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.
[tex]\Delta p = - p_{o} = -m*v = -55 kg*29m/s = -1595 kgm/s (1)[/tex]
- 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:
[tex]\Delta p = F* \Delta t (2)[/tex]
- 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:
[tex]F_{1} = \frac{\Delta p}{\Delta t_{1}} = \frac{1595kgm/s}{0.035s} = 45571 N (3)[/tex]
[tex]F_{2} = \frac{\Delta p}{\Delta t_{2}} = \frac{1595kgm/s}{0.07s} = 22786 N (4)[/tex]
[tex]F_{3} = \frac{\Delta p}{\Delta t_{3}} = \frac{1595kgm/s}{0.35s} = 4557 N (5)[/tex]
