I am basing this question off another one on this site, which is asking why if I human falls they don't bounce back to their original height. I understand that in inelastic collisions, an object loses energy to sound, heat, and also deformation. However, I am wondering why Newton's third law doesn't cause the object to bounce back to where it was. I read the answers to the other question, but I still couldn't grasp the topic. Also, my question revolved around why equal and opposite forces don't create an elastic collision, as when a ball hits a surface with a certain force, doesn't the surface exert the same force? Despite energy loss?
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1$\begingroup$ Newton's third law in this context states that the contact force you exert on the ground during the collision with it is the same as the force the ground exerts back on you. But it was not the contact force with the ground that caused you to fall down, it was gravity. So the only prediction Newton's third makes here is that the ground has the same acceleration per mass down as you have acceleration per mass up, while you and the ground are touching. $\endgroup$– Marius Ladegård MeyerCommented Jun 12 at 4:22
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1$\begingroup$ I started writing an answer, but couldn't understand what I'm trying to explain. What makes you think that equal forces should result in elastic collisions? $\endgroup$– AllureCommented Jun 12 at 5:25
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2 Answers
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It really comes down to the conservation of energy. In any given inelastic collision, a significant portion of the kinetic energy is transformed into internal energy, such as heat, sound, and deformation. When this energy is converted, it can no longer be returned to kinetic energy. As a result, the colliding objects will not be able to regain their initial kinetic energy.
Newton’s third law, which states that for every action, there is an equal and opposite reaction, applies to the forces during collisions, not the energy outcomes. The forces are equal and opposite, but the energy outcomes depend on how much kinetic energy is dissipated into other forms. It is these energy outcomes that determine whether or not an object bounces back. In an inelastic collision, since much of the kinetic energy is lost to other forms of energy, the object does not bounce back to its original position.
If that’s not convincing enough, think about it like this: Newton’s third law is the exact reason why inelastic and elastic collisions occur! When a clay ball hits the ground, it deforms because the ground is pushing and deforming the ball just as much as the ball is pushing against the ground. If the ground didn’t exert any force during this collision, the ball would simply pass through it without truly colliding. Newton’s third law doesn’t prevent inelastic collisions, it supports them!
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$\begingroup$ I never thought about it like that, thanks! $\endgroup$ Commented Jun 12 at 7:18
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Each of the two N3L forces acting on the colliding bodies do work during a collision.
This work manifests itself as elastic (temporary) deformation, heat, sound and plastic (permanently breaking bonds) deformation.
By the time the two colliding objects have stopped relative to one another only the elastic deformation ("spring" potential energy in the bonds) can be used for energy conversion back to kinetic energy.
During an elastic collision all the work done by the N3L forces is stored as "spring" potential energy which then is converted by the work done by the N3L forces back to kinetic energy.
The other extreme is when no "spring" potential energy is available for conversion back to kinetic energy and this usually visually results in the object being permanently deformed.
