In a one-dimensional elastic collision between two masses m1 and m2, which quantities are conserved?

In a one-dimensional elastic collision between two masses m1 and m2, which quantities are conserved?

• A. Total momentum and total kinetic energy
• B. Total momentum only
• C. Total kinetic energy only
• D. Individual momenta m1 u1 and m2 u2

Answer: (A)

In a closed, one-dimensional system with no external forces, total momentum is always conserved. In an elastic collision, the total kinetic energy is also conserved, so the two quantities remain the same before and after the collision. The masses can exchange momentum and kinetic energy during the interaction, but the sum of momenta and the sum of kinetic energies stay constant. Individual momenta of each mass don’t stay fixed because the impulse from the collision changes each object’s momentum. If the collision were not elastic, kinetic energy would not be conserved, even though momentum would still be conserved.

In a closed, one-dimensional system with no external forces, total momentum is always conserved. In an elastic collision, the total kinetic energy is also conserved, so the two quantities remain the same before and after the collision. The masses can exchange momentum and kinetic energy during the interaction, but the sum of momenta and the sum of kinetic energies stay constant. Individual momenta of each mass don’t stay fixed because the impulse from the collision changes each object’s momentum. If the collision were not elastic, kinetic energy would not be conserved, even though momentum would still be conserved.