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. part A A 57 person is in a head-on collision. The car's speed at impact is 18 . Estimate the net force on the person if he or she is wearing a seat belt and if the air bag deploys. Express your answer to two significant figures and include the appropriate units. F net = Part B Estimate the net force that ultimately stops the person if he or she is not restrained by a seat belt or air bag. Express your answer to two significant figures and include the appropriate units. F net = Part C How do the force in part A compare to the person

Explanation / Answer

d=1m

a)m=57kg ,Vi =18m/s

Vf2 =Vi2+2ad

for constant acceleration Vf=0

0=182+2a*1

a=-162m/s2

Fnet=F=ma =-162*57 =-9234N

b)If there are no restraints, then d = 5 mm

Vf2 =Vi2+2ad

0=182+2a*5*10-3

a=-32,400 m/s2

F=ma =-32400*57 =-1,846,800N

the net force 1.8468*106N to the left

C)the Passenger weight W=mg =57*9.8=558.6N

d)Fnet/W =1.8468*106/558.6 =3306.1

the result from part b is about 3306.1 times person weight

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