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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?

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  • $\begingroup$ Remember that work is force times the distance it was applied to the body. $\endgroup$
    – Triatticus
    Commented Nov 15, 2020 at 21:57

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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.

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Suppose you are on skating shoes near a rigid wall. You push the wall constantly till you leave the wall and move in backward direction. Now the question is there any work done on you by wall ? Surely not because wall was of course exerting force on your " HAND" and this part of body was continuously at rest all the time during which force was exerted. But during this time other parts of body were Surely moving ...here the fact is our body is not an example of single rigid body but combination of various movable parts. One thing is clear the wall did not exert any contact force on other parts of body. Wall exerted force on hand only which was at rest during the whole time of contact.

Ok the wall did not do any work on body then how come the body gained kinetic energy?? Of course at the cost of internal energy of the body .

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