Seat belts and air bags save lives by reducing the forces exerted on the driver and passengers in an automobile collision. Cars are designed with a "crumple zone" in the front of the car. In the event of an impact, the passenger compartment decelerates with the car. By contrast, an unrestrained occupant keeps moving forward with no loss of speed (Newton's first law!) until hitting the dashboard or windshield, as we saw in Figure 4.2. These are unyielding surfaces, and the unfortunate occupant then decelerates over a distance of only about 5 mm.
a. A 60 kg person is in a head-on collision. The car's speed at impact is 15 m/s.
Estimate the net force on the person if he or she is wearing a seat belt and if the air
bag deploys.
b. Estimate the net force that ultimately stops the person if he or she is not restrained
by a seat belt or air bag.
c. How does these two forces compare to the person's weight

a) Let's start by calculating the aceleration it takes for the person with a seat belt and air bag to stop, the approximate distance between the floor and the steering wheel is about 50 cm, let's use kinematics to calculate the acceleration

v² = v₀² - 2 a x

0 = v₀² - 2 a x

a = v₀² / 2 x

a = 15² / (2 0.50)

a = 225 m / s²

We calculate the force with Newton's second law

F = m a

F = 60 225

[tex]F_{belt}[/tex] = 1.35 10⁴ N

b) we perform the same calculation for a person without a belt

a = v₀² / 2x

a = 15² / (2 0.005)

a = 22500 m / s²

F = m a

F = 60 22500

F = 1.35 10⁶ N

c) let's calculate the relationship between these two forces

F / [tex]F_{belt}[/tex] = 1.35 10⁶ / 1.35 10⁴

F / [tex]F_{belt}[/tex] = 10²