Reference frame in collision problems

[feynman1]

2 balls (Ball 1 and Ball 2) collide fully elastically and their relative velocity stays the same as but in sign opposite to that before the collision. Is there any sort of reference frame in which Ball 2 is always fixed (at rest) so that one can look at their relative velocity always in that reference frame? Here 'always' includes before and after the collision.

 

[DrStupid]

Is there any sort of reference frame in which Ball 2 is always fixed (at rest) so that one can look at their relative velocity always in that reference frame?

Yes, the rest frame of Ball 2 is such a frame of reference (surprise!), but it is not inertial and therefore not necessarily a good choice to describe the process.

 

[feynman1]

Yes, the rest frame of Ball 2 is such a frame of reference (surprise!), but it is not inertial and therefore not necessarily a good choice to describe the process.

Do you mean it's not inertial at the instant of the collision but inertial before and after? If so, Ball 2 won't be fixed in that frame, which isn't what I look for.

 

[A.T.]

2 balls (Ball 1 and Ball 2) collide fully elastically and their relative velocity stays the same as that before the collision. Is there any sort of reference frame in which Ball 2 is always fixed (at rest) so that one can look at their relative velocity always in that reference frame? Here 'always' includes before and after the collision.

Relative velocity is per definition the velocity of ball A in the rest frame of ball B (or vice versa). But if the relative velocity doesn't change, then there is not much of a collision.

 

[DrStupid]

Do you mean it's not inertial at the instant of the collision but inertial before and after? If so, Ball 2 won't be fixed in that frame, which isn't what I look for.

It is not inertial at the instant of the collision because Ball 2 (which is accelerated during the collision) is fixed in that frame.

 

[feynman1]

Relative velocity is per definition the velocity of ball A in the rest frame of ball B (or vice versa). But if the relative velocity doesn't change, then there is not much of a collision.

Just edited the original question, relative v changes sign.

 

[feynman1]

It is not inertial at the instant of the collision because Ball 2 (which is accelerated during the collision) is fixed in that frame.

Right, then have you an answer to the original question?

 

[Dale]

Right, then have you an answer to the original question?

He already answered it in post 2!

 

[feynman1]

He already answered it in post 2!

I knew all along that such a frame written in post 2 doesn't work well. Then can we conclude that there's no inertial reference frame in which Ball 2 is always fixed?

 

[A.T.]

Then can we conclude that there's no inertial reference frame in which Ball 2 is always fixed?

Yes.