Question

A mass (m) with speed (v) experiences a perfectly elastic collision with an initially stationary mass (M). What is the ratio of the masses (m/M) if after the collision, m and M have the same speed (V) but opposite velocities?

Answer 1

Initial velocity of mass (m) = v

Initial velocity of mass (M)= 0

If mass m is traveling in the +ive x -axis initially, then after collision it will travel in -ive direction of the x-axis whereas M will travel in positive x direction. Therefore:

Final velocity of mass (m)= - V

Final velocity of mass (M)=V

As in perfectly elastic collision, both energy and momentum will be conserved.

Applying law of conservation of momentum:

Initial momentum= Final momentum

Rearranging we get:

We can also get the ratio by applying conservation of energy :

This both results when compared will result : v=2V which means that initially body of mass m was traveling with twice the velocity after collision. Which means that after collision speed gets equally distributed among two objects without any lots of energy.

You can use any of the ratio as your final answer.

Please give a up vote if you like the answer.

If you dislike the answer then put your queries, feedback, or suggestion in comments section.

If it doesn't get resolved then down vote the answer.