Question

13) In an elastic collision, energy is conserved but momentum is not.

Answer 1

That statement is false.

Correct points:
- In an isolated (no external forces) collision, momentum is always conserved, whether the collision is elastic or inelastic. Momentum conservation follows from Newton’s third law (internal forces cancel).
- An elastic collision is one in which kinetic energy (not just “energy”) is conserved in that isolated system. In an inelastic collision kinetic energy is not conserved (some is converted to internal energy, heat, deformation), but momentum still is.

So for an isolated two-body elastic collision both momentum and kinetic energy are conserved.

Example (one-dimensional, masses m1, m2, initial velocities v1, v2):
- Conservation of momentum: m1 v1 + m2 v2 = m1 v1' + m2 v2'
- Conservation of kinetic energy: 1/2 m1 v1^2 + 1/2 m2 v2^2 = 1/2 m1 v1'^2 + 1/2 m2 v2'^2

Solving gives the post-collision velocities:
v1' = [(m1 - m2)/(m1 + m2)] v1 + [2 m2/(m1 + m2)] v2
v2' = [2 m1/(m1 + m2)] v1 + [(m2 - m1)/(m1 + m2)] v2

If external forces act during the collision, total momentum of the two-particle system need not be conserved.