Section 1 of 5Momentum in Collisions
In any collision in a closed system, momentum is conserved, which allows the velocities before and after to be linked.
Momentum
- Momentum The product of mass and velocity, measured in kg m/s, where velocity includes direction.
Conservation of momentum
- Conservation of momentum In a closed system the total momentum before a collision equals the total momentum after it.
Closed system
- Closed system A system on which no external forces act, so no momentum is gained or lost from outside.
Objects sticking together
- Objects sticking together After a collision in which objects stick together, they share one velocity and their masses are added.
Section 2 of 5Solving a Collision Problem
Collision questions follow the same steps every time, so it is worth learning this order.
1
Write the momentum of each object before the collision using momentum = mass × velocity.
2
Add the momenta together to find the total momentum before the collision.
3
Set the total momentum after the collision equal to the total momentum before the collision.
4
Rearrange the equation to find the unknown velocity, paying attention to the direction and sign of each velocity.
Section 3 of 5Direction and Signs
Because momentum is a vector, the direction of each velocity must be kept track of.
Direction and Signs
Positive direction
- Positive direction Choose one direction as positive, then give velocities in the opposite direction a negative sign.
Stationary object
- Stationary object An object that is not moving has zero momentum before the collision, so it contributes nothing to the total.
Opposite velocities
- Opposite velocities Two objects moving in opposite directions have momenta that subtract from each other in the total.
| Object | Mass (kg) | Velocity before (m/s) | Velocity after (m/s) |
|---|---|---|---|
| Trolley A | 2 | 3 | 2 |
| Trolley B | 1 | 0 | 2 |
Section 4 of 5Worked Example
Question
- Trolley A (mass 2 kg) moves at 3 m/s and hits a stationary trolley B (mass 1 kg).
- The trolleys stick together.
- Calculate their common velocity after the collision.
- Momentum before = (2 × 3) + (1 × 0) = 6 kg m/s.
- Momentum after = (2 + 1) × v = 3v.
- Conservation of momentum3v = 6, so v = 2 m/s.
Answer 2 m/s, in the same direction as trolley A was moving.
Section 5 of 5Exam Checklist & Tips
5.9.3 – Key Points for the Exam
- Momentum The product of mass and velocity, a vector quantity in kg m/s.
- Conservation of momentum The principle that the total momentum of a closed system stays the same.
- Collision An event in which two or more objects come into contact and exert forces on each other.
- Closed system A system with no external forces acting on it.
- Vector A quantity that has both magnitude and direction.
Common Mistakes
- Adding the velocities of the two objects instead of adding their momenta.
- Forgetting to add the masses of objects that stick together, so the momentum after is wrongly calculated.
- Ignoring the direction of velocity and using positive values for two objects moving in opposite directions.
- Using speed instead of velocity in a question where the direction of motion matters.