Question

If a driver makes contact with a steering wheel during a 35 mph crash, she comes to rest in about Δ=15 ms. If, during an identical crash, the driver makes contact with an air bag, she comes to rest in about Δ=110 ms. What is the ratio of the force exerted by the steering wheel to the force exerted by the air bag on the driver?

Answer 1

Answer:

The ratio of forces is 22 : 3.

Explanation:

Case I:

initial velocity, u = 35 mph

final velocity, v = 0

time, t = 15 ms

Case II:

initial velocity, u = 35 mph

final velocity, v = 0

time, t' = 110 ms

let the mass is m.

According to the Newton's second law, the force is given by the rate of change of momentum.

So

$F =\frac{m(v-u)}{t}\\\\F'= \frac{m(v-u)}{t'}\\\\So, \frac{F}{F'} =\frac{t'}{t}\\\\\frac{F}{F'}=\frac{110}{15}=22:3$