I have been asked the following question:

Two billiard balls of the same size and mass are in contact on a billiard table. A third ball of the same mass and size strikes them symmetrically and remains at rest after the impact. Find the coefficient of restitution between the balls?

Given that I figure out the velocity of separation for the two billiard balls that were in touch, should I be considering the $v_\textrm{sep}$ for only one of the two balls (while it is clear that $v_\textrm{app}$ will be the same for both balls) when calculating the coefficient of restitution ($e$)?

If so, why?


The CoR is assumed to be the same for both impacts.

The entire forward momentum of the 3rd ball is transferred to the two balls equally, so each has exactly 1/2 of the momentum in the direction of motion of the 3rd ball.

From the contact geometry (I think contact normal is 30° from the symmetry plane) you work out the momentum perpendicular to the symmetry plane. This relationship is going to give you the CoR.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.