Chapter 9, Problem 36P

A biomedical engineer is evaluating an energy-absorbing aviation seat on a vertical deceleration tower, as shown in Fig. P9.36. The acceleration profile of the drop cage is given by

$a\left(t\right)=400\sin \left(50\pi t\right){\text{m/s}}^{\text{2}}$ (a) Knowing that $v\left(t\right)=v\left(0\right)+1{\displaystyle \underset{0}{\overset{1}{\int }}a\left(t\right)dt}$, find and plot the velocity $v\left(t\right)$ of the drop cage. Assume the drop cage starts from rest at $t=0s$.

(b) What is the impact velocity $v_{impact}$ of the drop cage if it takes 20 $ms$ to hit the ground?

(c) The total impulse I is equal to the change in momentum. i.e., $I=\Delta p=p_f-p_i=m{v}_{impact}-m{v}_0$, where in is the mass of the system, $v_0$ is the initial velocity, p is the momentum, and I is the impulse, Find the total impulse after 20 $ms$. Assume that the total mass of the drop cage, seat, and crash test dummy is 1200 kg.