On my honor, I have neither given nor received unauthorized aid on this examination.

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1 Instructor(s): Profs. D. Reitze, H. Chan PHYSICS DEPARTMENT PHY 2053 Exam 2 April 2, 2009 Name (print, last first): Signature: On my honor, I have neither given nor received unauthorized aid on this examination. YOUR TEST NUMBER IS THE 5-DIGIT NUMBER AT THE TOP OF EACH PAGE. (1) Code your test number on your answer sheet (use lines on the answer sheet for the 5-digit number). Code your name on your answer sheet. DARKEN CIRCLES COMPLETELY. Code your UFID number on your answer sheet. (2) Print your name on this sheet and sign it also. (3) Do all scratch work anywhere on this exam that you like. There are 2 blank sheets at the end if you need more space. Circle your answers on the test form. At the end of the test, this exam printout is to be turned in. No credit will be given without both answer sheet and printout. (4) Blacken the circle of your intended answer completely, using a #2 pencil or blue or black ink. Do not make any stray marks or some answers may be counted as incorrect. (5) The answers are rounded off. Choose the closest to exact. There is no penalty for guessing. (6) Hand in the answer sheet separately. Constants: G = N m 2 /kg 2 g = 9.80 m/s 2 1. A ping-pong ball with mass 50 g hits a wall at a speed of 2.0 m/s perpendicular to the surface. It bounces back with the same speed. Find the magnitude of the average force exerted on the ball by the wall if the ball is in contact with the wall for 0.20 s. (1) 1.0 N (2) 0.50 N (3) N (4) N (5) 0.10 N 2. A ping-pong ball with mass 50 g hits a wall at a speed of 4.0 m/s perpendicular to the surface. It bounces back with the same speed. Find the magnitude of the average force exerted on the ball by the wall if the ball is in contact with the wall for 0.20 s. (1) 2.0 N (2) 1.0 N (3) N (4) N (5) 0.40 N 3. A ping-pong ball with mass 50 g hits a wall at a speed of 7.0 m/s perpendicular to the surface. It bounces back with the same speed. Find the magnitude of the average force exerted on the ball by the wall if the ball is in contact with the wall for 0.20 s. (1) 3.5 N (2) 1.8 N (3) 0.14 N (4) N (5) 1.2 N 4. A 10-g bullet was traveling at 200 m/s when it hit a 2.0-kg ballistic pendulum. After the collision, the bullet remains stuck in the pendulum. Find the maximum height reached by the pendulum after the collision. (1) m (2) 0.11 m (3) 0.52 m (4) m (5) 0.37 m 5. A 10-g bullet was traveling at 250 m/s when it hit a 2.0-kg ballistic pendulum. After the collision, the bullet remains stuck in the pendulum. Find the maximum height reached by the pendulum after the collision. (1) m (2) 0.15 m (3) 0.75 m (4) m (5) 0.43 m 6. A 10-g bullet was traveling at 150 m/s when it hit a 2.0-kg ballistic pendulum. After the collision, the bullet remains stuck in the pendulum. Find the maximum height reached by the pendulum after the collision. (1) m (2) m (3) 0.24 m (4) m (5) 0.14 m

