# I Inelastic Collision

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1. Aug 15, 2016

### xxphysics

In an inelastic collision is the change in kinetic energy equal to the difference of final and initial momentum if one of the objects is initially at rest? For example:

m1v = (m1+m2)Vf -----> 0 = (m1+m2)Vf - m1v1

1/2(m1+m2)Vf^2 - 1/2m1v^2 = (m1+m2)Vf - m1v1

Or totally wrong? Thanks!

2. Aug 15, 2016

### Staff: Mentor

Totally wrong. The units don't even match.

3. Aug 15, 2016

### Staff: Mentor

Momentum is conserved, so the difference between the initial and final momentum has to be zero. You've captured that when you wrote $(m_1+m_2)v_f-m_1v_1=0$ for the particular case in which $m_2$ starts at rest and the two masses stick together in the inelastic collision.

So when you ask whether the change in kinetic energy is equal to the difference between the initial and final momentum, you're asking whether the change in kinetic energy is equal to zero.

This would be a good time to stop and think about the definition of "inelastic collision".

4. Aug 15, 2016

### ZapperZ

Staff Emeritus
OK, my take on this is that, this is a rather odd question. You're asking if

ΔK = Kf - Ki

This is odd because that is the DEFINITION of ΔK!

Zz.

5. Aug 16, 2016

### nasu

This is not what the quoted sentence says. :)

6. Aug 16, 2016

### ZapperZ

Staff Emeritus
I am aware that the OP is mixing momentum with kinetic energy. I was hoping that this was an oversight, and not out of ignorance.

Zz.

7. Aug 16, 2016

### sophiecentaur

It's more than possible that he didn't actually know??

8. Aug 16, 2016

### lychette

Zz

9. Aug 16, 2016

### lychette

Zz

10. Aug 16, 2016

### xxphysics

Thank you :) I just thought they were both looking at the change in velocity and in both equations there is a way to account for the differences in mass (before and after collision) so I didn't think was absurd to wonder if there is a connection between the formulas.

11. Aug 16, 2016

### xxphysics

No my question was if you could relate the momentum equation of an inelastic collision to the change in kinetic energy of that collision

12. Aug 17, 2016

### sophiecentaur

I see what you are after. There isn't a 1:1 relationship between the two quantities. Particular circumstances will give particular relationships.
Two situations with the same total momentum and different KE transferred to the collision. For convenience I have chosen to bring the motion to a halt. :
Two equal masses m&m, travelling towards each other at v and -v (Earth frame of reference) will have a total momentum of zero and a total KE of mv2. Now reduce one of the masses to 0.1m and increase its velocity to 10v. Total momentum is still zero but the KE is (mv2 +0.1m(100v2))/2 = (1+10)mv2/2 =5.5mv2.
This two trivial cases are enough to show that your idea can't be relied on. It's the squaring of the velocity that upsets things.

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