Question

A 77.5-kg person is riding in a car moving at 17.5 m/s (assume this is the positive direction) when the car runs into a bridge abutment. This problem will illustrate why the invention of the airbag dramatically improved the safety of automobiles. Calculate the horizontal component of the average force, in newtons, on the person if he is stopped by a padded dashboard that compresses an average of 0.85 cm. Calculate the horizontal component of the average force, in newtons, on the person if he is stopped by an air bag that compresses an average of 14 cm

Answer 1

The average force on a person in a car collision can be calculated using the change in momentum equation. The force can be calculated for both a padded dashboard and an airbag. The calculations involve factors such as mass, change in velocity, compression distance, elastic constant, pressure, and surface area.

Step-by-step explanation:

When a car stops suddenly, the person inside experiences a change in momentum. The average force on the person can be calculated using the equation:

F_avg = Δp / Δt

Where Δp is the change in momentum and Δt is the time taken for the person to come to a stop. In this case, the change in momentum can be calculated as:

Δp = mΔv

Where m is the mass of the person and Δv is the change in velocity. For the case of the padded dashboard, the average force can be calculated using the compression distance and the elastic constant of the dashboard material. For the case of the airbag, the average force can be calculated using the pressure inside the airbag and the surface area it exerts force on.