Question

Find the magnitude f of the force that the wooden block exerts on the nail, assuming that this force is independent of the depth of penetration of the nail into the wood. you may also assume that v0≫2gl−−−√, so that the change in the hammer's gravitational potential energy, as it drives the nail into the block, is insignificant. express the magnitude of the force

Answer 1

The answer would be (M * v_0^2) / (2L) 

The reason behind this is explained by the work theorem:

Kf – Ki = -.5Mv_0^2 
W = -FL 
Kf – Ki = W consulting to work energy theorem. This specifies that the alteration in the kinetic energy of a particle is equivalent to the whole work done on that particle through all the forces that act on it. 
To make things easier to find that F = (M*v_0^2)/2L