Question

the cable exerts a force of p = 6.4 kn at the end of the 8 - m - long crane boom (figure 1).
part a
if θ = 30°, determine the placement x of the boom at b so that this force creates a maximum moment about point o.
express your answer to three significant figures and include the appropriate units.

Explanation:

Step1: Recall moment formula

The moment $M$ of a force $P$ about a point $O$ is given by $M = P\times d$, where $d$ is the perpendicular - distance from the line of action of the force to the point $O$. Here, the perpendicular distance $d$ from point $O$ to the line of action of force $P$ is $x = 8\sin\theta+ 1$.

Step2: Substitute the given value of $\theta$

Given $\theta = 30^{\circ}$, we substitute $\theta$ into the formula for $x$. Using the trigonometric value $\sin30^{\circ}=\frac{1}{2}$, we have $x = 8\times\sin30^{\circ}+1$.

Step3: Calculate the value of $x$

$x = 8\times\frac{1}{2}+1=4 + 1=5.00$ m.

Answer:

$x = 5.00$ m