Maximum amount of energy that can be released as heat and sound

[DocZaius]

Homework Statement

A mass m moving at velocity v collides with a stationary target having the same mass m. Find the maximum amount of energy that can be released as heat and sound.

Homework Equations

KE = (1/2)mv^2
Momentum = mv

The Attempt at a Solution

I guessed at 1/2KE (or (1/4)mv^2)) and got it right. But I am trying to think of reasons why no more than half the kinetic energy can be released as heat and sound can't think of it.

 

[DocZaius]

Ok here's the way I thought about it. The most wasteful collision in terms of kinetic energy would be one in which the two masses merge and move together.

Since momentum must be conserved, this would entail that the initial momentum (mv) of the first mass would have to become (2m*v/2) of the merged masses.

Plugging in 2m and v/2 into the KE equation, I find that the moving merged masses's kinetic energy is the initial mass's KE divided by 2. Conservation of energy says that the other half of the energy had to go somewhere, and that is thus heat and sound.

Is that an ok approach?

 

[Doc Al]

Yep. Sounds good to me.