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# Energy and work

12. A rock is thrown straight up from the surface of the Earth. Which one of the following statements describes the energy transformation of the rock as it rises? Neglect air resistance.
13. A helicopter is cruising at a speed of 25.0 m/s at an altitude of 185 m. What is the total mechanical energy of the helicopter?
14. A pebble rolls off the roof of Science Hall and falls vertically. Just before it reaches the ground, the pebble's speed is 17 m/s. Neglect air resistance and determine the height of Science Hall.
15. A skier leaves the top a slope with an initial speed of 5.0 m/s. Her speed at the bottom of the slope is 13 m/s. What is the height of the slope?
16. A roller coaster starts from rest at the top of an 18-m hill as shown. The car travels to the bottom of the hill and continues up the next hill that is 10.0 m high. How fast is the car moving at the top of the 10.0-m hill if friction is ignored?
17. The initial velocity of a 4.0-kg box is 11 m/s, due west. After the box slides 4.0 m horizontally, its speed is 1.5 m/s. Determine the magnitude and the direction of the non-conservative force acting on the box as it slides.
18. An automobile approaches a barrier at a speed of 20 m/s along a level road. The driver locks the brakes at a distance of 50 m before the barrier. What minimum coefficient of kinetic friction is required to stop the automobile before it hits the barrier?
19. What power is needed to lift a 49-kg person a vertical distance of 5.0 m in 20.0 s?
20. How much power is needed to lift a 75-kg student vertically upward at a constant speed of 0.33 m/s.
21. The amount on energy needed to power a 0.10-kW bulb for one minute would be just sufficient to lift a 1.0-kg object through a vertical distance of
22. The force component acting on an object along the displacement varies with the displacement s as shown in the graph. Determine the work done on the object as it travels from s = 0.0 to 12 m.
23. A physics student shoves a 0.50-kg block from the bottom of a frictionless 30.0 degrees inclined plane. The student performs 4.0 J of work and the block slides a distance s along the incline before it stops. Determine the value of s.

#### Solution Preview

12. The potential energy increases as the rock goes up. So the kinetic energy decreases to keep the constant total energy.

13.

14. At the top of the roof, the total energy is only the potential energy. Just before it reaches the ground, the total energy is only the kinetic energy.
Using conservation of energy