Which statement correctly describes momentum and kinetic energy in a perfectly inelastic collision?

• A. Both momentum and kinetic energy are conserved.
• B. Momentum is not conserved; kinetic energy is not conserved.
• C. Momentum is not conserved; kinetic energy is conserved.
• D. Momentum is conserved; kinetic energy is not conserved.

Answer: (D)

Momentum is conserved in collisions because, for an isolated system, there are no external forces imparting impulse on the pair. In a perfectly inelastic collision, the objects stick together after impact, so the total momentum before equals the total momentum after, and the final velocity is determined by multiplying the total momentum by 1 over the combined mass.

Kinetic energy, however, does not stay the same in inelastic collisions. A lot of the initial kinetic energy is transformed into other forms of energy—deformation, heat, and sound—as the objects deform and fuse together. That’s why the final kinetic energy is smaller than the initial. So in a perfectly inelastic collision, momentum is conserved, but kinetic energy is not.