Work Energy and Power

Name: 2. WORK, ENERGY and POWER (10%)  42 Multiple Choice Questions Provincial) (~3 on  14 Long Answer Problems (1) Answers: Multiple Choice 1. c 2. b 3. b 4. d 5. b 6. d 7. a 8. b 9. b 10.b 11.b 12.c 13.a 14.c 15.b 16.b 17.d 18.d 19.c 20.d 21.c 22.c 23.b 24.a 25.d 26.d 27.c 28.b 29.d 30.b 31.c 32.b 33.d 34.d 35.b 36.a 37.a 38.a 39.d 40.d 41.b 42.a Long Answers 1. 2. 3. 4. 20.7 m/s 3.02 m/s 38.2° N of E 4.26 m/s 7.91° S of E a) i)108 m/s ii) 3.00 x 104 N.s 5. a) 0.9 J b) 7.75 m/s c) 20% 6. a) 1.33 m b) the same height 7. a) 51.6 m/s 8. a) 26.4 m/s b) equal to 9. a) 720 J b) 581 J c) 81% 10. 56.3 m/s 41.8° N of E 11. 2.17 m/s 43.7° 12.a) 38.3 m 13.a) 1.85 x 104 J 14. 24.1 J Multiple Choice: 1. The graph below shows how the force acting on an object varies with distance. What is the work done in moving the object from 20 m to 60 m? A. 50 J B. 100 J C. 400 J D. 900 J A. kg m/s2 B. N s 2. Which of the following are equivalent units for change in momentum? C. kg s/m D. N/s 3. A 1.2 kg ball moving due east at 40 m/s strikes a stationary 6.0 kg object. The 1.2 kg ball rebounds to the west at 25 m/s. What is the speed of the 6.0 kg object after the collision? A. 3.0 m/s B. 13 m/s C. 15 m/s D. 65 m/s 4. Are momentum and impulse scalar or vector quantities? 5. As a skier descends a slope, her kinetic energy increases from 600 J to 3 200 J while her gravitational potential energy decreases by 5 900 J. How much heat energy is created due to friction? A. 2 100 J B. 3 300 J C. 8 500 J D. 9 700 J 6. A 60 kg girl and her 45 kg brother are at rest at the centre of a frozen pond. He pushes her so that she slides away at 2.4 m/s. How much total work is done? (Ignore friction.) A. 58 J B. 170 J C. 350 J D. 400 J 7. Work is measured in which units? A. J B. N C. J/s D. N s 8. What is the minimum power developed by a 75 kg person who climbs a set of stairs 4.5 m high in 5.0 s? A. 6.8 101 W B. 6.6 102 W C. 1.7 103 W D. 3. 3 103 W 2 9. A 3.5 kg projectile was launched vertically at 75 m/s. The projectile reached a maximum height of 180 m. How much energy was lost to heat while the projectile was rising? A. 0 J B. 3.7 103 J C. 6.2 103 J D. 9.8 103 J 10. A puck sliding on a frictionless table undergoes a change in momentum due to a constant force. Which of the following expressions could be used to determine the change in momentum? A. F d B. F t C. F v D. F ( v / t ) 11. A basketball is thrown into the basket, as shown in the diagram below. The ball leaves the player’s hand at t = 0 s and reaches the basket at t = 3 s. Which of the following graphs best represents the ball’s kinetic energy Ek as a function of time? 12. What is the minimum power output of a small electric motor that lifts a 0.050 kg mass through 2.0 m in 30 s? A. 0.0017 W B. 0.017 W C. 0.033 W D. 15 W 13. An object travelling due north experiences an impulse due east. The direction of the change in momentum of this object is A. east. B. west. C. north. D. northeast. 3 14. A 1.5 kg ball falling vertically strikes the floor with a speed of 12 m/s and rebounds upward with a speed of 8.0 m/s. What is the magnitude and direction of the impulse given to the ball? 15. A net force of 20 N acts for 1.5 s on a 4.0 kg object initially at rest. What is the final kinetic energy of the object? A. 30 J B. 110 J C. 230 J D. 440 J 16. A 900 kg car travelling at 12 m/s due east collides with a 600 kg car travelling at 24 m/s due north. As a result of the collision, the two cars lock together and move in what final direction? A. 45N of E B. 53N of E C. 63N of E D. 69N of E 17. Which of the following is a correct unit for impulse? A. N B. Nm C. N/s D. Ns 18. A 0.15 kg ball travelling at 25 m/s strikes a wall and bounces back in the opposite direction at 15 m/s. The ball is in contact with the wall for 0.030 seconds. What average force does the wall exert on the ball? A. 25 N B. 50 N C. 1.0 102 N D. 2.0 102 N 19. The graph below shows the relationship between the force applied and the distance moved for a 3.5 kg object on a frictionless horizontal surface. If the object was initially at rest, what is its kinetic energy after travelling 8.0 m? A. 2.0 J B. 32 J C. 64 J D. 130 J 20. Impulse is defined as A. total energy. C. a change in energy. B. total momentum. D. a change in momentum. 