In a one-dimensional collision between two carts, which quantities are conserved in a perfectly elastic collision?

• A. Only momentum is conserved.
• B. Momentum and kinetic energy are conserved in an ideal elastic collision.
• C. Neither momentum nor kinetic energy is conserved.
• D. Kinetic energy is conserved but momentum is not.

Answer: (B)

In a perfectly elastic collision, both momentum and kinetic energy are conserved. The collision between the carts involves no external forces along the track, so the total momentum (the combined mass times velocity) before and after the collision stays the same. At the same time, no energy is lost to deformation, heat, or sound in an ideal elastic collision, so the total kinetic energy before equals the total kinetic energy after. That combination—momentum conservation from the internal impulses and kinetic energy conservation from the absence of energy loss—defines the ideal elastic case. The other descriptions miss one of these essential features: momentum alone ignores the energy bookkeeping, or kinetic energy alone ignores that momentum must also be preserved in the absence of external forces.