A particle of mass #m# moving with speed #v# hits elastically another stationary particle of mass #2m# inside a smooth horizontal circular tube of radius #r#. The time after which the second collision will happen?
1 Answer
The circumference of the circle is
Explanation:
The momentum before the collision will be
Call the velocity of the particle of mass
We can cancel out
Since the collision is elastic, kinetic energy is conserved in the collision
Canceling out
The two equations can be rewritten in the form
Dividing both sides of the second equation by
gives
(Note that the last equation could have been directly obtained by using the alternative definition of elastic collisions - relative speed of approach equals that of separation - that would considerably shorten the answer!)
This implies that the relative speed of separation of the two objects is
When the two bodies collide again, the distances traveled by them must differ by
The time taken for this must be