problem 5. determine the moment of the force about point o in the figure.

Explanation:

Step1: Recall moment formula

The moment of a force $\vec{F}$ about a point $O$ is given by $\vec{M}=\vec{r}\times\vec{F}$, and its magnitude $M = rF\sin\theta$, where $r$ is the position - vector magnitude from the point $O$ to the point of application of the force, $F$ is the magnitude of the force, and $\theta$ is the angle between $\vec{r}$ and $\vec{F}$. Here, $r = 3m$, $F=500N$, and $\theta = 45^{\circ}$.

Step2: Calculate the moment

Substitute the values into the formula $M = rF\sin\theta$. $M=(3m)\times(500N)\times\sin45^{\circ}$ Since $\sin45^{\circ}=\frac{\sqrt{2}}{2}$, we have $M = 3\times500\times\frac{\sqrt{2}}{2}N\cdot m$. $M = 750\sqrt{2}N\cdot m\approx1060.66N\cdot m$.

Answer:

$1060.66N\cdot m$