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Why does this question give an answer of zero?

Physics Asked by HateThisPlatoform on May 13, 2021

A boy jumps from rest straight upward from a flat, stationary concrete surface. The boy, of mass M, leaves the concrete surface with speed v and his center of mass rises a distance d to the highest point of the motion. How much work did the normal force of contact (N) between the boy’s feet and the concrete do on the boy?

So here, essentially what happens is the boy pushes on the floor and the normal force exerted back onto him by the floor propels him by a distance d. Hence that means the work done by normal force should be Mgd – a normal force was applied on him and that caused him to move by a distance d- however the answer that is given is 0. I dont understand this result as there is a clear force and displacement here. Or am I misunderstanding the question somehow?

Edit:- "In the jumping example, the floor is not doing work. After all, it is just a floor, it has nowhere to get the energy from to do work on you. (The floor of the elevator gets it from the motor running the elevator.) When you jump, the force from the floor on your shoes increases, but there is no displacement between the floor and your shoes until your shoes leave the floor, and at that point there’s no force any more. Your torso is moving upwards while you jump, but there’s no force from the floor on your torso, so the floor isn’t doing work. All the energy of a jump comes from internal energy, not external work." But even then my doubt persists- it was the normal force that allowed this upward acceleration to take place right? So why does it not do any work?

One Answer

The floor provides a constraint allowing your body to jump. When you jump, you increase the force on the ground, and the equal but opposite reactive normal force on you is increased above that of gravity thereby pushing you off the ground. However this normal force does no work. You can search this site for questions on jumping for the details.

For a force to do work it must act through a distance. The normal force does not act on you as you leave the ground: force, yes; work, no.

It is similar to rolling friction; rolling friction provides a force and torque to counter motion thereby causing the object to rotate, but rolling friction does no work. For rolling friction there is no relative motion between the instantaneous point of contract and the ground. As another example, consider a fluid flowing in a pipe; with the no-slip condition at the pipe walls, the pipe does no work on the fluid. But the frictional force at the pipe walls does cause velocity gradients in the flowing fluid thereby causing energy (pressure) loss along the flow path.

Correct answer by John Darby on May 13, 2021

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