Which box ends up moving faster

[05holtel]

Homework Statement

Two balls of equal mass are thrown horizontally with the same initial velocity. They hit identical stationary boxes resting on a frictionless horizontal surface. The ball hitting box 1 bounces back,while the ball hitting box 2 gets stuck. Which box ends up moving faster

The Attempt at a Solution

I would think that box 2 ends up moving faster. Is this correct
Thanks

 

[hage567]

Why do you think that? I would think you would need to show it mathematically. Have you done that?

 

[thomate1]

for your question! I would approach this problem by analyzing the conservation of momentum and energy in the system. Since the initial velocity of both balls is the same, we can assume that they have the same momentum. When the ball hits box 1, it bounces back with the same momentum in the opposite direction, while the box acquires some momentum in the same direction as the ball's initial velocity. This results in a decrease in the overall momentum of the system, as some of it is transferred to the box.

On the other hand, when the ball hits box 2 and gets stuck, the box acquires the full momentum of the ball, resulting in a larger increase in the overall momentum of the system compared to the case of box 1. This means that box 2 will end up moving faster than box 1, as it has a larger momentum and therefore a higher velocity.

Additionally, we can also consider the conservation of energy in the system. When the ball hits box 1, some of the energy is transferred to the box as it moves, resulting in a decrease in the kinetic energy of the ball. However, when the ball hits box 2 and gets stuck, all of the energy is transferred to the box, resulting in a larger increase in its kinetic energy. This also supports the conclusion that box 2 will end up moving faster.

In conclusion, based on the principles of conservation of momentum and energy, box 2 will end up moving faster than box 1 in this scenario.