State the principle of conservation of momentum and the condition under which it applies.
State what is conserved in an elastic collision and what is conserved in an inelastic collision.
A 3.0 kg trolley moving at 4.0 m s−1 collides with a stationary 2.0 kg trolley and they stick together. Find the common velocity after the collision.
A 2.0 kg gun fires a 0.010 kg bullet at 400 m s−1. The gun and bullet are at rest before firing. Find the recoil velocity of the gun.
A 0.20 kg ball moving at 5.0 m s−1 collides with a stationary 0.30 kg ball. After the collision the 0.20 kg ball continues in the same direction at 1.0 m s−1. (a) Find the velocity of the 0.30 kg ball. (b) By comparing kinetic energy, state whether the collision is elastic or inelastic.
In an inelastic collision the total kinetic energy decreases. Explain where this energy goes and why the total momentum is still conserved.
Use Newton's third law to explain why momentum is conserved during a collision.
Total: 24 marks. Original work by the TheLucidSTEM team. Written in the style of the papers; no past paper question is reproduced.
Answer key · full worked solutionsclick to reveal
for a closed system with no external resultant force, the total momentum before an interaction equals the total momentum after.
in an elastic collision both momentum and kinetic energy are conserved. In an inelastic collision momentum is conserved but kinetic energy is not.
3.0 × 4.0 + 2.0 × 0 = (3.0 + 2.0)v, so 12 = 5.0v and v = 2.4 m s−1.
total momentum before = 0. After: 0 = 0.010 × 400 + 2.0 × v, so 2.0v = −4.0 and v = −2.0 m s−1. The gun recoils at 2.0 m s−1 in the opposite direction to the bullet.
(a) momentum: 0.20 × 5.0 = 0.20 × 1.0 + 0.30 × v, so 1.0 = 0.20 + 0.30v, giving v = 0.80 / 0.30 = 2.7 m s−1.
(b) KE before = ½ × 0.20 × 5.0² = 2.5 J. KE after = ½ × 0.20 × 1.0² + ½ × 0.30 × 2.67² = 0.10 + 1.07 = 1.2 J. KE is not conserved, so the collision is inelastic.
the lost kinetic energy is transferred to other forms: heat, sound and the energy of permanent deformation. Momentum is still conserved because the forces between the colliding bodies are internal and, by Newton's third law, equal and opposite, so they cannot change the total momentum of the system.
during the collision each body exerts a force on the other. By Newton's third law these forces are equal and opposite and act for the same time, so the impulses are equal and opposite. The changes in momentum are therefore equal and opposite and cancel, leaving the total momentum unchanged.