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 75 kg person is in a head-on collision. The car's speed at impact is 17 m/s. Estimate the net force on the person if he or she is wearing a seat belt and if the air bag deploys.
__________N

b) estimate the net forces that ultimately stop the person if he or she is not restrained by a seat belt or air bag _____________N

c) How do these two forces compare to a person's weight?
F(a) / W = _________
F(b) / W = _________

Explanation / Answer

    Given that the mass of the person M = 75 Kg              Initial car speed is U = 17 m/s              Final speed of the car is V = 0 m/s             The distance travelled by the man before comming to rest is S = 5mm = 5*10-3m     --------------------------------------------------------------------------------------------------                     The equation of motion is   V2 - U2= 2aS           where V and U are the initial and final vcelocities of thebodies.                              0 - ( 17 m/s)2 = 2*a*5*10-3m             then we get accelaration fo the man is a = ---------m/s    Thennet force on the person if he or she iswearing a seat belt and if the air bag deploys is F = m*a =--------- N ----------------------------------------------------------------------------------------------------------------------       The slove the above equationsfor the distance S = 1m then we get    Net force that ultimately stops the personif he or she is not restrained by a seat belt or air bag F =--------N .     Given that the mass of the person M = 75 Kg              Initial car speed is U = 17 m/s              Final speed of the car is V = 0 m/s             The distance travelled by the man before comming to rest is S = 5mm = 5*10-3m     --------------------------------------------------------------------------------------------------                     The equation of motion is   V2 - U2= 2aS           where V and U are the initial and final vcelocities of thebodies.                              0 - ( 17 m/s)2 = 2*a*5*10-3m             then we get accelaration fo the man is a = ---------m/s    Thennet force on the person if he or she iswearing a seat belt and if the air bag deploys is F = m*a =--------- N ----------------------------------------------------------------------------------------------------------------------       The slove the above equationsfor the distance S = 1m then we get    Net force that ultimately stops the personif he or she is not restrained by a seat belt or air bag F =--------N .

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