2 7. The masses of objects A and B are 2.0 kg and 4.0 kg respectively. They travel on a frictionless surface. Object A travels to the right at 5.0 m/s. Object B travels to the left at 7.0 m/s. The two objects collide in a perfectly inelastic collision. Find the change in kinetic energy for this system of two objects. (1) 96 J (2) 2.7 J (3) 192 J (4) 47 J (5) 21 J 8. The masses of objects A and B are 2.0 kg and 4.0 kg respectively. They travel on a frictionless surface. Object A travels to the right at 5.0 m/s. Object B travels to the left at 9.0 m/s. The two objects collide in a perfectly inelastic collision. Find the change in kinetic energy for this system of two objects. (1) 131 J (2) 11 J (3) 263 J (4) 64 J (5) 31 J 9. The masses of objects A and B are 2.0 kg and 4.0 kg respectively. They travel on a frictionless surface. Object A travels to the right at 5.0 m/s. Object B travels to the left at 3.0 m/s. The two objects collide in a perfectly inelastic collision. Find the change in kinetic energy for this system of two objects. (1) 43 J (2) 2.7 J (3) 85 J (4) 23 J (5) 12 J 10. A toy car and a toy truck undergo an elastic head-on collision. The mass of the car is 500 g. The mass of the truck is 900 g. Immediately before the collision, the car traveled at 11.0 mm/s eastwards and the truck traveled at 7.0 mm/s westwards. Find the speed of the truck immediately after the collision. (1) 5.9 mm/s (2) 12.1 mm/s (3) 0.57 mm/s (4) 3.1 mm/s (5) 9.4 mm/s 11. A toy car and a toy truck undergo an elastic head-on collision. The mass of the car is 500 g. The mass of the truck is 1100 g. Immediately before the collision, the car traveled at 11.0 mm/s eastwards and the truck traveled at 7.0 mm/s westwards. Find the speed of the truck immediately after the collision. (1) 4.3 mm/s (2) 13.8 mm/s (3) 1.4 mm/s (4) 2.2 mm/s (5) 9.9 mm/s 12. A toy car and a toy truck undergo an elastic head-on collision. The mass of the car is 500 g. The mass of the truck is 1300 g. Immediately before the collision, the car traveled at 11.0 mm/s eastwards and the truck traveled at 7.0 mm/s westwards. Find the speed of the truck immediately after the collision. (1) 3.0 mm/s (2) 15 mm/s (3) 2.0 mm/s (4) 1.2 mm/s (5) 7.6 mm/s 13. A pendulum consists of a heavy sphere attached to one end of a massless string. The other end of the string is fixed. The dashed line represents the vertical. Find the direction of the acceleration of the sphere at the highest point (indicated by arrow). (1) (2) (3) (4) (5) 14. A 0.70 kg object attached to the end of a string of length 0.60 m is swung in a circular path and in a vertical plane. The angular speed is maintained at 9.0 rad/s. What is the tension in the string when the object is at the top of the circular path? (1) 27 N (2) 41 N (3) 101 N (4) 88 N (5) 34 N

3 15. A 0.70 kg object attached to the end of a string of length 0.80 m is swung in a circular path and in a vertical plane. The angular speed is maintained at 9.0 rad/s. What is the tension in the string when the object is at the top of the circular path? (1) 39 N (2) 52 N (3) 78 N (4) 64 N (5) E. 45 N 16. A 0.70 kg object attached to the end of a string of length 0.60 m is swung in a circular path and in a vertical plane. The angular speed is maintained at 11.0 rad/s. What is the tension in the string when the object is at the top of the circular path? (1) 44 N (2) 58 N (3) 148 N (4) 134 N (5) 51 N 17. Two ice hockey pucks slide without friction on a flat surface of ice. Puck A (mass = 0.1 kg) traveled at 5.0 m/s eastward and puck B (mass = 0.2 kg) traveled at 7.0 m/s southward. They collide and remain stuck together. Find the speed after the collision. (1) 5.0 m/s (2) 4.7 m/s (3) 1.6 m/s (4) 8.6 m/s (5) 12 m/s 18. Two ice hockey pucks slide without friction on a flat surface of ice. Puck A (mass = 0.1 kg) traveled at 5.0 m/s eastward and puck B (mass = 0.3 kg) traveled at 7.0 m/s southward. They collide and remain stuck together. Find the speed after the collision. (1) 5.4 m/s (2) 1.3 m/s (3) 5.5 m/s (4) 8.6 m/s (5) 12 m/s 19. Two ice hockey pucks slide without friction on a flat surface of ice. Puck A (mass = 0.1 kg) traveled at 5.0 m/s eastward and puck B (mass = 0.05 kg) traveled at 7.0 m/s southward. They collide and remain stuck together. Find the speed after the collision. (1) 4.1 m/s (2) 3.3 m/s (3) 2.3 m/s (4) 8.6 m/s (5) 12 m/s 20. A merry-go-round with radius 5.0 meters starts from rest and undergoes constant angular acceleration of rad/s 2. After 4 complete revolutions, find the tangential speed at the edge. (1) 1.1 m/s (2) 0.22 m/s (3) 0.65 m/s (4) 1.5 m/s (5) 2.3 m/s 21. A merry-go-round with radius 5.0 meters starts from rest and undergoes constant angular acceleration of rad/s 2. After 3 complete revolutions, find the tangential speed at the edge. (1) 0.97 m/s (2) 0.19 m/s (3) 0.59 m/s (4) 1.36 m/s (5) 1.98 m/s 22. A merry-go-round with radius 6.0 meters starts from rest and undergoes constant angular acceleration of rad/s 2. After 4 complete revolutions, find the tangential speed at the edge. (1) 1.3 m/s (2) 0.22 m/s (3) 0.65 m/s (4) 1.7 m/s (5) 2.3 m/s 23. The gravitational force exerted on an astronaut on Earth s surface is 700 N. She was transported by a space shuttle to a space station at distance 2r E from the earth surface (where r E is the radius of the Earth). What is the gravitation force on the astronaut at the space station? (1) 77.8 N (2) 175 N (3) 350 N (4) 233 N (5) 1400 N

