Question

Determine the magnitude of the resultant force and the moment about the origin. Note: the symbol near the 140 N-m moment are not additional forces. They represent the rotation caused with a magnitude of 140 N-m.

Answer 1

R = 148.346 N

M₀ = - 237.2792 N-m

Step-by-step explanation:

Point O is selected as a convenient reference point for the force-couple system which is to represent the given system

We can apply

∑Fx = Rx = - 60N*Cos 45° + 40N + 80*Cos 30° = 66.8556 N

∑Fy = Ry = 60N*Sin 45° + 50N + 80*Sin 30° = 132.4264 N

Then

R = √(Rx²+Ry²) ⇒ R = √((66.8556 N)²+(132.4264 N)²)

⇒ R = 148.346 N

Now, we obtain the moment about the origin as follows

M₀ = (0 m*40 N)-(7 m*60 N*Sin 45°)+(4 m*60 N*Cos 45°)-(5 m*50 N)+ 140 N-m + (0 m*80 N*Cos 30°) + (0 m*80 N*Sin 30°) = - 237.2792 N-m (clockwise)

We can see the pic shown in order to understand the question.