Question

In a one dimensional collision between two identical particles $A$ and $B$, $B$ is stationary and $A$ has momentum $p$ before impact. During impact, $B$ gives impulse $J$ to $A$.

• A. The total momentum of the $A+B$ system is $p$ before and after the impact, and $(p-J)$ during the impact
• B. During the impact $A$ gives impulse of magnitude $J$ to $B$
• C. The coefficient of restitution is $\frac{2J}{p}-1$
• D. The coefficient of the restitution is $\frac{J}{p}+1$

Answer 1

Answer: (B), (C)

During the impact $A$ gives impulse of magnitude $J$ to $B$
The coefficient of restitution is $\frac{2J}{p}-1$

At any moment the momentum remains conserved.
Both blocks receives equal in magnitude and opposite direction impulse from each other.
$J=\Delta mvP=m{u}_A\&P-J=m{v}_{A}J=m{v}_B\therefore e=\frac{v_B-v_A}{u_A}=\frac{J-(P-J)}{P}=\frac{2J}{P}-1$