Why is more impulse delivered during a collision when bouncing occurs than during one when it doesn't?

To understand why more impulse is delivered during a collision when bouncing occurs, let's first define impulse. Impulse is the change in momentum of an object and is calculated by multiplying the force acting on the object by the time interval over which the force is applied.

During a collision, when bouncing occurs, the objects involved experience a relatively larger force for a shorter period of time compared to a collision where bouncing does not occur. This results in a greater change in momentum and therefore more impulse being delivered.

Now, to explain how this happens, let's break it down into two scenarios:

1. Collision with bouncing:
When two objects collide and bounce off each other, there is an elastic deformation of the objects. This deformation stores potential energy, which is then released as kinetic energy when the objects start to separate. The release of this kinetic energy contributes to a larger force exerted over a short period of time, leading to a higher impulse being delivered.

2. Collision without bouncing:
In a collision where objects do not bounce, such as in a sticky collision or an inelastic collision, the objects stick together after impact. In this case, there is a more prolonged deformation and a slower separation of the objects. The force exerted during this longer time interval is smaller, resulting in a lower impulse being delivered.

Therefore, the key difference lies in the nature of the collision and the resulting deformation. When bouncing occurs, the release of stored energy leads to a larger force exerted in a shorter time, resulting in a higher impulse delivered compared to a collision where bouncing does not occur.