A trapeze artist, starting from rest, swings downward on the bar, lets go at the bottom of the swing, and falls freely to the net. An assistant, standing on the same platform as the trapeze artist, jumps from rest straight downward. Friction and air resistance are negligible. On which person, if either, does gravity do the greatest amount of work?

Question

09-06-2024
Physics

High School

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A trapeze artist, starting from rest, swings downward on the bar, lets go at the bottom of the swing, and falls freely to the net. An assistant, standing on the same platform as the trapeze artist, jumps from rest straight downward. Friction and air resistance are negligible. On which person, if either, does gravity do the greatest amount of work?

Answer :

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AkhilSachdeva AkhilSachdeva · Answer 1 · 2024-11-11T05:25:02-05:00

Final answer:

The work done by gravity on both the trapeze artist and the assistant is the same since both fall the same vertical distance and gravity is the only significant force acting on them.

Explanation:

The student's question is about which person, a trapeze artist who swings on a bar and then drops, or an assistant who jumps straight down from the same height, has the most work done on them by gravity.

In both cases, as long as the two individuals start from the same height and fall to the same level without any external forces acting on them other than gravity, the work done by gravity will be the same.

It is because the work done by gravity is the product of the force of gravity, the displacement in the direction of the force, and the cosine of the angle between the force and displacement, which for vertical fall is zero degrees and thus the cosine is one.

Both fall the same vertical distance, so the work done by gravity, which is equal to force times distance (W = Fd), will be the same for both individuals.