Question

Abby, who has a mass of 45.0 kg, is riding at 40.0 m/s in her red sports car whenshe must suddenly slam on the brakes to avoid hitting a deer crossing the road. Shestrikes the air bag, that brings her body to a stop in 0.500 s. What average forcedoes the seat belt exert on her?

Answer 1

We are given the following information

Mass = m = 45.0 kg

Initial speed = vi = 40.0 m/s

Time = t = 0.500 s

We are asked to find the average force that the seat belt exerted on her.

Recall from Newton's second law of motion,

$F=m\cdot a$

Where a is the acceleration of the car and is given by

$v_f=v_i+a\cdot t$

Where vf is the final velocity of the car that must be 0 since the car was stopped.

$\begin{gathered} 0=40.0+a\cdot0.500 \\ a=\frac{-40.0}{0.500} \\ a=-80\; \; \frac{m}{s^2} \end{gathered}$

The negative sign indicates deacceleration since the card was stopped.

So, the force is

$\begin{gathered} F=m\cdot a \\ F=45\cdot80 \\ F=3600\; N \end{gathered}$

Therefore, the seat belt exerted a force of 3600 N on her.