A solid cylinder of mass 3 kg is rolling on a horizontal surface with ve...

Q. A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 ms−1. It collides with a horizontal spring of force constant 200 N m−1. The maximum compression produced in the spring will be

AIPMT/NEET 2012 | W.P.E Q 2 | You can consider this qus from Rotational motion as well as W.P.E but in my opinion since it includes more parameters of W.P.E its better to discuss here . A rolling body has two types of kinetic energies, translational as well as rotational. Compression can be called as maximum when kinetic energy will be lost completely and will store in form of potential energy which is actually happening here. Since there is no external force as well as non-conservative force so mechanical energy will remain conserved. Conservation of Mechanical Energy

The work-energy theorem, shows that the change DKE in a body’s kinetic energy is equal to the net work done on it:
 DKE = Wnet
Consider separately the work Wc done by conservative force and the work Wnc done by nonconservative forces. Then
DKE = Wc+ Wnc
We’ve defined the change in potential energy DU as the negative of the work done by conservative forces. So we can write
DKE = – DU + Wnc
or DKE + DU = Wnc
We define the sum of the kinetic and potential energy as the mechanical energy. Then Equation shownthat the change in mechanical energy is equal to the work downe by non-conservative forces.
i.e. DE = Wnc
D \E = 0 if Wnc= 0
Thus if work done by non-conservative forces is zero the mechanical energy of the system is unchanged.
This called law of conservation of mechanical energy. It may also be written as
DU + DK E = 0
or DU = – DKE
or U + K E = constant
or Uin + K Ein = Uf + K Ef

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