A 60-kg person is traveling in a car moving at 16 m/s, when the car hits a barrier. The person is not wearing a seat belt, but is stopped by an air bag in a time interval of 0.20 s. Determine the average force that the air bag exerts on the person?

Oct 6, 2016

$\vec{F} = - 4800 \text{ } N$

$\text{Negative sign means opposite direction.}$

Explanation:

$\vec{F} \cdot \Delta t : \text{impulse}$
$m \cdot \Delta \vec{v} : \text{change of momentum}$

$\vec{F} \cdot \Delta t = m \cdot \Delta \vec{v}$

$\vec{F} : \text{Force}$

$\Delta t : \text{Time interval. } \left(0.20 s\right)$

$m : \text{mass of person. } \left(60 k g\right)$

$\Delta v = \left({v}_{f} - {v}_{i}\right)$

${v}_{f} : \text{final velocity of person. } \left({v}_{f} = 0\right)$

${v}_{i} : \text{initial velocity of person. "(v_i=16" "m/s}$

$\vec{F} \cdot 0.2 = 60 \left(0 - 16\right)$

$\vec{F} \cdot 0.2 = 60 \cdot \left(- 16\right)$

$\vec{F} \cdot 0.2 = - 960$

$\vec{F} = - \frac{960}{0.20}$

$\vec{F} = - 4800 \text{ } N$