How to find the start point of the force vector when given only the end point. Plz click URL for diagram?

Question

I can't seem to figure out where the left most vector starts. I have drawn a diagram, you can view it by going to the following link

http://individual.utoronto.ca/asadzaman/problemdiagram.jpg

Answer 1

I looked at your diagram. For what you're doing -- find the sum of the moments about A, B, and C -- it doesn't matter where you start that force vector on the left.

The vector has both magnitude (25kN) and direction (30 degrees), and it acts on a point (0,3). That's all you need to know.

What matter is how you solve the problem. Resolve each of your three vectors into i and j components:

Through (0,3): 25 sin 30 i - 25 cos 30 j = 12.5 i - 12.5 sqrt(3) j
Through (6.0): 40 j
Through (14,5): - 60(3/5) - 60(4/5) = -36 i - 48 j

You can treat these as six (actually 5, because the x-component of the (6,0) vector is zero) horizontal or vertical vectors, and the moments are easy to determine.

Let's do the moment about the origin (point A). Use the right-hand rule for counterclockwise positive, clockwise negative.

For (0,3) vector: Moment = -12.5*3 + 12.5 sqrt(3) * 0 = -37.5
For (6,0) vector: Moment = +40*6 = +240
For (14,5) vector: Moment = +36*5 - 48*14 = -492

So the moment about the origin A = -37.5 + 240 - 492 = -289.5 kN-m (assuming your distances are in meters).

You can do the same with points B and C, although there's a bit more arithmetic for those points.