Where does the missing energy go in an inelastic collision?

[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.

 

[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.

 

[Lukeblackhill]

'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.

Thank you, @sophiecentaur.