# Conservation of Momentum involving Vf, elastic collisions

## Homework Statement:

A billiard ball of mass 0.155kg moves with a velocity of 12.5m/s toward a stationary billiard ball of identical mass and strikes it in a head-on collision. The first billiard ball comes to a complete stop. Determine whether the collision was elastic.

## Relevant Equations:

Pt=Pt
m1v1+m2v2=m1v1+m2v2
I tried solving it using this method and I got 12.5m/s, and assumed the collision was elastic.

The answer is actually 6.32m/s [41.5 degrees counterclockwise from the original direction of the first ball]; the collision is not elastic: Ek = 12.1J Ek= 10.2J

I have absolutely no idea how the textbook could even get this answer. If you could explain the steps and why that would be greatly appreciated. Thanks!

## Answers and Replies

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kuruman
Homework Helper
Gold Member
Please show the details of your calculation. If the collision is head-on, there is no scattering angle involved. Where did the 41.5 deg. counterclockwise come from?

That was the textbooks answer, I have no idea how they got that. The collision is head-on. I used m1v1=m2v2 and subbed in all the values except for v2 and got 12.5m/s for m2. This means that when I solved for the total energies before and after the collision to check if it was elastic, they were both the same (12.1=12.1). Would you say my answer is right?

kuruman
Homework Helper
Gold Member
That was the textbooks answer, I have no idea how they got that. The collision is head-on. I used m1v1=m2v2 and subbed in all the values except for v2 and got 12.5m/s for m2. This means that when I solved for the total energies before and after the collision to check if it was elastic, they were both the same (12.1=12.1). Would you say my answer is right?
Yes. When balls of identical mass collide and the collision is elastic, they simply exchange velocities. This is the case here. I have no idea where the textbook got that answer either. Are there more parts to this problem? Maybe the answer belongs to a different part.

ericcy
Yes. When balls of identical mass collide and the collision is elastic, they simply exchange velocities. This is the case here. I have no idea where the textbook got that answer either. Are there more parts to this problem? Maybe the answer belongs to a different part.
Nope. Just that question. That's what made me so confused because I had literally no idea whatsoever how they could have gotten that answer. Must have been a mix up. Thanks for the confirmation on the answer :)

kuruman
kuruman
Homework Helper
Gold Member
You were rightfully confused. The answer appears to belong to a two-dimensional collision problem.

haruspex