 10 s? The rotational inertia of a cylinder is given by I = (1/2) MR 2. A) 20 W B) 40 W C) 160 W D) 200 W 6. A solid sphere of radius R rotates about a diameter with an angular speed ω. The sphere then collapses under the action of internal forces to a final radius R/3. What is the final angular speed of the sphere? (The rotational inertia of a solid sphere is I = (2/5) MR 2.) A) ω/12 B) ω/3 C) 3ω D) 9ω Use the following to answer question 7: A 2.0-kg hoop rolls without slipping on a horizontal surface so that its center proceeds to the right with a constant linear speed of 6.0 m/s. Page 2

3 7. What is the total kinetic energy of the hoop? A) 36 J B) 54 J C) 72 J D) 96 J 8. A 1.0-kg object is attached to a horizontal spring with k = 16 N/m. The mass is pulled 0.25 m from its equilibrium position and allowed to oscillate. What is the maximum kinetic energy of the object? A) 0.25 J B) 0.50 J C) 1.0 J D) 2.0 J 9. A spring with constant k = 40.0 N/m is at the base of a frictionless, inclined plane. A 0.50-kg block is pressed against the spring, compressing it 0.20 m from its equilibrium position. The block is then released. If the block is not attached to the spring, how far along the incline will it travel before it stops? A) m B) 0.16 m C) 0.33 m D) 1.6 m Page 3

4 10. A ping-pong ball weighs N. The ball is placed inside a cup that sits on top of a vertical spring. If the spring is compressed m and released, the maximum height above the compressed position that the ball reaches is 2.84 m. Neglect air resistance and determine the spring constant. A) 47 N/m B) 24 N/m C) 11 N/m D) 5.2 N/m 11. The spring constant for the spring in a special cannon is 1800 N/m. In cocking the cannon, the spring is compressed 0.55 m, and a 7.0-kg cannball is placed at the end of the spring. What maximum speed will this ball acquire after the spring is released? A) 77 m/s B) 140 m/s C) 12 m/s D) 8.8 m/s 12. A cable stretches by an amount d when it supports a crate of mass M. The cable is replaced by another cable of the same material having twice the length and three times the diameter. If the same crate is supported by the longer, thicker cable, by how much will the cable stretch? A) d/18 B) d/2 C) d D) 2d/9 13. Young's modulus of nylon is N/m 2. A force of N is applied to a 2-m length of nylon of cross sectional area 0.1 m 2. By what amount does the nylon stretch? A) m B) m C) m D) m Page 4

5 14. The radius of a sphere of lead (B = N/m 2 ) is m on the surface of the earth where the pressure is N/m 2. The sphere is taken by submarine to the deepest part of the ocean to a depth of m where it is exposed to a pressure is N/m 2. What is the volume of the sphere at the bottom of the ocean? A) m 3 B) m 3 C) m 3 D) m During the spin-dry cycle of a washing machine, the motor slows from 95 rad/s to 30 rad/s while the turning the drum through an angle of 402 radians. What is the magnitude of the angular acceleration of the motor? A) 64 rad/s 2 B) 32 rad/s 2 C) 10 rad/s 2 D) 20 rad/s An airplane engine starts from rest; and 2 seconds later, it is rotating with an angular speed of 300 rev/min. If the angular acceleration is constant, how many revolutions does the propeller undergo during this time? A) 5 B) 10 C) 50 D) 300 Use the following to answer question 17: A grindstone of radius 4.0 m is initially spinning with an angular speed of 8.0 rad/s. The angular speed is then increased to 10 rad/s over the next 4.0 seconds. Assume that the angular acceleration is constant. 17. Through how many revolutions does the grindstone turn during the 4.0-second interval? A) 0.64 B) 3.8 C) 4.0 D) 5.7 Page 5

6 18. What is the tangential speed of Nairobi, Kenya, a city near the equator? The earth makes one revolution every h and has an equatorial radius of 6380 km. A) m/s B) 116 m/s C) 148 m/s D) 232 m/s 19. A circular disk of radius m rotates with a constant angular speed of 5.0 rev/s. What is the acceleration of a point on the edge of the disk? A) 0.31 m/s 2 B) 1.6 m/s 2 C) 5.9 m/s 2 D) 2500 m/s A bicycle with wheels of radius 0.4 m travels on a level road at a speed of 8 m/s. What is the angular speed of the wheels? A) 10 rad/s B) 20 rad/s C) (π/10) rad/s D) (10 π) rad/s E) (20/π) rad/s Page 6

7 Answer Key 1. A 2. E 3. D 4. C 5. E 6. E 7. C 8. B 9. C 10. A 11. D 12. D 13. C 14. A 15. C 16. A 17. D 18. A 19. E 20. B Page 7

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