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Equal masses collide elastically
Intermediate
They exchange velocities in one dimension.
With equal masses in a 1-D elastic collision the bodies exchange velocities. A moving ball hitting a stationary equal one stops dead, and the target moves off.
Newton's cradle.
This holds only head-on and elastic.
In more detail
When two equal masses collide elastically head-on, they exchange velocities. A stationary mass hit by a moving one of equal mass stops, and the moving one stops, with the target moving off at the original speed.
Real-world uses
- Billiard shots that send the cue ball to a stop and the target ball away use this result.
- Newton's cradle relies on equal masses exchanging velocities.
- In a demonstration with two identical carts, one moving cart stops and the other moves off with the original speed.
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Frequently asked questions
Why do the velocities swap?
Because momentum and kinetic energy conservation both hold only for this exchange when the masses are equal.
What if the masses are not equal?
Then the velocities do not simply swap, and the general formula applies.
Why do equal masses swap velocities?
The momentum and energy equations have a solution in which each body takes on the other's velocity, which is the only nontrivial one.
Related topics in Momentum & Collisions
Perfectly inelastic collision · Coefficient of restitution · Elastic head-on collision velocities · Light hits heavy object · Heavy hits light object · Energy lost in inelastic collision