4 24. The gravitational force exerted on an astronaut on Earth s surface is 500 N. She was transported by a space shuttle to a space station at distance 2r E from the earth surface (where r E is the radius of the Earth). What is the gravitation force on the astronaut at the space station? (1) 55.6 N (2) 125 N (3) 250 N (4) 167 N (5) 1000 N 25. The gravitational force exerted on an astronaut on Earth s surface is 600 N. She was transported by a space shuttle to a space station at distance 2r E from the earth surface (where r E is the radius of the Earth). What is the gravitation force on the astronaut at the space station? (1) 66.7 N (2) 150 N (3) 300 N (4) 200 N (5) 1200 N 26. A 500 kg elevator starts from rest and moves upward for 4.00 s with a constant acceleration until it reaches a velocity of 2.50 m/s. What is the average power of the elevator during this period? (1) 6520 W (2) 390 W (3) 1280 W (4) 790 W (5) 3230 W 27. A 600 kg elevator starts from rest and moves upward for 3.00 s with a constant acceleration until it reaches a velocity of 2.50 m/s. What is the average power of the elevator during this period? (1) 8000 W (2) 900 W (3) 4510 W (4) 5540 W (5) 280 W 28. A 800 kg elevator starts from rest and moves upward for 4.00 s with a constant acceleration until it reaches a velocity of 1.50 m/s. What is the average power of the elevator during this period? (1) 6110 W (2) 230 W (3) 3020 W (4) 490 W (5) W 29. A 0.6 kg block is pressed against a spring (k = 300 N/m), compressing the spring by 4.3 cm. The block is released. It first travels on a frictionless track and then up a θ = 45 inclined plane. How high (vertically) does the block rise above the track? (1) 4.7 cm (2) 10.4 cm (3) 1.2 cm (4) 21.2 cm (5) not enough information given to solve the problem 30. A 0.3 kg block is pressed against a spring (k = 500 N/m), compressing the spring by 5.1 cm. The block is released. It first travels on a frictionless track and then up a θ = 45 inclined plane. How high (vertically) does the block rise above the track? (1) 22.1 cm (2) 14.9 cm (3) 4.2 cm (4) 1.7 cm (5) not enough information given to solve the problem 31. A 0.4 kg block is pressed against a spring (k = 100 N/m), compressing the spring by 10.8 cm. The block is released. It first travels on a frictionless track and then up a θ = 45 inclined plane. How high (vertically) does the block rise above the track? (1) 14.9 cm (2) 6.2 cm (3) 34.3 cm (4) 12.0 cm (5) not enough information given to solve the problem 32. Three rigid objects, a solid cylinder (I = (1/2)MR 2 ), a hoop (I = MR 2 ), and solid sphere (I = (2/5)MR 2 ) have the same mass, radius, and angular speed about their central axis. If the same braking torque is applied to each object, which object takes the longest to stop? (1) the hoop (2) the solid cylinder (3) the solid sphere (4) they all come to rest at the same time (5) not enough information given

