When a beanbag hits the wall, it transfers all its forward momentum to the wall and comes to a stop. When a rubber ball hits the wall, it transfers all its forward momentum, comes to a stop, and then rebounds. During the rebound, it transfers still more forward momentum to the wall. If you wanted to knock over a weighted bowling pin at the county fair, which would be the more effective projectile: the rubber ball or the beanbag, assuming they have identical masses and you throw them with identical velocities?

When discussing collisions, it's essential to understand how objects interact upon impact. In our exercise, we look at how a beanbag and a rubber ball, both with the same mass and velocity, behave when they hit a wall. A collision occurs when two objects come into contact with each other, resulting in a transfer of energy and momentum.
In this scenario, the beanbag transfers its forward momentum to the wall and stops, whereas the rubber ball also transfers its forward momentum but rebounds, which means it changes its direction.
The behavior of these objects upon hitting the wall demonstrates different types of collisions:

• **Elastic Collision:** The rubber ball exhibits an elastic collision by rebounding after hitting the wall. Both its kinetic energy and momentum are conserved.
• **Inelastic Collision:** The beanbag, on the other hand, stops upon hitting the wall. It's an inelastic collision where kinetic energy isn't conserved.

As we'll elaborate, these differing behaviors significantly impact the momentum transferred to the wall and, by extension, their effectiveness in knocking over something like a bowling pin.

The principle of momentum conservation is a cornerstone in physics. It states that the total momentum of a closed system remains constant if no external forces act upon it.
For our exercise, consider the beanbag and the rubber ball as examples of how momentum behaves. Initially, both objects have momentum given by the formula:
\[ p = m \times v \] where:

• \( p \) is momentum,
• \( m \) is mass,
• \( v \) is velocity.

When the objects collide with the wall, they transfer this momentum. However, the processes differ:

• **Beanbag:** Transfers all its forward momentum to the wall and stops.
• **Rubber Ball:** First transfers its forward momentum to the wall, stops momentarily, and then rebounds. This means it transfers additional momentum in the opposite direction.

Because the rubber ball changes direction and transfers even more momentum upon rebounding, it demonstrates more effectively how momentum conservation plays out in different collision types.

Impact force is the force exerted by one object on another during a collision. The magnitude of this force depends on the rate of momentum transfer and the interaction time. For the given objects (beanbag and rubber ball), we analyze the total momentum they transfer to the wall:
**Beanbag:** Upon hitting the wall, it transfers momentum equal to:
\( p = m \times v \)
The beanbag's impact force is limited to this amount.
**Rubber Ball:** Transfers momentum twice due to rebounding. First, the forward momentum:
\( p_1 = m \times v \)
Upon rebounding, it adds a second momentum equal in magnitude but opposite in direction:
\( p_{total} = m \times v + m \times v = 2m \times v \)
**Conclusion:** Since the rubber ball exerts twice the momentum transfer compared to the beanbag, it applies a larger impact force. This greater force makes the rubber ball more effective for tasks like knocking over a bowling pin. Understanding these intricacies helps illustrate why elastic collisions (like that of the rubber ball) result in higher impact forces than inelastic ones (like that of the beanbag).