Elastic collision
Newton's Laws & Momentum - OCR A-Level Physics
Key Definition
Elastic collision
A collision in which both momentum AND kinetic energy are conserved. No energy is dissipated.
A collision in which both momentum AND kinetic energy are conserved. No energy is dissipated.
Key Definition
Inelastic collision
A collision in which momentum is conserved but kinetic energy is NOT conserved. Some KE is converted to heat, sound or deformation.
A collision in which momentum is conserved but kinetic energy is NOT conserved. Some KE is converted to heat, sound or deformation.
Key Definition
Perfectly inelastic collision
A collision where the objects stick together after impact, moving with the same velocity. Maximum kinetic energy is lost while still conserving momentum.
A collision where the objects stick together after impact, moving with the same velocity. Maximum kinetic energy is lost while still conserving momentum.
- Momentum is ALWAYS conserved in all collisions and explosions (provided no external resultant force acts)
- 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 only conserved in perfectly elastic collisions
- Most real collisions are inelastic: some KE is converted to heat, sound or permanent deformation
- To test if a collision is elastic: calculate total KE before and after. If equal, it is elastic
- Collisions between subatomic particles and between very hard objects approximate elastic collisions
Common Mistake
MEDIUM
Students often: It's common to state that momentum is not conserved in inelastic collisions.
Instead: Momentum is ALWAYS conserved in ALL types of collision (elastic and inelastic), provided no external resultant force acts. It is KINETIC ENERGYThe capacity to do work. Measured in joules (J).The energy an object possesses due to its motion. that is not conserved in inelastic collisions.
Instead: Momentum is ALWAYS conserved in ALL types of collision (elastic and inelastic), provided no external resultant force acts. It is KINETIC ENERGYThe capacity to do work. Measured in joules (J).The energy an object possesses due to its motion. that is not conserved in inelastic collisions.
Worked Example [5 marks]
A 2.0 kg trolley moving at 3.0 $m s^{-1}$ collides with a stationary 1.0 kg trolley. After the collision they stick together. Calculate (a) the velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. after the collision, (b) the kinetic energyThe energy an object possesses due to its motion. lost.
Show Solution
1
Conservation of momentumIn a closed system (no external forces), the total momentum before an event equals the total momentum after.
$m_1 u_1 +\;\text{m}_2 u_2 = (m_1 +\;\text{m}_2)v$
[1]2
$(2.0)(3.0) + (1.0)(0) = (2.0 + 1.0)v \Rightarrow 6.0 = 3.0v \Rightarrow v = 2.0 \text{ m s}^{-1}$
[1]3
$KE before = \frac{1}{2}(2.0)(3.0)^{2} = 9.0 \text{ J}$
[1]4
$KE after = \frac{1}{2}(3.0)(2.0)^{2} = 6.0 \text{ J}$
[1]5
$KE lost = 9.0 - 6.0 = 3.0 \text{ J (converted to heat, sound and deformation)}$
[1]Answer
(a) 2.0 $m s^{-1}$. (b) 3.0 J lost.