Two equal masses m = 1 kg, one moving at 2 m/s collides elastically with the other at rest along the same line. After collision, what are their velocities?

Two equal masses m = 1 kg, one moving at 2 m/s collides elastically with the other at rest along the same line. After collision, what are their velocities?

• A. The first mass stops; the second mass moves at 2 m/s
• B. Both masses move at 2 m/s
• C. The first mass moves at 2 m/s; second stops
• D. Both masses stop

Answer: (A)

In a one-dimensional elastic collision between two identical masses, they exchange velocities. The mass that was moving ends up with the velocity the other mass had, and the initially at-rest mass takes on the moving mass’s speed. Here, the moving mass starts at 2 m/s and the other is at rest. After the collision, the moving mass ends up at rest and the stationary mass moves with 2 m/s. This also preserves momentum and kinetic energy: initial momentum is m·2 = 2 kg·m/s, and final momentum is 0 + m·2 = 2; initial kinetic energy is 1/2 m·2^2 = 2 J, and final kinetic energy is 0 + 1/2 m·2^2 = 2 J. So the velocities are: the first mass stops, and the second moves at 2 m/s.

In a one-dimensional elastic collision between two identical masses, they exchange velocities. The mass that was moving ends up with the velocity the other mass had, and the initially at-rest mass takes on the moving mass’s speed.

Here, the moving mass starts at 2 m/s and the other is at rest. After the collision, the moving mass ends up at rest and the stationary mass moves with 2 m/s. This also preserves momentum and kinetic energy: initial momentum is m·2 = 2 kg·m/s, and final momentum is 0 + m·2 = 2; initial kinetic energy is 1/2 m·2^2 = 2 J, and final kinetic energy is 0 + 1/2 m·2^2 = 2 J.

So the velocities are: the first mass stops, and the second moves at 2 m/s.