Shock absorbers

Problem

Shock absorbers. A car falls from a small height onto a track. Explain why shock absorbers increase safety, reasoning in terms of impulse.

Solution

On landing, the change in momentum — that is, the impulse $J = m\,\Delta v$ — is fixed by the falling speed and the mass: it does not depend on how the stop happens.

But $J = F\,\Delta t$: for a fixed impulse, the average force is $F = J/\Delta t$. Shock absorbers, by compressing, lengthen the time $\Delta t$ of the stop. As $\Delta t$ increases, the force $F$ decreases proportionally: $\ev{J = m\,\Delta v \text{ fixed} \Rightarrow F = \frac{J}{\Delta t} \text{ falls if } \Delta t \text{ grows}}$ Long, soft shock absorbers spread the impact over more time, reducing the peak forces on passengers and frame: that’s why they increase safety.

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