Why a seatbelt works

When a car stops suddenly, your body must lose all its momentum. Impulse is the change in momentum, and it equals the force acting multiplied by the time it acts. For a fixed change in momentum, a longer stopping time means a smaller force.

A seatbelt stretches slightly and holds you against the seat, so you slow down over a fraction of a second rather than instantly. Without it, you would keep moving forward by inertia and stop very abruptly against the steering wheel or windscreen, over a much shorter time, so the force on you would be far greater.

The same idea explains crumple zones, airbags and even bending your knees when you land from a jump: each lengthens the stopping time to reduce the impulsive force.

In SPM you are expected to link impulse, momentum change and time, and to explain safety features qualitatively.

Force and Motion I

The physics behind it

A seatbelt works through the impulse–momentum principle. Momentum is p = mv, measured in kilogram metres per second (kg m s⁻¹).

The impulse of a force equals the change in momentum, and it also equals force multiplied by the time for which the force acts: FΔt = Δp. Rearranged, F = Δp/Δt, with force in newtons (N) and time in seconds (s).

Because Δp is fixed by how fast you were going and your mass, the only way to reduce the force on you is to increase the stopping time Δt. Consider a 60 kg passenger moving at 20 m s⁻¹ who must come to rest:

• abrupt stop, Δt = 0.10 s: F = Δp/Δt = (60 kg × 20 m s⁻¹) ÷ 0.10 s = 12000 N
• belted stop, Δt = 0.50 s: F = (60 kg × 20 m s⁻¹) ÷ 0.50 s = 2400 N

Both remove the same 1200 kg m s⁻¹ of momentum, but stretching the stop five times longer cuts the force to a fifth. That smaller force is what the belt spreads across your chest and hips.

See it in everyday life

Watch a goalkeeper gather a hard, fast shot. Instead of holding the hands rigid, a good keeper draws the hands and arms backward as the ball arrives, cushioning it into the body.

The ball still has to lose all its momentum, but by moving with it the keeper stretches the time over which it stops, so the force on the fingers is far gentler and the ball is less likely to bounce out or sting.

Try it yourself by catching a heavy ball thrown to you. Snatch at it with stiff arms and it stings your palms; let your hands travel back a short way and the same catch feels soft.

Nothing about the ball changed, only the stopping time.

The same reasoning shapes the thick foam mattress in a high-jump pit. It squashes slowly under the falling athlete, lengthening the time to stop from full speed to rest, so the landing force stays small enough to be safe.

A bare concrete floor would stop the body almost instantly, delivering a dangerous force.

How this comes up in SPM

In Paper 2 this is tested with command words such as explain how a safety feature reduces injury, describe the effect of increasing the collision time, and relate impulsive force to the time of impact. Questions often give a situation in words or a graph and ask you to reason from FΔt = Δp.

Within the Force and Motion chapter it follows on from momentum and the principle of conservation of momentum, and it belongs to the standard on impulse and impulsive force. The same reasoning supports the study of other safety features in vehicles, such as crumple zones, airbags and padded dashboards, and it rests on Newton's laws of motion.

A frequent way to compare situations is to explain why a longer stopping time gives a smaller impulsive force for the same change in momentum. Being able to link mass, velocity, time and force in a clear chain of reasoning is what these items reward.

Source: DSKP KSSM Physics Form 4 and 5 (Versi English) (Bahagian Pembangunan Kurikulum (BPK), KPM)