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

Step-by-step 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=(v^2)/(2d)`

`a=((11.2)^2)/(2* 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* 78.4`

F = 5880 N

Taking ratios,

`(F)/(W)=(ma)/(mg)`

`(F)/(W)=(a)/(g)`

`(F)/(W)=(78.4)/(9.8)`

`(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.