Question

f4 - 1. in each case, determine the moment of the force about point o. (a) 2 m 500 n 3 4 5 (b) 500 n 2 m 3 m 3 4 5

Explanation:

Step1: Recall moment formula

The moment of a force $M$ about a point is given by $M = Fd$, where $F$ is the force and $d$ is the perpendicular - distance from the point to the line of action of the force. First, find the perpendicular component of the force with respect to the line connecting the point $O$ and the point of application of the force.

Step2: For part (a)

The perpendicular component of the $500$ N force with respect to the line from $O$ to the point of application of the force: The vertical distance from $O$ to the point of application of the force is $2$ m. The perpendicular component of the $500$ N force to the rod is $F_{\perp}=500\times\frac{3}{5}=300$ N. Then the moment about point $O$ is $M = F_{\perp}d=(300)\times(2)=600$ N·m (counter - clockwise).

Step3: For part (b)

The perpendicular component of the $500$ N force with respect to the line from $O$ to the point of application of the force: The vertical distance from $O$ to the point of application of the force is $2 + 3=5$ m. The perpendicular component of the $500$ N force to the rod is $F_{\perp}=500\times\frac{3}{5}=300$ N. Then the moment about point $O$ is $M = F_{\perp}d=(300)\times(5)=1500$ N·m (clockwise).

Answer:

(a) $600$ N·m (counter - clockwise)
(b) $1500$ N·m (clockwise)