# Elastic collision and conservation of momentum

I have read that if two balls with the same mass collide together at the same velocity, the momentum cancels out. All that's left is kinetic energy due to potential stored energy, if I have understood it correctly (like that of a compressed spring), which causes both balls to move in the opposite direction from which they started.

Can someone confirm if this is true? This video I was told to watch seems to suggest that the momentum is conserved but it doesn't state if that's kinetic energy or not.

See video:

Inelastic and Elastic Collisions: What are they? (youtube.com)
(edited 1 month ago)
I agree with the video
For the 2 balls, the total momentum before = 0 = total momentum after.
Since the 2 balls have same m and magnitude of v,
their KE is transferred to EPE which is transferred back to KE
and total KE before = total KE after since there are no external resultant forces acting.
(edited 1 month ago)
Original post by mosaurlodon
I agree with the video
For the 2 balls, the total momentum before = 0 = total momentum after.
Since the 2 balls have same m and magnitude of v,
their KE is transferred to EPE which is transferred back to KE
and total KE before = total KE after since there are no external resultant forces acting.

The video describes that after an elastic collision, both momentum and kinetic energy are conserved, but I thought momentum was lost and kinetic energy was the only thing remaining.

Is the information here wrong then?
(edited 1 month ago)
I think you have a slight misunderstanding - momentum is never 'lost'.
momentum is ALWAYS conserved but KE is ONLY conserved if its an elastic collision.
The picture you sent is correct - momentum is conserved
initially the total momentum is m(v) + m(-v) = 0 (as velocity and momentum are scalars)
after the the total momentum is m(-v) + m(v) = 0
so total momentum before = total momentum after

KE is only conserved when the collision is elastic - so be careful when setting up equations trying to solve for a variable using conservation of energy - ALWAYS first set up the equations conserving momentum as momentum is always conserved.
(edited 1 month ago)
Original post by mosaurlodon
I think you have a slight misunderstanding - momentum is never 'lost'.
momentum is ALWAYS conserved but KE is ONLY conserved if its an elastic collision.
The picture you sent is correct - momentum is conserved
initially the total momentum is m(v) + m(-v) = 0 (as velocity and momentum are scalars)
after the the total momentum is m(-v) + m(v) = 0
so total momentum before = total momentum after
KE is only conserved when the collision is elastic - so be careful when setting up equations trying to solve for a variable using conservation of energy - ALWAYS first set up the equations conserving momentum as momentum is always conserved.

I see. If the mass of the first ball and second ball, let's say is 0.5kg.

0.5 kg (5ms) +0.5 kg (- 5ms) = 0 Before. They bounce back in opposite directions, meaning the left ball then follows in the negative direction while the right ball goes in the positive direction, and the momentum remains the same afterwards.

I clearly chose to ignore the direction of one being negative and one being positive.

Thank you for clearing that up for me