3.4.1.6
Elastic collisions conserve kinetic energy; inelastic collisions do not
Newton's Laws & Momentum — AQA A-Level Physics
Key Definition
Elastic collision — A collision in which both momentum and kinetic energy are conserved.
Key Definition
Inelastic collision — A collision in which momentum is conserved but kinetic energy is not. Some kinetic energy is converted to other forms (heat, sound, deformation).
- Momentum is always conserved in both types (provided no external forces).
- To determine the type: calculate total KE before and total KE after.
- If KE $before = KE after$, the collision is elastic.
- If KE before > KE after, the collision is inelastic.
- Objects that stick together always produce an inelastic collisionA collision in which momentum is conserved but kinetic energyThe capacity to do work. Measured in joules (J).The energyThe capacity to do work. Measured in joules (J). an object possesses due to its motion. is not. Some kinetic energyThe capacity to do work. Measured in joules (J).The energy an object possesses due to its motion. is converted to heat, sound, or deformation..
- Kinetic energyThe energy an object possesses due to its motion.: $E_{k} = 0.5mv^2$.
Worked Example
Trolley A (0.80 kg, 3.0 m s^-1) hits stationary trolley B (1.60 kg). They stick together at 1.0 m s^-1. Is this elastic or inelastic?
Show Solution
1
Calculate KE before
$$KE_{\text{before}} = \frac{1}{2}(0.80)(3.0)^2 + 0 = 3.6 \text{ J}$$
2
Calculate KE after
$$KE_{\text{after}} = \frac{1}{2}(0.80 + 1.60)(1.0)^2 = \frac{1}{2}(2.4)(1.0) = 1.2 \text{ J}$$
3
Compare
3.6 J > 1.2 J, so kinetic energy is not conserved.
Answer
This is an inelastic collisionA collision in which momentum is conserved but kinetic energy is not. Some kinetic energy is converted to heat, sound, or deformation.. 2.4 J of kinetic energy was lost (converted to heat, sound, deformation).