GCSE Physics revision

Changes in momentum (physics only)

Momentum (HT only)

AQA 4.5.7.3

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AQA student objectives

Learning pathway

ALL 🎯

Explain how airbags, seat belts and helmets reduce injury by increasing the time over which momentum changes.

MOST 🎯🎯

Apply the relationship between force and rate of change of momentum to explain how safety features reduce forces during a collision.

SOME 🎯🎯🎯

Analyse and compare how different safety features reduce the force experienced during a collision.

Revision summary

Read on screen, then print for Cornell-style active revision.

Newton's Second Law states that force equals mass multiplied by acceleration: F = ma.
Acceleration is defined as the change in velocity divided by the time taken: a = rac{Δ v}{t}.

Substituting the expression for acceleration into Newton's Second Law gives: F = rac{m Δ v}{t}.
Since m Δ v represents the change in momentum, this simplifies to F = rac{Δ p}{t}, meaning force equals the rate of change of momentum.
A large change in momentum occurring over a very short time produces a very large force.

2. The Force–Momentum EquationAQA

Substituting the expression for acceleration into Newton's Second Law gives: F = rac{m Δ v}{t}.
Since m Δ v represents the change in momentum, this simplifies to F = rac{Δ p}{t}, meaning force equals the rate of change of momentum.
A large change in momentum occurring over a very short time produces a very large force.

A car of mass 1,500 kg travelling at 20 m/s comes to a stop in 0.5 s when it hits a wall.
Using F = rac{m Δ v}{t}, the calculation gives F = rac{1500 × 20}{0.5} = 60{,}000 N.
This enormous force of 60,000 N illustrates why high-speed collisions over short time intervals are so dangerous.

3. Worked Example: Car Crash CalculationAQA

A car of mass 1,500 kg travelling at 20 m/s comes to a stop in 0.5 s when it hits a wall.
Using F = rac{m Δ v}{t}, the calculation gives F = rac{1500 × 20}{0.5} = 60{,}000 N.
This enormous force of 60,000 N illustrates why high-speed collisions over short time intervals are so dangerous.

The key principle behind all safety features is to extend the time over which the momentum change occurs, which reduces the force experienced.
This is a direct consequence of the equation F = rac{Δ p}{t}: keeping Δ p the same but increasing t makes F smaller.

Airbags inflate and compress as the passenger's head hits them, increasing the time of the momentum change and reducing the force on the head.
Seat belts are designed to stretch slightly during a collision, extending the time taken for the passenger to decelerate and lowering the force on the body.
Crumple zones are built into the front of cars so they deform during a crash, increasing the collision time and reducing the force transmitted to the driver.

5. Safety Features in CarsAQA

Airbags inflate and compress as the passenger's head hits them, increasing the time of the momentum change and reducing the force on the head.
Seat belts are designed to stretch slightly during a collision, extending the time taken for the passenger to decelerate and lowering the force on the body.
Crumple zones are built into the front of cars so they deform during a crash, increasing the collision time and reducing the force transmitted to the driver.

Cycle helmets contain a polystyrene lining that compresses on impact, extending the time of the momentum change and cushioning the blow to the head.
Rubber tiles in playgrounds and crash mats in gymnastics halls compress when landed on, increasing collision time and reducing the force on the body.

Momentum: p = mv Force as rate of change of momentum: F = rac{Δ p}{t} All safety devices work by increasing t so that F decreases, even though the total change in momentum Δ p stays the same.