21. Calculate the minimum power of a cyclist who can increase his kinetic energy from 480 J to 2 430 J by travelling 26 m in 4.0 s. A. 75 W B. 3.6 102 W C. 4.9 102 W D. 7.3 102 W 4 22. A small explosive device sliding to the right breaks into two pieces. The momentum of fragment 1 after the explosion is 23 kg m/s. What is the momentum of fragment 2 after the explosion? A. 22 kg m/s B. 23 kg m/s C. 30 kg m/s D. 32 kg m/s 23. Which set of conditions is true in all inelastic collisions? 24. Two carts collide while travelling on a smooth surface. It is found that the sum of the kinetic energies of the carts after the collision is the same as before the collision. This collision must be A. elastic. B. inelastic. C. between carts of identical mass. D. between carts that stick together. 25. A 0.15 kg ball moving at 40 m/s is struck by a bat. The bat reverses the ball’s direction and gives it a speed of 50 m/s. What average force does the bat apply to the ball if they are in contact for 6.0 103 s? A. 14 N B. 2.5 102 N C. 1.3 103 N D. 2.3 103 N 26. In order to stop two sliding objects, the greater impulse must be given to the one having the greater A. mass. B. speed. C. velocity. D. momentum. 27. A cyclist increases his kinetic energy from 1100 J to 5 200 J in 12 s. His power output during this time is A. 92 W B. 260 W C. 340 W D. 430 W 28. Which of the following best represents the momentum of a small car travelling at a city speed limit? A. 1 000 kgm/s B. 10 000 kgm/s C. 100 000 kgm/s D. 1 000 000 kgm/s 5 29. A 0.080 kg tennis ball travelling east at 15 m/s is struck by a tennis racquet, giving it a velocity of 25 m/s, west. What are the magnitude and direction of the impulse given to the ball? 30. Which of the following is a definition of power? A. Power is the rate of change of flux. B. Power is the rate of change of energy. C. Power is the rate of change of momentum. D. Power is the rate of change of displacement. 31. Two blocks are initially held together on a frictionless surface as shown in the diagram to the right. When the string is cut, the blocks fly apart as shown. What work was done on the blocks by the spring? A. 0 J B. 0.29 J C. 0.43 J D. 0.58 J 32. A ball is thrown at 15 m/s towards various barriers. In which case does the ball experience the greatest impulse? A. The ball hits a wall and rebounds at 2.0 m/s. B. The ball hits a wall and rebounds at 7.0 m/s. C. The ball hits a wall, sticks to it and stops moving. D. The ball breaks a window and continues moving at 10 m/s in the same direction. 33. Which of the following describes kinetic energy and momentum before and after a perfectly elastic collision? 34. The 2.0 kg head of an axe strikes a tree horizontally at 40 m/s. The blade penetrates 0.040 m into the tree. What is the average force exerted by the blade on this tree? A. 2.0 101 N B. 2.0 103 N C. 2.0 104 N D. 4.0 104 N 6 35. A 0.30 kg ball rolls off a horizontal surface as shown in the diagram. What is the magnitude of the impulse given to the ball by gravity during the 0.90 s it takes the ball to fall to the ground? A. 1.5 Ns B. 2.6 Ns C. 3.0 Ns D. 4.1 Ns 36. A uniform ladder leans against a frictionless wall as shown. Which of the following diagrams best shows the forces acting on the ladder? 37. Which expression is equal to the net force on an object? 38. The diagram shows a collision between a 4.0 kg toy car and a stationary 8.0 kg toy truck. After the collision, the car bounces back at 1.0 m/s while the truck goes forward at 2.0 m/s. Based on these values, are momentum and kinetic energy conserved? 