The head of a hammer (m = 1 kg) moving at 4m/s strikes a nail and bounces back w

Question

The head of a hammer (m = 1 kg) moving at 4m/s strikes a nail and bounces back with the same speed after an elastic collision lasting 0.075 s. What is the magnitude of the average force the hammer exerts on the nail?

This is how I solved the problem:

At the time when I working on this, I did realize that zero as an answer for this kind of problem seemed wrong but I couldn't figure out how else to do it. I was thinking 4-4=0 and 0 divided by anything would be 0. I think the correct answer is supposed to be 106.6-107 N, but I don't know how to ge to that.

Explanation / Answer

  the change in momentum, P = mvf-(-mvi)       p = mvf+mvi            = 2mv            = 2*1*4            = 8.0 kg-m/s since it bounces back same speed the average force ,    F = P/t          = 8/0.075          = 106.66 N

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