Question

The main purpose of an air bag is to stop a passenger during a car accident in a greater amount of time than if the air bag were not present. For example, consider a 55 kg person traveling at 29 m/s (about 65 mph). Use impulse and momentum to calculate how many newtons of force would be required to stop the person in 0.035 s, 0.070 s, and 0.35 s. Note how the force changes with increased time. (Enter the magnitudes.)

Answer 1

Answer:

a) 45571 N  

b) 22786 N

c) 4557 N

Explanation:

• Since the goal of the airbag is helping the person to stop after the collision in a greater time, this means that the change in momentum must finish when this is just zero.
• In other words, the change in momentum, must be equal to the initial one, but with opposite sign.

       $\Delta p = - p_{o} = -m*v = -55 kg*29m/s = -1595 kgm/s (1)$

• Now, just applying the original form of  Newton's 2nd Law, we know that this change in momentum must be equal to the impulse needed to stop the person:

       $\Delta p = F* \Delta t (2)$

• So, as we know the magnitude of Δp from (1) and we have different Δt as givens, we can get the different values of F (in magnitude) required to stop the person for each one of them, as follows:

       $F_{1} = \frac{\Delta p}{\Delta t_{1}} = \frac{1595kgm/s}{0.035s} = 45571 N (3)$

       $F_{2} = \frac{\Delta p}{\Delta t_{2}} = \frac{1595kgm/s}{0.07s} = 22786 N (4)$

       $F_{3} = \frac{\Delta p}{\Delta t_{3}} = \frac{1595kgm/s}{0.35s} = 4557 N (5)$