Question

Solve the foregoing problem for the case of the pan having a mass M.

Answer 1

Unlike the previous (4.40) problem the kinetic energy of body m decreases due to the perfectly inelastic collision with the pan. obviously the body m comes to strike the pan with velocity v0= √(2gh).if v be the  common velocity of the '' body m+ pan'' system due to the collision then from the conservation of linear momentum



At the moment the body m strikes the pan, the spring is compressed due to the weight of the pan by the amount Mg/k. if l be the further compression of the spring due to the velocity acquired by the ''pan - body m'' system, then from the conservation of mechanical energy of the said system in the field generated by the joint action of both the gravity and spring forces

 









If the oscillating ''pan + body m'' system were at rest it correspond to their equilibrium position i.e. the spring were compressed by ((M + m)g)/k therefore the amplitude of oscillation



The mechanical energy of oscillation which is only conserved with the restoring forces becomes E = Uextreme = 1/2ka2 (Because spring force is the only restoring force not the weight of the body)