Dark85
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- TL;DR Summary
- Proof of why objects bounce using conservation of momentum and energy
Consider a body of mass m held above a rigid surface at a height h. Let the surface have such a large mass that any force exerted by the body during this entire scenario practically does not move the surface. This implies that before the body hits the surface and after hitting it, the momentum of the surface is zero throughout. Let the body, after hitting the surface, attain a final momentum of mv Since the body is initially held at rest, it's initial momentum is zero. Since there is no external force on the body-surface system, momentum is conserved i.e. :
initial momentum = final momentum
mu + 0 = mv + 0
0 = mv
v = 0 m s-1
This implies the final possible state can be at rest on the surface or at rest after bouncing to any height, including the initial height h(We assume there is no dissipation of energy as heat or sound)
But if it is at rest on the surface, it implies kinetic energy is 0 J. Since we assumed that no energy is dissipated, it implies energy is not conserved hence this final state is not possible. It is the same for all other states where the ball bounces to a smaller height because in this case also energy is not conserved as the kinetic the initial energy mgh is not equal to the final energy mg*(a height smaller than h). Only if the ball bounces back to the same height h is when momentum and energy is conserved. Hence, this why an object bounces rather than just hitting the surface and staying at rest.
initial momentum = final momentum
mu + 0 = mv + 0
0 = mv
v = 0 m s-1
This implies the final possible state can be at rest on the surface or at rest after bouncing to any height, including the initial height h(We assume there is no dissipation of energy as heat or sound)
But if it is at rest on the surface, it implies kinetic energy is 0 J. Since we assumed that no energy is dissipated, it implies energy is not conserved hence this final state is not possible. It is the same for all other states where the ball bounces to a smaller height because in this case also energy is not conserved as the kinetic the initial energy mgh is not equal to the final energy mg*(a height smaller than h). Only if the ball bounces back to the same height h is when momentum and energy is conserved. Hence, this why an object bounces rather than just hitting the surface and staying at rest.