| 19. |  The graph shows the magnitude of the force exerted by a given spring as a function of the distance x the spring is stretched, measured in centimeters. How much work is needed to stretch the spring a distance of 5.0 cm from its equilibrium position? |
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| 21. | 
The diagram shows a 0.12-kg square block at four positions along a track. The track is frictionless between points A and B. Elsewhere, the coefficient of static friction on the block is 0.26. Initially, the block is held in place against a spring by a horizontal external force of magnitude 35 N. Then the external force is removed, and the block is projected forward with speed V1=1.2m/s. The block descends a ramp and has speed V2=1.4m/s at the bottom. At point C, its speed is V3=1.4m/s. The block stops at point D. What is the initial compression of the spring? |
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| 36. |  The diagram shows a 0.74-kg square block at four positions along a track. The track is frictionless between points A and B. Elsewhere, the coefficient of static friction on the block is 0.36.
Initially, the block is held in place against a spring by a horizontal external force of magnitude 29 N. Then the external force is removed, and the block is projected forward with speed V1=1.2m/s. The block descends a ramp and has speed V2=1.9m/s at the bottom. At point C, its speed is V3=1.4m/s. The block stops at point D. What is the height h of the ramp? |
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37.  |
A steel wire of length L connects a hook on the ceiling to a bowling ball, With the steel wire kept taut, the bowling ball is lifted to a height h above the floor, and then released. The bowling ball swings back and forth in the motion of a pendulum. After the bowling ball is released, what is the maximum height above the floor that it reaches? Assume that friction does not affect its motion. |
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| 39. | A total of 55 J of work is needed to stretch a spring from x = 0.40m to x = 2.7m , in which x is displacement from equilibrium. What is the value of the spring constant? | ||||||||
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| 40. | A mass of 9.22 kg gains 506 J of gravitational potential energy. To what height was it lifted? | ||||||||
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