I Where does the energy go to?

1. May 9, 2018

Lukeblackhill

Morning,

I was thinking about a simple example of inelastic collision: A ball of mass m1, moving with a certain velocity v1, collides and sticks with another mass m2, at rest. The whole system (m1 + m2) will then move with a certain speed v3.

If we take m1=m2, so that after the collision we have a single mass of 2m1 mass, by the conservation of momentum, v3 = v1/2. If we work out the kinetic energy of the system before and after the collision, we have K(after) = K(before)/2.

The question is...where does the other half of kinetic energy goes to? In such a collision, must we necessarily expect losses in terms of heat and sound, or can we find that other half transformed in some sort of "gluing energy"?

Cheers,
Luke.

2. May 9, 2018

sophiecentaur

'All' the missing energy will go into the deformation process, heat and sound. It can require a lot of work to deform materials. There will often be some damped oscillation during the process, in which the energy is dissipated over a significant length of time.

3. May 9, 2018

Lukeblackhill

Thank you, @sophiecentaur.