Spec links: 4.5.7.1 Momentum is a property of moving objects (HT) · 4.5.7.2 Conservation of momentum (HT) · 4.5.7.3 Changes in momentum (Physics only) (HT) · Reading time: about 4 minutes
Crashing on purpose
In a test centre, a brand-new car speeds along a track. Inside sits a crash test dummy, covered in sensors. The car slams into a solid barrier. Metal crumples, glass shatters and an airbag bursts open in a fraction of a second. Engineers then study the data to find out what would have happened to a real person. Cars are wrecked on purpose like this so that real drivers are more likely to walk away from real crashes.
What is momentum?
Every moving object has momentum. It depends on the object’s mass and velocity. We calculate it using p = m v, where p is momentum in kilogram metres per second (kg m/s), m is mass in kilograms (kg) and v is velocity in metres per second (m/s).
A car of mass 1000 kg moving at 15 m/s has a momentum of p = 1000 × 15 = 15 000 kg m/s. Momentum has a direction, just like velocity. A lorry moving at the same speed has much more momentum, because its mass is much bigger.
Momentum is conserved
In a closed system, no external forces act. In this case, the total momentum before an event is equal to the total momentum after the event. This is called conservation of momentum.
Imagine the 1000 kg car hits a stationary 1500 kg van from behind, and the two lock together. The total momentum before is 15 000 kg m/s, because the van was not moving. Afterwards, the same momentum is shared by a combined mass of 2500 kg. So the velocity just after the collision is v = 15 000 ÷ 2500 = 6 m/s. Accident investigators use ideas like this to work out how fast vehicles were going before a crash.
Force and changing momentum
When a force acts on a moving object, its momentum changes. The force is equal to the rate of change of momentum: F = m Δv ÷ Δt. Here Δv is the change in velocity and Δt is the time taken for the change.
In a crash, your momentum must drop to zero. The change in momentum is fixed. But the time it takes is not. If the change happens very quickly, the force is huge. If the same change is spread over a longer time, the force is smaller.
Think about a 70 kg driver travelling at 15 m/s. If they hit a hard dashboard and stop in 0.01 s, the force is F = 70 × 15 ÷ 0.01 = 105 000 N. If an airbag makes the stop take 0.1 s, the force is F = 70 × 15 ÷ 0.1 = 10 500 N. Ten times longer means one tenth of the force.
Safety features
This one idea explains many safety features.
- Crumple zones at the front and back of a car squash in a crash. This increases the time the car takes to stop.
- Seatbelts stretch slightly, so the passenger slows down over a longer time instead of hitting the windscreen.
- Airbags inflate in front of the driver. The body sinks into the bag, increasing the stopping time.
- Cycle helmets contain a foam layer that squashes on impact, increasing the time for the head to stop.
In every case, the rate of change of momentum is reduced. That means a smaller force on the body and less chance of serious injury.
Key words
- Momentum: a property of moving objects, equal to mass × velocity; measured in kg m/s.
- Closed system: a system on which no external forces act.
- Conservation of momentum: in a closed system, the total momentum before an event is equal to the total momentum after the event.
- Rate of change of momentum: the change in momentum divided by the time taken; equal to the resultant force.
- Velocity: speed in a given direction.
- Crumple zone: part of a vehicle designed to deform in a collision, increasing the time taken to stop.
Questions
- Give the unit of momentum. [1 mark]
- What is meant by a closed system? [1 mark]
- Name two car safety features described in the article. [2 marks]
- A lorry and a car travel at the same velocity. Explain which has more momentum. [2 marks]
- Explain how a cycle helmet reduces the force on a cyclist’s head in a fall. [3 marks]
- A 1200 kg car travelling at 10 m/s collides with a stationary 800 kg car. The two cars move off together.
a) Calculate the momentum of the moving car before the collision. [2 marks]
b) Calculate the velocity of the two cars just after the collision. Give the unit. [2 marks] - A passenger of mass 60 kg is travelling at 20 m/s. In a crash, a seatbelt brings the passenger to rest in 0.15 s. Calculate the average force on the passenger. Give the unit. [3 marks]
- Explain how crumple zones, seatbelts and airbags reduce the risk of injury in a car crash. Use ideas about momentum in your answer. [6 marks]
Show answers
- kg m/s / kilogram metres per second (1)
- A system on which no external forces act (1)
- Any two from: crumple zones; seatbelts; airbags (1 each, max 2)
- The lorry (1); because it has a greater mass and momentum = mass × velocity (1)
- The foam squashes on impact (1); increasing the time taken for the head to stop / for the momentum to change (1); so the rate of change of momentum is smaller, so the force is smaller (1)
- a) p = 1200 × 10 (1); p = 12 000 kg m/s (1)
b) 12 000 = (1200 + 800) × v, so v = 12 000 ÷ 2000 (1); v = 6 m/s (1) (allow error carried forward from part a) - F = m Δv ÷ Δt = 60 × 20 ÷ 0.15 (1); F = 1200 ÷ 0.15 = 8000 (1); N (1)
- Indicative content: in a crash, the momentum of the car and the people inside changes to zero; the change in momentum is the same whatever the safety features; force = rate of change of momentum (F = m Δv ÷ Δt); crumple zones deform, increasing the time taken for the car to stop; seatbelts stretch slightly, increasing the time taken for the passenger to stop and stopping them hitting the windscreen or dashboard; airbags inflate and the body sinks into them, increasing the time taken for the head and chest to stop; airbags also spread the force over a larger area; a longer time means a smaller rate of change of momentum; so a smaller force acts on the people; smaller forces mean less serious injuries.
Level 3 (5–6 marks): a clear explanation of all three features, each linked to an increase in time, a smaller rate of change of momentum and a smaller force; Level 2 (3–4 marks): at least two features explained with some reference to increased time and reduced force; Level 1 (1–2 marks): simple statements about features protecting people, with little or no reference to momentum, time or force.
More reading: See all 30 GCSE Physics comprehension articles