Seatbelt

Problem

Seatbelt. A car brakes sharply. Explain in five lines why an unbelted passenger is thrown forward, and why the seatbelt does not violate Newton’s first law.

Solution

Before braking, passenger and car move together at the same speed $v$. When the car brakes, the brakes decelerate the car, but no horizontal force acts, by itself, on the passenger’s body. By the principle of inertia (first law) the passenger therefore tends to continue in a straight line at speed $v$: relative to the slowing cabin, it looks as if they are “flung forward”, but in reality it is the car slowing down beneath them. There is no force pushing them forward: there is the absence of a force that would slow them down.

The seatbelt does not violate the first law — indeed it confirms it: precisely because, unconstrained, the body would continue undisturbed, a real external force is needed to decelerate it together with the car. The seatbelt is that external force, directed backward. Without it, the only braking force would be the impact against the steering wheel or windscreen, in a very short time and with enormous forces.

$\ev{\text{Inertia: the body continues straight; the seatbelt supplies the external force that decelerates it.}}$

Links

Topics: Dynamics Concepts: Newton’s first law