Airbag

Problem

Airbag. The airbag saves lives because it “cushions” the impact of the body against the dashboard. Explain why it works, in terms of impulse and force.

Solution

In the impact, the change in momentum of the body — the impulse $J = m\,\Delta v$ — is fixed by the collision speed: the body must go from $v$ to $0$ regardless. What the airbag changes is the time over which this happens.

Against the rigid dashboard the stop lasts very little time ($\Delta t \sim 2\;\text{ms}$); with the airbag it extends to $50$–$100\;\text{ms}$. Since $F = J/\Delta t$, lengthening $\Delta t$ by about $25$ times reduces the average force by about $25$ times: $\ev{J \text{ identical}, \quad F \approx \frac{J}{\Delta t} \text{ about } 25\times \text{ smaller}}$ In addition, the airbag spreads the force over a larger area, reducing the local pressure. Less force and less pressure: that’s why it saves lives.

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Topics: Quantità di moto e urti Concepts: Impulso Skills: Analisi di casi limite e fantafisica