7 39. Impulse is measured in which units? (Yes, this is the same as #17) A. J B. N C. Nm D. Ns 40. How much work must be done to stop a 1 800 kg vehicle travelling at 30 m/s? A. 1.8 104 J B. 5.4 104 J C. 5.3 105 J D. 8.1 105 J 41. A 0.15 kg ball rolls off a bench at 2.4 m/s as shown in the diagram below. What is the vertical component of the ball’s momentum when it strikes the floor 0.85 m below? A. 0.36 kg m/s B. 0.61 kg m/s C. 0.71 kg m/s D. 1.2 kg m/s 42. A 2.0 kg puck travelling due east at 2.5 m/s collides with a 1.0 kg puck travelling due south at 3.0m/s. They stick together on impact. What is the resultant direction of the combined pucks? A. 31S of E B. 40S of E C. 50S of E D. 59S of E 8 Written Problems: 1. A 250 kg roller coaster passes point A at 12.0 m/s. What is the speed of the roller coaster at point B at the bottom of the hill if 8 500 J of energy is transformed to heat during the journey? (7 marks) 2. Two air pucks approach each other, stick together and then travel due east as shown below. Find the initial velocity (magnitude and direction) of puck A. (7 marks) 3. A 2.0 kg bowling ball travelling 5.0 m/s collides with a stationary 0.30 kg bowling pin. After the collision, the pin moves at a speed of 6.5 m/s in the direction shown in the diagram. What is the velocity (magnitude and direction) of the bowling ball after the collision? (7 marks) 9 4. A 4 000 kg space vehicle consists of a 2 500 kg main capsule and a 1 500 kg probe. The space vehicle is travelling at 120 m/s when an explosion occurs between the capsule and the probe. As a result, the probe moves forward at 140 m/s, as shown in the diagram below. a) (i) What is the speed of the main capsule after the explosion? (3 marks) (ii) What is the magnitude of the impulse given to the probe? (2 marks) b) Define impulse and briefly explain why the impulse on the probe is equal in magnitude to the impulse on the main capsule. (4 marks) 5. A 0. 030 kg toy car is pushed back against a spring-based launcher as shown in Diagram 1. Diagram 2 shows a graph of the force required to compress the spring 0. 090 m. a) What is the work done in compressing the spring? (3 marks) b) Assuming no losses due to heat, what maximum speed is reached by the toy car when it is released? (3 marks) c) If in fact the maximum kinetic energy of the car is 0.18 J, what is the efficiency of the spring-based launcher? (1 mark) 10 6. A 3.0 kg car A travelling 8.5 m/s on a frictionless track collides and sticks on to a stationary 2.0 kg car B. a) The combined cars will reach what height h? (5 marks) b) The steepness of the slope is decreased as shown below. With this decreased slope, the combined cars will reach (check one response) (1 mark) c) Using principles of physics, explain your answer to b). (3 marks) 7. A 24 kg rocket car is initially at rest on a frictionless horizontal surface. The engine is ignited and the graph below shows thrust force, F, versus distance travelled, d, for the rocket car. Find the rocket car’s speed after it has travelled 200 m. (7 marks) 8. A 150 kg roller coaster car passes the crest of a hill at 15.0 m/s. a) What is the speed of the car at point B at the bottom of the hill? (Neglect friction.)(5 marks) b) i) If the mass of the roller coaster car is increased by adding a passenger, how will the speed at B now compare to your answer for part a)? (Circle one.) (1 mark) A. equal to B. less than C. greater than ii) Explain your answer using principles of physics. (3 marks) 9. Starting from rest, a farmer pushed a cart 12 m. The graph shows the force F which he applied, plotted against the distance d. 11 a) How much work did the farmer do moving the cart 12 m? (3 marks) b) After the farmer had pushed the 240 kg cart 12 m, it was moving with a velocity of 2.2 m/s. What was the cart’s kinetic energy? (2 marks) c) What was the efficiency of this process? (2 marks) 10. A 7.0 kg object moving at 12 m/s to the east explodes into two unequal fragments. The larger 5.0 kg fragment moves at 15 m/s south. What is the velocity (speed and direction) of the smaller 2.0 kg fragment? (7 marks) 11. Two steel pucks collide as shown in the diagram below. Determine the speed and direction (angle ) of the 0.30 kg puck after the collision. (7 marks) 12 12. As a 62 kg skier descends from A to B her velocity increases from 8.5 m/s to 23.3 m/s. Friction between A and B generates 8 700 J of heat energy. Through what vertical height, h, did the skier descend? (7 marks) 13. A 250 kg roller coaster car travels past points A and B with speeds shown in the diagram below. How much heat energy is produced between these points? (7 marks) 14. A 5.20 kg block sliding at 9.40 m/s across a horizontal frictionless surface collides head on with a stationary 8.60 kg block. The 5.20 kg block rebounds at 1.80 m/s. How much kinetic energy is lost during this collision? (7 marks) 13