Question

suppose that f1 = 240 n and f2 = 450 n. in the case (b) (figure 2), determine the moment of the force about point o. express your answer to three significant figures and include the appropriate units. enter positive value if the moment is counterclockwise and negative value if the moment is clockwise. in the case (c) (figure 3), determine the moment of the force about point o. express your answer to three significant figures and include the appropriate units. enter positive value if the moment is counterclockwise and negative value if the moment is clockwise.

Explanation:

Step1: Recall moment formula

The moment of a force $M$ about a point is given by $M = F\times d$, where $F$ is the force and $d$ is the perpendicular - distance from the point to the line of action of the force.

Step2: Analyze the direction and calculate

The force $F_1 = 240\ N$ acts at a distance $d_1=1\ m$ from point $O$. The moment due to $F_1$, $M_1=F_1\times d_1$. The force $F_2 = 450\ N$ acts at a distance $d_2 = 1 + 3=4\ m$ from point $O$. The moment due to $F_2$, $M_2=F_2\times d_2$. The net moment $M_O$ about point $O$ is $M_O=F_1\times d_1+F_2\times d_2$.
Substitute $F_1 = 240\ N$, $d_1 = 1\ m$, $F_2 = 450\ N$, and $d_2 = 4\ m$ into the formula:
\[

$$\begin{align*} M_O&=240\times1 + 450\times4\\ &=240+1800\\ &=2040\ N\cdot m \end{align*}$$

\]
Since the combined effect of the two forces creates a counter - clockwise moment, the value is positive.

Answer:

$2040\ N\cdot m$