Question

A 75.0-kg person is riding in a car moving at 20.0 m/s when the car runs into a bridge abutment.

1. The average force on the person if he is stopped by a padded dashboard that compresses an average of 1.00 cm is
2. The average force on the person if he is stopped by an airbag that compresses an average of 15.0 cm is

Answer 1

1) Let's first find the acceleration of the car:

$$a=\dfrac{v_f^2-v_i^2}{2d},$$ $$a=\dfrac{0-(20\ \dfrac{m}{s})^2}{2\cdot1.0\cdot10^{-2}\ m}=-2\cdot10^{4}\ \dfrac{m}{s^2}.$$

The sign minus means that the car decelerates.

Finally, we can find the average force on the person:

$$F_{avg}=ma=75\ kg\cdot(-2\cdot10^{4}\ \dfrac{m}{s^2})=-1.5\cdot10^{6}\ N.$$

The sign minus means that the average force on the person directed away from the bridge abutment.

2) Let's first find the acceleration of the car:

$$a=\dfrac{v_f^2-v_i^2}{2d},$$ $$a=\dfrac{0-(20\ \dfrac{m}{s})^2}{2\cdot15.0\cdot10^{-2}\ m}=-1.33\cdot10^{3}\ \dfrac{m}{s^2}.$$

The sign minus means that the car decelerates.

Finally, we can find the average force on the person:

$$F_{avg}=ma=75\ kg\cdot(-1.33\cdot10^{3}\ \dfrac{m}{s^2})=-1.0\cdot10^{5}\ N.$$

The sign minus means that the average force on the person directed away from the bridge abutment.