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.

1- A 65 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.

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

3- How do the force in part A compare to the person’s weight?

4- How do the force in part B compare to the person’s weight?

Explanation / Answer

1)
A 65kg person is in a head-on collision.
Car's speed at impact = 17m/s
Distance Travelled by passenger = 1m

Deceleration Vf^2 = Vi^2 -2ad

0 = 17^2 - 2*a*1m
a = 17^2/ 2
a = 144.5 m/sec^2
F= ma
F = 65 x 144.5
F = 9392.5N

2)
Estimate the net force that ultimately stops the person if he or she is not restrained by a seat belt or air bag
Distance Travelled by passenger = 5mm = 0.005 m
Vf^2 = Vi^2 -2ad
0= 17^2 - 2*a*(.005)
a = 17^2 / (2 x 0.005)
a =28900 m/s^2

F= ma
F = 65kg x (28900 m/s^2)
F =1.878 * 10^6 N

3)
Weight of person = 65 * 10 = 650 N
9392.5/650 = 14.44
In part 1, With the airbag/seatbelt, person would feel the force of ~ 14 times his/her weight.

4)
Weight of person = 65 * 10 = 650 N
1.878 * 10^6/650 = 2889.2
In part 2, Without airbag/seatbelt, person would feel the force of ~ 2889 times his/her weight.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.