Please explain why I keep getting the incorrect moment about O

[SlothNast]

Please explain why I keep getting the "incorrect" moment about O

Homework Statement

on the xy plane (in mm), there is a 50 N force that travels from point A (-15 , -20) , to point B (40 , 10). The first part of this question asks to find the moment of this force about the origin using Varignon's theorem. the second part asks to find the moment about a point C (0 , 25) using a vector approach.

Homework Equations

theta = arctan (opp / adj)

M = (F)(d)

Fx = F sin(theta) (in my case, for you you can do cosine of complementary, same thing)

Fy = F cos(theta) (again, could do sine of complentary angle if desired)

The Attempt at a Solution

Using Varignons theorem, I broke the force up at point A (going up, and going right, tail to tail). Then, I found the angle between the original force and the horizontal (28.6 degrees for me). Using this, I found that Fx = 43.9 N and Fy = 23.9 N. Since Fy is 15 units left of origin, I found the moment to be (23.9 N)(15 mm) = 358.5 Nmm CW. Then, I did the same for Fx and got (43.9 N)(20 mm) = 878 Nmm CCW. Using conventional directions, I found the net moment to be 878 - 358.5 = 519.5 Nmm CCW. This seems perfectly correct to me, but for some the book claims the correct answer is found by instead doing this.

(43.9 N)(15mm) - (23.9 N)(20 mm) = 179.6

This seems wrong to me, it looks they got the torque arm lengths mixed up, please tell me this seems to be the case, as I have been pulling my hair out all day trying to see why they did what they did.

Thanks

 

[PhanthomJay]

Your answer appears correct, which you can check using the T= r X F vector approach. Looks like they used the wrong lever arm or messed up sin vs. cos . You actually did Fx = F cos theta, and Fy = F sin theta, where theta = 28.6 degrees, which is correct.