Chapter 9, Problem 1EP

In terms of the variables given in GL Fig. 9.1, what is the momentum of the system immediately after the mass m becomes embedded in the pendulum bob?

To determine

The momentum of the system immediately after the mass $m$ becomes embedded in the pendulum bob.

Answer to Problem 1EP

The momentum of the system immediately after the mass $m$ becomes embedded in the pendulum bob is $p_{\text{after}}=\left(m+M\right)V$.

Explanation of Solution

In the ballistic pendulum arrangement shown in GL Figure 9.1, a projectile of mass $m$ is fired with velocity $v_{x0}$ hits and gets embedded in the bob of the pendulum which has a mass $M$. Before the collision, the momentum of the system will be $p_{\text{before}}=m{v}_{x0}$. The combined system has a velocity $V$ immediately after collision. After collision, the system executes oscillatory motion.

Immediately after the collision, the momentum of the system can be computed by taking the product of the combined mass and the velocity with which it start moving. The combined mass of the system will be $m+M$. Thus, the momentum of the system immediately after the mass $m$ becomes embedded in the pendulum bob will be $p_{\text{after}}=\left(m+M\right)V$.