Question

In a crash test the strapped-in, 75-kg dummy moves a distance of 0.80 m when the test car is slammed straight into a wall at 11.2 m/s (~25 mph). The average force acting on the dummy during the collision is how many times his own weight?

Answer 1

Explanation:

It is given that,

Mass of the dummy, m = 75 kg

Distance, d = 0.8 m

Initial speed of the dummy, u = 0

Final speed of the dummy, v = 11.2 m/s

Firstly finding the acceleration of the test car. Using third equation of motion to find it as :

$v^2-u^2=2ad$

$v^2=2ad$

$a=\dfrac{v^2}{2d}$

$a=\dfrac{(11.2)^2}{2\times 0.8}$

$a=78.4\ m/s^2$

Let F is the average force. It is given by the product of mass and acceleration. It is given by :

$F=ma$

$F=75\times 78.4$

F = 5880 N

Taking ratios,

$\dfrac{F}{W}=\dfrac{ma}{mg}$

$\dfrac{F}{W}=\dfrac{a}{g}$

$\dfrac{F}{W}=\dfrac{78.4}{9.8}$

$\dfrac{F}{W}=8$

$F=8W$

The average force acting on the dummy during the collision is 8 times of his weight. Hence, this is the required solution.