Physics 201 Exam 3 (Monday, November 5) Fall 2012 (Saslow) Name (printed) Lab Section(+2 pts) Name (signed as on ID) Multiple choice Section. Circle the correct answer. No work need be shown and no partial credit. Check whiteboard for additional information. Come to front to ask questions. 1. (6 pts) A support bar of 0.5 m length and cross-sectional area 4 cm 2 has a Hooke s Law constant of 6.0 10 7 N/m. The Hooke s Law constant for a support bar made of the same material, but of twice the length and three times the cross-sectional area is (a) 36.0 10 7 N/m (b) 9.0 10 7 N/m (c) 4.0 10 7 N/m (d) 1.0 10 7 N/m 2. (6 pts) A man stands with weights in his hand, pulled to his chest, on a platform that rotates about a vertical axis. Initially he and the platform rotate with angular velocity 0.600 rad/s. The initial moment of inertia of the system (man + platform + weights) is 2.00 kg-m 2. When he extends his arms the angular velocity of the system becomes 0.400 rad/s. The new moment of inertia is (a) 1.33 kg-m 2 (b) 2.00 kg-m 2 (c) 3.00 kg-m 2 (d) 4.00 kg-m 2 3. (6 pts). A block of mass 0.4 kg is attached to one end of a horizontal spring and moves on a horizontal frictionless surface. The other end of the spring is attached to a wall. When the amplitude of the motion is 0.060 m, the block undergoes 2 complete oscillations each second. The frequency in cycles/s (Hz) if the amplitude is changed to 0.180 m is (a) 0.5 s 1 (b) 1.5 s 1 (c) 2.0 s 1 (d) 3.0 s 1 1
Work-out section; show all your work. If earned, partial credit will be given: include figures, definitions, signs, and units. 4. (12 pts) A solid disk of mass 0.016 kg and radius 0.200 m is initially at rest. (I = 1 2 MR2.) It then starts to rotate about an axle at its center with a constant angular acceleration of 0.800 rad/s 2. a) How long does it take to turn through an angle of 2.5 radians? b) What is the velocity of a point halfway along a spoke of the wheel at this time? 5. (14 pts) A wheel of radius 0.4 m is mounted on a frictionless axle that passes through the center the wheel. A light rope is wrapped around the wheel and a 2 N block is suspended from the free end of the rope. When the system is released from rest, the block has a downward acceleration of magnitude 3.00 m/s 2. a) What is the angular acceleration of the wheel? b) What is the moment of inertia of the wheel, about an axis at its center? 2
6. (18 pts) A wall extends leftward from x = 5 cm. The left end of a relaxed spring of force constant 200 N/m is attached to the wall. The spring s right end is at x = 0, where it is attached to a block of mass 0.250 kg that can slide on a horizontal frictionless surface. At x = 0.2 m its speed is +4.00 m/s. a) What is the amplitude of the motion (largest positive or negative extension of the spring)? b) At what position does the block reach its maximum speed, and what is that maximum speed? c) How long does it take for the block to reach x = 0.2 m? 3
7. (20 pts) A thin-walled hollow cylinder with mass M = 2.00 kg and radius R = 0.0500 m has moment of inertia I = MR 2 for rotation about an axis through its center. The sphere rolls without slipping on a ramp that is inclined at 30 above the horizontal. It starts at the top of the ramp, which is 2 m long. a) What is the kinetic energy (translational plus rotational) of the sphere when it reaches the bottom of the ramp? b) What is the sphere s linear velocity when it ireaches the bottom of the ramp? c) What is the magnitude of the friction force that the ramp exerts on the sphere while the sphere is rolling down the ramp? d) If there were no friction, what would be the sphere s linear velocity when it reaches the bottom of the ramp? 4
8. (18 pts) A uniform bar (I = 1 3 ML2 ) has mass of 2.5 kg and length 4.00 m. The lower end of the bar is attached to the wall by a frictionless hinge. The bar is held stationary at an angle of 30 above the horizontal by a cable that runs from the upper end of the bar to the wall. The cable makes an angle of 37 with the bar. a) For an axis at the hinge, what is the torque due the weight of the bar? b) What is the tension in the cable? c) If the cable breaks, what is the initial angular acceleration of the bar right after the cable breaks? Extra Credit (6 pts): What are the force components acting on the bar, from the hinge? 5