Question: Jimmy has two options for moving a piano up to the second floor of a hotel, which is 10 m above his current position. He can push the piano up 50 m ramp or lift the piano up with a rope wrapped around a pulley. Which option will require him to exert a greater average force? Neglecting friction, which option will require more work?

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Physics

Daffodil

1 March, 14:03

Question: Jimmy has two options for moving a piano up to the second floor of a hotel, which is 10 m above his current position. He can push the piano up 50 m ramp or lift the piano up with a rope wrapped around a pulley. Which option will require him to exert a greater average force? Neglecting friction, which option will require more work?

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Joel Schaefer · Answer 1

Lifting straight up, even with a rope and pulley, always takes more force than going up a slanted ramp to the same height.

But if you use the ramp, then you have to exert the force over a greater distance (pull more rope to lift to the same height).

Astonishingly, the product of (force) x (distance) is the same number either way. So without friction, the total amount of work required is the SAME whichever way the piano is lifted.