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This lesson covers momentum, conservation of momentum, and the relationship between force and rate of change of momentum — as required by the Edexcel GCSE Physics specification (1PH0), Topic 1: Key Concepts of Physics. You need to be able to calculate momentum, apply conservation of momentum to collisions and explosions, and explain how safety features reduce forces (Higher tier).
Momentum is a measure of how difficult it is to stop a moving object. It depends on both the object's mass and its velocity.
momentum = mass × velocity
p=mv
Where:
Example 1: A car of mass 1200 kg travels at 25 m/s. Calculate its momentum.
p = mv = 1200 × 25 = 30 000 kg m/s
Example 2: A 0.16 kg cricket ball has a momentum of 6.4 kg m/s. What is its velocity?
v = p ÷ m = 6.4 ÷ 0.16 = 40 m/s
Exam Tip: Always assign a positive direction in momentum questions. Objects moving in opposite directions have opposite signs. This is crucial for collision calculations.
In a closed system (where no external forces act), the total momentum before an event equals the total momentum after the event.
Total momentum before = Total momentum after
This is called the law of conservation of momentum. It applies to all collisions and explosions.
A 2 kg trolley moving at 3 m/s collides with a stationary 1 kg trolley. They stick together. Calculate the velocity after the collision.
Step 1: Total momentum before:
Step 2: Total momentum after (they stick together, total mass = 3 kg):
A 3 kg ball moving at 4 m/s to the right collides head-on with a 2 kg ball moving at 5 m/s to the left. They stick together. Find the velocity after the collision.
Take right as positive:
Step 1: Total momentum before:
Step 2: After collision (total mass = 5 kg):
In an explosion, objects start together (total momentum = 0) and move apart. Conservation of momentum means the total momentum after must also be zero.
A cannon of mass 500 kg fires a 2 kg cannonball at 100 m/s. Calculate the recoil velocity of the cannon.
Total momentum before = 0 (everything is stationary)
Total momentum after = 0:
0 = 200 + 500v 500v = −200 v = −200 ÷ 500 = −0.4 m/s
The negative sign means the cannon moves in the opposite direction to the cannonball (recoil).
Exam Tip: In explosion questions, always start by stating that total momentum before = 0 (because everything is initially stationary). This makes the calculation straightforward — the momenta of the two objects must be equal in size and opposite in direction.
Newton's Second Law can also be expressed in terms of momentum:
force = rate of change of momentum
F=ΔtΔp=tmv−mu
Where:
This equation tells us:
A 60 kg person falls and their velocity changes from 8 m/s to 0 m/s. Calculate the force if they stop in (a) 0.1 s and (b) 1.0 s.
Change in momentum: Δp = mv − mu = 60 × 0 − 60 × 8 = −480 kg m/s
(a) F = Δp ÷ Δt = 480 ÷ 0.1 = 4800 N (b) F = Δp ÷ Δt = 480 ÷ 1.0 = 480 N
Stopping over a longer time dramatically reduces the force. This is the principle behind safety features.
Many safety features in vehicles work by increasing the time over which the momentum changes to zero, thereby reducing the force on the person.
| Safety Feature | How It Works |
|---|---|
| Crumple zones | The front and rear of the car are designed to crumple and deform in a collision, increasing the time of impact |
| Seat belts | Stretch slightly during a collision, increasing the time over which the person decelerates |
| Airbags | Inflate and compress during a collision, increasing the time for the head/body to decelerate |
| Crash helmets | Contain a layer of foam that compresses, increasing the time of impact on the head |
| Crash barriers | Deform on impact, increasing the time the vehicle takes to stop |
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