We have the following situation: In space, a basketball flies and hits another resting basketball.

What happens next?

a) Both balls fly in the original direction (but slightly slower) = momentum conservation (inelastic collision)

b) First ball stops, second ball flies in original direction with originally speed = momentum conservation (elastic shock) (newton's cradle)

c) Both balls repel each other and fly in different directions = action-reaction

And again the same with metal balls?

  • $\begingroup$ In sufficient information $\endgroup$ – Tojrah May 13 '19 at 1:46
  • $\begingroup$ A classic example used in many books. $\endgroup$ – user207455 May 13 '19 at 4:26

The word you are looking for is the Coefficient of Restitution.

The coefficient of restitution$(e)$ decides whether the collision is elastic or inelastic. It depends on the surfaces of contact between the balls. The value of $e$ is generally between $0$ and $1$. With $0$ representing completely inelastic, and $1$ representing completely elastic.

  • If $e=0$, then the balls would stick together at contact. They would move together with a velocity lower than that of the original in the same direction. The law of conservation of momentum will be valid here.
  • If $0<e<1$, then a partially elastic collision will take place. According to the masses, the balls could move in the same direction, with different velocities. Or move in opposite directions and still satisfy the law of conservation of momentum.
  • If $e=1$, then the collision is completely elastic. The incoming ball might rebound and the second ball might move in the original direction. All this happens in accordance with the laws of conservation of momentum and energy. In a special case, if the masses of the balls are equal, then the first ball could stop, and the second one moves in the same direction with the same velocity.

In short, the coefficient of restitution tells us how much loss energy loss occurs to heat. The law of conservation of momentum is valid in all three cases. But only for $e=1$ is the energy not lost to the surrounding as heat.


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