Two identical blocks A and B of mass M each are kept on each other on a smooth horizontal plane. There exists friction between A and B. If a bullet of mass m hits the lower block with a horizontal velocity v and gets embedded into it, the work done by friction between A and B is
Let the velocity of lower block just after collision be V1
∴ Applying conservation of liner momentum between bullet and lower block as impluse due to friction is negligible.
∴ mv = (M + m )V1 ⇒ V1 = ( mM+m) V
After collision frictional force acts on both and will act till velocities of both blocks become equal.
∴ (M + m )V1 = (2M + m )V2 ⇒ V2 ( m2M+m) V
Applying work energy theorem ,WFriction = Kf - Ki = 12 [2 M + m] V22
⇒ Kfriction = −Mm2v22(m+2M)(m+M)