Inelastic Collision

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
Mentor
Totally wrong. The units don't even match.

Nugatory
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".

Biker and Chestermiller
ZapperZ
Staff Emeritus
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 = Kf - Ki

This is odd because that is the DEFINITION of ΔK!

Zz.

nasu
Gold Member
This is not what the quoted sentence says. :)

xxphysics
ZapperZ
Staff Emeritus
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
Gold Member
2020 Award
I was hoping that this was an oversight, and not out of ignorance.
It's more than possible that he didn't actually know??

xxphysics
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.
Zz

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

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.

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.
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