Momentum and Conservation of Momentum
Momentum and Conservation of Momentum
Momentum is a measure of how difficult it is to stop a moving object. It depends on both the mass and velocity of the object and is a key concept for understanding collisions and explosions.
Defining Momentum
momentum = mass x velocity
p = m x v
Where:
- p = momentum (kilogram metres per second, kg m/s)
- m = mass (kilograms, kg)
- v = velocity (metres per second, m/s)
Momentum is a vector quantity — it has both magnitude and direction. An object moving to the right has positive momentum; an object moving to the left has negative momentum (or vice versa, depending on your chosen direction).
Example: A 1,200 kg car travelling at 15 m/s has momentum:
p = 1,200 x 15 = 18,000 kg m/s
Conservation of Momentum
In a closed system (no external forces acting), the total momentum before an event equals the total momentum after the event. This is the law of conservation of momentum.
This applies to:
- Collisions (objects crashing together)
- Explosions (objects moving apart from rest)
total momentum before = total momentum after
Collisions
Example: A 2 kg trolley moving at 3 m/s collides with a stationary 1 kg trolley. They stick together. What is their velocity after the collision?
Before: momentum = (2 x 3) + (1 x 0) = 6 kg m/s
After: momentum = (2 + 1) x v = 3v
By conservation: 3v = 6, so v = 2 m/s
When objects stick together, it is called a perfectly inelastic collision. Kinetic energy is not conserved (some is converted to thermal and sound energy), but momentum IS always conserved.
Example with objects moving in opposite directions: A 3 kg ball moving at 4 m/s to the right collides with a 2 kg ball moving at 5 m/s to the left. They stick together.
Taking right as positive:
Before: (3 x 4) + (2 x (-5)) = 12 + (-10) = 2 kg m/s
After: (3 + 2) x v = 5v
5v = 2, so v = 0.4 m/s to the right
Explosions
Before an explosion, the objects are stationary, so total momentum = 0.
After the explosion, momentum is still zero — the objects move in opposite directions with equal and opposite momenta.
Example: A 60 kg astronaut pushes away from a 5 kg tool kit in space. The tool kit moves at 6 m/s. How fast does the astronaut move?
Before: total momentum = 0
After: (60 x v) + (5 x 6) = 0
60v + 30 = 0
60v = -30
v = -0.5 m/s (the astronaut moves at 0.5 m/s in the opposite direction)
Force, Momentum, and Time (Higher Tier)
Newton's second law can be expressed in terms of momentum:
force = change in momentum / time taken
F = (mv - mu) / t
or: F = delta-p / delta-t
Where delta-p is the change in momentum.
This explains why:
- Catching an egg — you move your hands back to increase the time of deceleration, reducing the force and preventing the egg from breaking
- Crumple zones in cars increase the time of collision, reducing the force on passengers
- Air bags and seat belts also increase the deceleration time, reducing the force on the body
- Crash helmets contain padding that compresses on impact, extending the time and reducing the peak force
Momentum in Vehicle Safety
Modern cars are designed to protect occupants using momentum principles:
| Safety feature | How it works |
|---|---|
| Crumple zones | Front and rear of car deform, increasing collision time, reducing force |
| Seat belts | Stretch slightly, increasing time for passenger to decelerate |
| Air bags | Inflate and deflate slowly, cushioning the passenger over a longer time |
| Side impact bars | Rigid bars distribute force over a larger area |
| Crash helmets | Padding extends impact time; hard shell distributes force |
All of these work on the same principle: increasing the time over which momentum changes reduces the force.
Exam Tips
- Always define your positive direction before calculating momentum in collisions with objects moving in opposite directions
- In explosion questions, remember total momentum before = 0, so the momenta after must be equal and opposite
- When asked about safety features, always link to the equation F = delta-p / delta-t and explain that increasing time decreases force
- Momentum is ALWAYS conserved in collisions; kinetic energy is only conserved in perfectly elastic collisions (rare in real life)