Can someone please explain to me how to calculate the rebound velocity, rebound acceleration, and rebound height of an object of mass=m dropped from height=h? Thank you.

  • $\begingroup$ Do you know the coefficient of restitution of the ground and ball ? $\endgroup$ – Tausif Hossain Jun 13 '17 at 6:11
  • $\begingroup$ Can you please add more details and what you've tried? $\endgroup$ – QuirkyTurtle98 Jun 13 '17 at 6:18
  • $\begingroup$ @quirkyturtle98 - I've tried ALOT of googling but most information is related to before impact or at impact and not much is out there about the post impact dynamics $\endgroup$ – PhysicsMakesTheWorldGoRound Jun 13 '17 at 6:35
  • $\begingroup$ @ Tausif Hossain - Thanks for your help. Unfortunately, I dont know the coefficient of restitution. Any good sources that you can recommend or ways to determine it empirically? $\endgroup$ – PhysicsMakesTheWorldGoRound Jun 13 '17 at 6:38

In order to calculate the rebound velocity and rebound height you need to know something called the coefficient of restitution which tells you how elastic/ inelastic the collision between the ground and object is.

The coefficient of restitution,$e$ is: $$e=\frac{v_(rebound)}{v_(impact)}$$ Thus if you know $e$ then you can find rebound velocity.( Notice if collision is perfectly elastic then e=1 and rebound velocity = impact velocity and rebound height= original height)

For rebound height just use $v^2=u^2+2gh$ to find $h_(after-rebound)$ setting $v=0$ and $u=v_(rebound)$. Now to find the acceleration you need to know the collision time between object and ground. Then acceleration,$a$ is simply given by : $$a=\frac{v_(impact)+v_(rebound)}{Collision Time}$$

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  • $\begingroup$ Thank you very much Tausif. It seems that determining the coefficient of restitution is the tricky part. $\endgroup$ – PhysicsMakesTheWorldGoRound Jun 13 '17 at 6:47
  • $\begingroup$ You don't have to determine it as it's usually given in questions like this. You're welcome. Please verify the answer if you find it satisfactory. $\endgroup$ – Tausif Hossain Jun 13 '17 at 6:54
  • $\begingroup$ In reality we can actually measure the coefficient of restitution by measuring the rebound heights. $\endgroup$ – Tausif Hossain Jun 13 '17 at 6:55

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