## Mastering Physics Solutions: Energy Required to Lift a Heavy Box

Energy Required to Lift a Heavy Box

Part A = F = mg/2
Part B = Wd / Wp = 1.00

Solution Below:

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. There is no one around to help, so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. You pull up on the rope to lift the box.

Use g for the magnitude of the acceleration due to gravity and neglect friction forces.

Part A

What is the magnitude F of the upward force you must apply to the rope to start raising the box with constant velocity?

F = mg/2

Part B

Consider lifting a box of mass m to a height h using two different methods: lifting the box directly or lifting the box using a pulley (as in the previous part).

What is Wd / Wp, the ratio of the work done lifting the box directly to the work done lifting the box with a pulley?
Express the ratio numerically.

Since the box is going to the same height, it will have the same potential energy. This means an equal amount of work must be done, no matter whether you lift it by hand or with the pulley.

Wd / Wp = 1.00

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