Question

Determine the moment of the couple for the system shown below. The forces shown lie in the x-y plane.

d. None of the above

a. -2400k^ ft-lb

c. 2400k^ ft-lb

b. -4800k^ ft-lb

Answer 1

Torque due to a force $\vec{F}$ is $\vec{\tau}=\vec{r}\times\vec{F}$

In the above figure the forces are $\vec{F_1}=F(-\sin\theta\hat{i}+\cos\theta\hat{j})$

$\vec{F_2}=F(\sin\theta\hat{i}-\cos\theta\hat{j})$

where F = 800 lb and $\theta$ is the angle between forces and positive Y-axis.

The forces are acting at points $\vec{r_1}=l\hat{j}$ and $\vec{r_2}=l\hat{j}+\frac{3}{\sin\theta}\hat{j}$

net torque is $\vec{\tau}=\vec{r_1}\times\vec{F_1}+\vec{r_2}\times\vec{F_2}$

$\vec{\tau}=Fl\sin\theta \hat{k}+F(l\sin\theta+\frac{3}{\sin\theta}\sin\theta)(\hat{-k})$

$\vec{\tau}=-3F\hat{k}=-3\times800\hat{k}=-2400\hat{k}\,ft.lb$

answer is (a) $-2400\hat{k}\,ft.lb$