# Conservation of Momentum vs. Energy in sticking collisions

1. Oct 31, 2008

### Tibriel

Conservation of Momentum vs. Energy in "sticking" collisions

1. The problem statement, all variables and given/known data

So here's the deal I'm wondering why when you have a collision where the two objects stick together momentum is conserved but energy isn't. (or at least that's how I'm reading what my math is telling me)

Example problem: 2 cars going into a head-on collision that stick together upon contact
Car 1:
m = 10kg
v = 5m/s

Car 2
m = 10kg
v = -10m/s

What is the velocity after the collision assuming no energy is lost to Friction/sound/heat etc.

2. Relevant equations

p(before) = mv[car 1] + mv[car 2] = p(after) = (m + m)v [car 1&2 combined]
KE = (1/2)*mv^2

3. The attempt at a solution

well I get a p(total) = -50kgm/s
and a v(combined) = -2.5m/s
I get an inital KE of 375J (500J - 125J) and a final KE of 62.5J if I use the new velocity from the momentum equations

So why is energy decreased when they stick together?
My assumption is that the KE of each car gets decreased because they are doing work on each other. This explanation sounds incomplete to me. I'm thinking that the rest of the explanation involves the change in velocity for each car. Here both have a change of 7.5m/s

Any help would be greatly appreciated

2. Oct 31, 2008

### Staff: Mentor

Re: Conservation of Momentum vs. Energy in "sticking" collisions

If the cars stick together then you cannot assume that no energy is "lost" to other forms. In fact, in such a perfectly inelastic collision the maximum amount of kinetic energy is lost.

3. Oct 31, 2008

### LowlyPion

Re: Conservation of Momentum vs. Energy in "sticking" collisions

When there is a car collision do you hear the wreck? Because there's some sound energy that has to come from somewhere.

When you rapidly bend metal have you ever touched it? You will find that it is warmer I think.

If the car's wrap around each other how much force does it take to simply bend the frames and panels about and over what distances are these forces applied? But does any of that necessarily go back into kinetic energy?

In short all the energies have to come from somewhere, from the smallest like the sound it makes to the largest like what is needed to pretzel the frame. The result is that while momentum conservation can be easily measured still with mass (that didn't change) and velocity, these others are a little harder to quantify.

So the short answer is that momentum translates into momentum. But KE doesn't necessarily translate into KE as there are other forms of energy that it can result in.