5 33. A dumbbell is made of two masses (m = 10.0 kg) connected together by a rigid massless rod (length L = 0.40 m). The dumbbell rotates on an axis perpendicular to the page through the midpoint as shown. Forces F 1 = 100 N and F 2 = 40 N are exerted on the masses as shown. If the dumbbell starts from rest, what is the angular speed after 3 s? (1) 45 rad/s (2) 15 rad/s (3) 25 rad/s (4) 75 rad/s (5) 10 rad/s 34. A dumbbell is made of two masses (m = 8.0 kg) connected together by a rigid massless rod (length L = 0.60 m). The dumbbell rotates on an axis perpendicular to the page through the midpoint as shown. Forces F 1 = 70 N and F 2 = 60 N are exerted on the masses as shown. If the dumbbell starts from rest, what is the angular speed after 3 s? (1) 6.3 rad/s (2) 12.5 rad/s (3) 2.4 rad/s (4) 25.0 rad/s (5) 3.2 rad/s 35. A dumbbell is made of two masses (m = 3.0 kg) connected together by a rigid massless rod (length L = 1.40 m). The dumbbell rotates on an axis perpendicular to the page through the midpoint as shown. Forces F 1 = 50 N and F 2 = 20 N are exerted on the masses as shown. If the dumbbell starts from rest, what is the angular speed after 3 s? (1) 21.4 rad/s (2) 32.1 rad/s (3) 12.9 rad/s (4) 25.0 rad/s (5) 6.3 rad/s 36. An ice skater is initially spinning with her arms extended away from her body. Her angular velocity is 6.0 rad/s and her moment of inertia is 12 kg m 2. When she pulls her arms in, her moment of inertia decreases to 8.0 kg m 2. What is her final rotational kinetic energy? (1) 320 J (2) 180 J (3) 540 J (4) 420 J (5) 210 J 37. An ice skater is initially spinning with her arms extended away from her body. Her angular velocity is 5.0 rad/s and her moment of inertia is 15 kg m 2. When she pulls her arms in, her moment of inertia decreases to 9 kg m 2. What is her final rotational kinetic energy? (1) 310 J (2) 110 J (3) 45 J (4) 540 J (5) 220 J 38. An ice skater is initially spinning with her arms extended away from her body. Her angular velocity is 6.0 rad/s and her moment of inertia is 13 kg m 2. When she pulls in her arms, her moment of inertia decreases to 7 kg m 2. What is her final rotational kinetic energy? (1) 430 J (2) 210 J (3) 100 J (4) 55 J (5) 35 J 39. A uniform beam of mass m 1 = 20 kg and length L = 2.0 m extends out from the wall as shown. A mass m 2 = 10 kg hangs from its end. The beam is supported by a cable that makes an angle of θ = 45 with the beam. The system is in equilibrium. What is the tension in the cable? (1) 280 N (2) 140 N (3) 370 N (4) 85 N (5) 780 N

6 40. A uniform 15 kg beam of length 2 m extends out from the wall as shown. A 20 kg mass hangs from its end. The beam is supported by a cable that makes an angle of θ = 45 with the beam. The system is in equilibrium. What is the tension in the cable? (1) 380 N (2) 230 N (3) 95 N (4) 820 N (5) 780 N 41. A uniform 25 kg beam of length 2 m extends out from the wall as shown. A 30 kg mass hangs from its end. The beam is supported by a cable that makes an angle of θ = 45 with the beam. The system is in equilibrium. What is the tension in the cable? (1) 590 N (2) 430 N (3) 75 N (4) 940 N (5) 320 N 42. An isolated object with a rotational kinetic energy of 120 J and a moment of inertia equal to 120 kg m 2. What is its angular momentum? (1) 170 kg m 2 / s (2) 95 kg m 2 / s (3) 250 kg m 2 / s (4) 410 kg m 2 / s (5) 63 kg m 2 / s 43. An isolated object with a rotational kinetic energy of 140 J and a moment of inertia equal to 80 kg m 2. What is its angular momentum? (1) 150 kg m 2 / s (2) 48 kg m 2 / s (3) 320 kg m 2 / s (4) 270 kg m 2 / s (5) 76 kg m 2 / s 44. An isolated object with a rotational kinetic energy of 220 J and a moment of inertia equal to 20 kg m 2. What is its angular momentum? (1) 94 kg m 2 / s (2) 140 kg m 2 / s (3) 34 kg m 2 / s (4) 320 kg m 2 / s (5) 250 kg m 2 / s 45. An ice skater is spinning with her hands extended outward from her body. When she pulls her arms in, she spins with a different angular speed. Which quantity (quantities) below is (are) conserved? (1) Angular momentum (2) Rotational kinetic energy (3) Angular momentum and rotational kinetic energy (4) Neither angular momentum nor rotational kinetic energy are conserved (5) Not enough information is given to answer this question. 46. A solid cylinder (moment of inertia I = (1/2)MR 2 ) starts from rest at the top of an inclined plane and rolls down without slipping. If the inclined plane is 1.0 m high, what is the speed of the cylinder when it reaches the bottom of the inclined plane? (1) 3.6 m/s (2) 4.4 m/s (3) 2.1 m/s (4) 9.8 m/s (5) 7.6 m/s

