Chapter 9, Problem 94A

To determine

To explain: The difference in the momentum of the system before and after the collision.

Answer to Problem 94A

The momentum of the system before and after the collision is conserved as no external force is acting on the system.

Explanation of Solution

Given:

The mass of the ball A is $m_{\text{A}}=0.400\text{kg}$ .

The mass of the ball B is $m_{\text{B}}=0.600\text{kg}$ .

Formula used:

Conservation of linear momentum:

Consider two balls moving at particular velocity collides and after collision these balls moves with different velocity. The momentum of the balls before and after the collision is conserved as no external force is acting on the system.

Calculation:

Consider two balls A and B moving from left collides, and bounces away.

The velocity of the ball A before and after the collision is denoted by $v_{\text{A1}}$ and $v_{\text{A2}}$ .

The velocity of the ball B before and after the collision is denoted by $v_{\text{B1}}$ and $v_{\text{B2}}$ .

The vector diagram of the collision of the balls A and B is shown below.

  

The dotted line in the vector diagram indicates that the momentum of the balls A and B before the collision is equal and opposite to the momentum of the balls A and B.

The momentum of the system of the balls is conserved as no external force is acting on the system.

  $\Delta \left(m_{\text{A}}{v}_{\text{A}}\right)=\Delta \left(m_{\text{B}}{v}_{\text{B}}\right)$

The ratio of changes in the mass of the ball A and B is $2:3$ . So, the ratio of changes in the velocity of the ball A and B will be $3:2$ in order to conserve the momentum of the system.

Hence, the momentum of the balls A and B is conserved as no external force is acting on the system.

Conclusion:

Thus, the momentum of the balls A and B is conserved as no external force is acting on the system.