Question

two forces P and Q pass through a point A which is 4 ft to the right of and 3 ft above a moment center O. force P is 200 lb directed up to the right at 30degrees with the horizontal and force Q is 100 lb directed up to the left at 60degrees with the horizontal, determine the moment of the resultant of these two forces with respect to O.

Answer 1

Drawing the situation described in the problem is extremely helpful. I've included a sketch of what things look like (bear with me, it's not a high quality image).

We're given P & Q and asked to find their resultant; so we have to find their x and y components first.

P = 200 lb
Px = P * cos 30 = 200 * cos 30
Py = P * sin 30 = 200 * sin 30

Q = 100 lb
Qx = Q * cos 60 = 100 * cos 60
Qy = Q * sin 60 = 100 * sin 60

It's asking for a resultant, Fr, of the two forces, so I'll make a table to help you see what's going on.

Force | x component | y component
P + 200 * cos 30 + 200 * sin 30
Q - 100 * cos 60 + 100 * sin 60
__________________________________________________________________________
Fr +200 * cos 30 - 100 * cos 30 +200 * sin 30 + 100 * sin 60

Note: Qx is negative because of my sign convention. I'm considering the positive x and positive y directions as positive. Qx is pointing in the negative x direction so we have to include a negative sign with Qx.

Now you can calculate the x and y components of the resultant force, Fr.
I'm not yet done but I want to make sure you're following along.

If you understand what I just did, which direction is the x component of Fr pointing in and which direction is the y component of Fr pointing in?