## Statement

difficulty

Alice has had a traffic accident when she was driving at 90 km/h. Thanks she was wearing the seatbelt she survived. Can you say what average force has the seatbelt exerted if the impact last 0.05 s and Alice weights 55 kg?

## Solution

Data

• Alice´s mass: m = 55kg
• Velocity before the impact: vi = 90 km/h = 90·1000/3600 = 25 m/s
• Duration of the impact: t = 0.05 s

Previous considerations

Observe when we say Alice "weights" 55 kg, is just a popular way of saying that the mass of Alice is 55 kg, since the weight is, actually, a force.

Resolution

Impulse-momentum theorem connects the variation of the linear momentum to the impulse itself:

$\stackrel{\to }{J}=\stackrel{\to }{F}·∆t=∆\stackrel{\to }{p}⇒J=F·∆t=∆p$

We know that, after the accident, the final velocity is zero, so we can write:

That variation coincides numerically with the impulse, thus we can write:

Where the sign - indicates the force is against the initial sense of the motion. Observe the relation   $F=\frac{∆p}{∆t}$ belongs to the Newton´s second law, from which we could have started to resolve the problem without the need to recur to the impulse.

## Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

Formulas
Related sections
$\sum _{}\stackrel{\to }{F}=\frac{\Delta \stackrel{\to }{p}}{\Delta t}$
$\stackrel{\to }{p}=m·\stackrel{\to }{v}$