A question about elastic collision of bodies.

[pmascaros]

English is not my native language.

My question is about what happens when we throw a ball on the floor. I understand why the ball bounces off it. But I have a question, I wonder why almost all the kinetic energy get back to the ball, rather than lost in the land, that is, why this energy is not dispersed by the planet.

Thank's

 

[raopeng]

It is an extreme condition when the mass of the floor M is taken to be a lot bigger than the mass of the ball m. You can take M as arbitrarily big in the formula of speed after collision and you will see it(it follows from the conservation of momentum and energy, and intuitively if M is very big its velocity cannot be of significant magnitude). But of course some energy is always dispersed to the planet.

 

[pmascaros]

Thanks raopeng.

But still I wonder. When I throw the ball, If instead of bouncing the ball, all stones or elements on the planet raised a little, it would maintain the momentum, why is it that gets the ball back almost all the energy, and not get distributed?

 

[raopeng]

Yes the momentum is conserved in all cases. But you also assume that the collision is elastic, hence the conservation of energy. Then it is obvious that the velocities after collision cannot be arbitrarily decided because they must satisfy both laws. Mathematically from the 2 conservation laws we obtain 2 equations respectively, and there are in total 2 variables, so the values of variables can be determined. But if the assumption of elastic collision is withdrawn, then there can be a range of possibilities, but if the coefficient of restitution(mathematically it offers the second equation) is given we can still determine the outcome.

 

[raopeng]

http://en.wikipedia.org/wiki/Coefficient_of_restitution
I hope this can help if I fail to explain it well.

 

[olivermsun]

Well, imagine a sort of "ideal bouncy-ball," which might consist of a thin sphere of perfectly rubbery skin containing a bunch of air. The ball acts just like a spring. When the ball hits the ground, it begins flattening out because the front part is touching the ground while the back is still moving downward. As it flattens, the ball's volume decreases, compressing the air inside and causing the skin to start stretching. Eventually, all the energy of moving downward has gone into compressing/stretching the ball. Then the ball begins to spring back, unflattening itself and releasing all the stored energy back into kinetic energy as it springs back up from the floor.

 

[pmascaros]

Thank you, very much. I think I understand better. Thanks