Seat belts and air bags save lives by reducing the forces exerted on the driver

Question

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 over a distance of about 1 m as the front of the car crumples. An occupant restrained by seat belts and air bags 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. These are unyielding surfaces, and the unfortunate occupant then decelerates over a distance of only about 5 mm.

a). A 58kg  person is in a head-on collision. The car's speed at impact is 13m/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.

Explanation / Answer

a). A 58kg person is in a head-on collision. The car's speed at impact is 13m/s . Estimate the net force on the person if he or she is wearing a seat belt and if the air bag deploys.

F=-mv^2 /2 delta x= -58x13^2 / 2x1=-4901N

where the negative just means that it's pushing the passenger back into the seat

b). Estimate the net force that ultimately stops the person if he or she is not restrained by a seat belt or air bag.

F=-mv^2 /2 delta x= -58x13^2 / 2x0.005=-980200N

This is much bigger than the restrained case

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