Key ideas
Momentum is mass times velocity. In a collision or explosion with no outside force, the total momentum of the system is conserved, even when kinetic energy is not.
- Impulse is force times the time it acts and equals the change in momentum: FΔt = Δp.
- In a perfectly inelastic collision the objects stick together and move with v′ = (m₁v₁ + m₂v₂) ÷ (m₁ + m₂).
- In an elastic collision both momentum and kinetic energy are conserved.
- Momentum is a vector. Give directions signs, such as right positive and left negative, before adding.
Key equations
p = mvJ = FΔt = Δpm₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′v′ = (m₁v₁ + m₂v₂) ÷ (m₁ + m₂) (perfectly inelastic)
Worked example
A 1000 kg car at 20 m/s hits a stationary 1000 kg car and they lock together. Momentum before: 1000 × 20 = 20 000 kg·m/s. After: 2000 × v′ = 20 000, so v′ = 10 m/s. Kinetic energy falls from 200 kJ to 100 kJ, so half of it was lost to deformation and heat.
Common mistakes
- Adding momenta without signs, so a leftward velocity is counted as if it were rightward.
- Assuming kinetic energy is conserved in every collision. It is conserved only in elastic ones.
- Using the mass of one object only when objects stick together.
Practice
Test yourself with practice questions on this topic: Momentum and collisions