In a perfectly inelastic collision, which statement is true?

In a perfectly inelastic collision, which statement is true?

• A. Momentum is conserved; Kinetic energy is conserved.
• B. Momentum is not conserved; Kinetic energy is lost.
• C. Momentum is conserved; Kinetic energy is lost.
• D. Momentum is conserved; Kinetic energy is gained.

Answer: (C)

In a collision, momentum is conserved when there are no external forces acting on the system, because the internal forces between the colliding bodies only transfer momentum between them. In a perfectly inelastic collision, the objects stick together after impact, so they move with one common final velocity. That velocity depends on the total momentum divided by the total mass of the combined object. Kinetic energy, on the other hand, is not conserved in this case. The sticking process deforms the bodies and converts part of the initial kinetic energy into internal energy, heat, and other forms of energy, so the final kinetic energy is less than the initial amount. So the true statement is: momentum is conserved; kinetic energy is lost.

In a collision, momentum is conserved when there are no external forces acting on the system, because the internal forces between the colliding bodies only transfer momentum between them. In a perfectly inelastic collision, the objects stick together after impact, so they move with one common final velocity. That velocity depends on the total momentum divided by the total mass of the combined object.

Kinetic energy, on the other hand, is not conserved in this case. The sticking process deforms the bodies and converts part of the initial kinetic energy into internal energy, heat, and other forms of energy, so the final kinetic energy is less than the initial amount.

So the true statement is: momentum is conserved; kinetic energy is lost.