In a closed system the total momentum before a collision equals the total after, whether the objects stick together or bounce apart.
What you will learn
- State the conservation of momentum for a closed system
- Find the velocity after two objects stick together
- Find the velocity of one object after a collision
The total stays the same
In a closed system (no outside forces such as friction acting) the total momentum before an event equals the total momentum after it.
total momentum before = total momentum after
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Here u is a velocity before and v a velocity after. Each object's momentum changes in a collision; only the total is fixed.
Momentum is conserved in every collision, sticky or bouncy. Kinetic energy is a different story (lesson 5).
When objects stick together, some kinetic energy is always transferred to other stores: the thermal stores of the objects and surroundings, and away as sound. Work out ½ m v² for every moving object before and after: kinetic energy lost = total before − total after.
The rest of this lesson and its 9 practice questions are locked.
In this lesson
- The total stays the same
- Sticking together
- Bouncing apart
- Try it: Check it with the simulation
- Try it: Your first collision
9 practice questions, marked as you go; about 25 minutes in all.
Key terms
Closed system
In this unit: Momentum
Momentum as mass times velocity, its conservation in collisions and explosions, force as the rate of change of momentum, safety features and kinetic energy in collisions (Higher tier).
- Momentum, p = mv
- Conservation of momentum in collisions
- Explosions and recoil
- Force and the rate of change of momentum
- Collisions and kinetic energy