Chapter 5, Problem 5TS

A $2-\text{kg}$ ball of putty moving to the right has a head-on inelastic collision with a $1-\text{kg}$ putty ball moving to the left. If the combined blob doesn't move just after the collision, what can you conclude about the relative speeds of the balls before they collided?

To determine

The conclusion about the relative speeds of the balls before collision.

Answer to Problem 5TS

The $1\text{kg}$ ball moves with twice the relative speed of the $2\text{kg}$ ball before the collision of both balls.

Explanation of Solution

The mass of the body and the velocity it possesses are the only dependent parameter on which the momentum of the body is dependent. If a body is in straight line motion, then heavier the object, lesser will be its velocity.

The head-on inelastic collision takes place between the $2\text{kg}$ ball and $1\text{kg}$ ball. The momentum of both balls does not remain conserve in the inelastic collision. The combined blob of both balls doesn't move just after the collision. It shows that the both the ball are at rest just after the collision.

The $2\text{kg}$ ball moves toward right and $1\text{kg}$ ball moves toward left, so both the balls move opposite to each other. The balls come at rest just after the collision only if the momentum of both the balls is same. The momentum of both balls can be same only if the $2\text{kg}$ ball moves with half of the speed of the $1\text{kg}$ ball.

Conclusion:

Therefore, the $1\text{kg}$ ball moves with twice the relative speed of the $2\text{kg}$ ball before the collision of both balls.