Question

Two identical blocks $A$ and $B$, connected by a massless string, are placed on a frictionless horizontal plane. A bullet having the same mass, moving with speed $u$, strikes block $B$ from behind as shown. If the bullet gets embedded into block $B$, then find
a) the velocity of A, B, C after collision.
b) impulse on $A$ due to tension in the string
c) impulse on $C$ due to normal force of collision
d) impulse on $B$ due to normal force of collision.

Answer 1

a) By conservation of linear momentum, $\nu =b/3$.

b) $\int Tdt=\frac{mu}{3}$

c) $\int Ndt=m(\frac{u}{3}-u)=\frac{-2mu}{3}$

($-ve$ sign indicates left direction)

d) $\int (N-T)dt=\int Tdt=\frac{mu}{3}⟹\int Ndt=\frac{2mu}{3}$