7 47. A solid cylinder (moment of inertia I = (1/2)MR 2 ) starts from rest at the top of an inclined plane and rolls down without slipping. If the inclined plane is 1.5 m high, what is the speed of the cylinder when it reaches the bottom of the inclined plane? (1) 4.4 m/s (2) 5.4 m/s (3) 8.8 m/s (4) 2.8 m/s (5) 2.1 m/s 48. A solid cylinder (moment of inertia I = (1/2)MR 2 ) starts from rest at the top of an inclined plane and rolls down without slipping. If the inclined plane is 1.2 m high, what is the speed of the cylinder when it reaches the bottom of the inclined plane? (1) 4.0 m/s (2) 4.8 m/s (3) 1.3 m/s (4) 7.9 m/s (5) 2.0 m/s 49. In the figure, m 1 = 20 kg, m 2 = 35 kg, and the pulley is a solid cylinder with mass M = 25.0 kg, radius R = 0.30 m and moment of inertia I = (1/2)MR 2. The masses begin at rest, and then start to move, with the heavier mass accelerating downward and light mass accelerating upward. The rope applies a torque to the pulley, rotating the pulley about a frictionless axle. Find the acceleration. (1) 2.2 m/s 2 (2) 9.8 m/s 2 (3) 2.8 m/s 2 (4) 3.6 m/s 2 (5) 1.5 m/s In the figure below, m 1 = 15 kg, m 2 = 55 kg, and the pulley is a solid cylinder with mass M = 10.0 kg, radius R = 0.30 m and moment of inertia I = (1/2)MR 2. The masses begin at rest, and then start to move, with the heavier mass accelerating downward and light mass accelerating upward. The rope applies a torque to the pulley, rotating the pulley about a frictionless axle. Find the acceleration. (1) 5.2 m/s 2 (2) 9.8 m/s 2 (3) 3.1 m/s 2 (4) 7.2 m/s 2 (5) 1.2 m/s In the figure below, m 1 = 10 kg, m 2 = 15 kg, and the pulley is a solid cylinder with mass M = 20.0 kg, radius R = 0.30 m and moment of inertia I = (1/2)MR 2. The masses begin at rest, and then start to move, with the heavier mass accelerating downward and light mass accelerating upward. The rope applies a torque to the pulley, rotating the pulley about a frictionless axle. Find the acceleration. (1) 1.4 m/s 2 (2) 9.8 m/s 2 (3) 2.8 m/s 2 (4) 5.1 m/s 2 (5) 2.1 m/s 2

8 52. In order to receive credit for this problem, you must correctly code ( bubble in ) your UFID and your 5-digit test number (located at the top left and right hand corners of this test) onto your scan sheet and also select the correct response below. Please check now that you have correctly coded your exam number on the scan sheet. (1) I have correctly bubbled my UFID number and 5-digit test code. (2) I won t do this because I don t need the credit. (3) I don t know what my UFID number is. (4) If I don t pick the answer that was stated in class, will I still get credit? (5) I don t understand what is being asked. FOLLOWING GROUPS OF QUESTIONS WILL BE SELECTED AS ONE GROUP FROM EACH TYPE TYPE 1 Q# S 1 Q# S 2 Q# S 3 TYPE 2 Q# S 4 Q# S 5 Q# S 6 TYPE 3 Q# S 7 Q# S 8 Q# S 9 TYPE 4 Q# S 10 Q# S 11 Q# S 12 TYPE 5 Q# S 14 Q# S 15 Q# S 16 TYPE 6 Q# S 17 Q# S 18 Q# S 19 TYPE 7 Q# S 20 Q# S 21 Q# S 22 TYPE 8 Q# S 23 Q# S 24 Q# S 25 TYPE 9 Q# S 26 Q# S 27 Q# S 28 TYPE 10 Q# S 29 Q# S 30 Q# S 31 TYPE 11 Q# S 33 Q# S 34 Q# S 35 TYPE 12 Q# S 36 Q# S 37 Q# S 38 TYPE 13 Q# S 39 Q# S 40 Q# S 41 TYPE 14 Q# S 42 Q# S 43 Q# S 44 TYPE 15

9 Q# S 46 Q# S 47 Q# S 48 TYPE 16 Q# S 49 Q# S 50 Q# S 51