Inelastic Collision: Kinetic Energy vs Momentum

[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!

 

[Chestermiller]

Totally wrong. The units don't even match.

 

[Nugatory]

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".

 

[ZapperZ]

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?

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

ΔK = K_f - K_i

This is odd because that is the DEFINITION of ΔK!

Zz.

 

[nasu]

This is not what the quoted sentence says. :)

 

[ZapperZ]

This is not what the quoted sentence says. :)

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.

 

[sophiecentaur]

I was hoping that this was an oversight, and not out of ignorance.

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

 

[lychette]

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

ΔK = K_f - K_i

This is odd because that is the DEFINITION of ΔK!

Zz.

Zz

 

[lychette]

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.

Zz

 

[xxphysics]

Totally wrong. The units don't even match.

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

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.

 

[xxphysics]

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

ΔK = K_f - K_i

This is odd because that is the DEFINITION of ΔK!

Zz.

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

 

[sophiecentaur]

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

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, traveling 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.