Question

question 23 of 26
highway safety engineers want to design roadside barriers that will crumple in the event that a car drives off the road and collides with them, slowing down the car more gradually. the average person has a mass of 68 kg and travels on a highway at a velocity of 27 m/s. if the engineers know that the maximum force that a person can safely withstand is 1180 n, approximately how much time is required to crumple the barrier to safely slow the person with this force?
a. 2.5 s
b. 3.7 s
c. 4.1 s
d. 1.6 s

Explanation:

Step1: Recall impulse - momentum theorem

The impulse - momentum theorem is $J = \Delta p$, and impulse $J = F_{avg}\times t$, and change in momentum $\Delta p=m\Delta v$. Here the car comes to rest, so $\Delta v = v_f - v_i=0 - 27\ m/s=- 27\ m/s$, $m = 68\ kg$ and $F_{avg}=1180\ N$.

Step2: Set up the equation

Since $J=\Delta p$, we have $F_{avg}\times t=m\Delta v$. We want to solve for $t$, so $t=\frac{m\vert\Delta v\vert}{F_{avg}}$.

Step3: Substitute values

Substitute $m = 68\ kg$, $\vert\Delta v\vert=27\ m/s$ and $F_{avg}=1180\ N$ into the formula: $t=\frac{68\times27}{1180}$.
$t=\frac{1836}{1180}\approx1.6\ s$

Answer:

D. 1.6 s