Calculating net torque on a plate

[tdashrom]

Homework Statement

I'm supposed to be finding the net torque on a square plate. The sides are 1.7 m in length, with a force acting on each corner (30 N top left pointed right, 60 N top right pointed down, 20 N bottom left pointed up, and 40 N bottom right at an angle of 37 degrees). Just for simplicity I have included the picture of the question, and WebAssign has given the answer.

Homework Equations

τ=Frsin(Θ)

The Attempt at a Solution

I understand how to get part b from the solution in part a. However, I'm completely stuck on how the answer in part a is reached.

The radius in this case should be 1/2 of the side length, so 0.85 m. The 20, 30, and 60 N forces should all have negative torque values because they are turning clockwise, and the 40 N force will be positive. I have tried -.85*(20+30+60)+(40*sin(37)*.85), which does not give the correct answer. If you multiply the three CW forces by sin(45) you get -45.6, which while close is not accepted by the system. I've reworked this 10 times multiple different ways, but still to no avail. Where am I going wrong?

 

[haruspex]

Always double check whether it should be sin or cos.

Btw, the question should make clear it is the torque about the plate's centre that is required. Since there is a net linear force, the torque depends on the axis.

 

[SteamKing]

You have assumed that the force of 40N @ 37° is resolved into only one component which produces a torque around the center of the plate. Is this what really happens?

 

[haruspex]

You have assumed that the force of 40N @ 37° is resolved into only one component which produces a torque around the center of the plate. Is this what really happens?

Yes, that's a better response, thankyou.

 

[tdashrom]

You have assumed that the force of 40N @ 37° is resolved into only one component which produces a torque around the center of the plate. Is this what really happens?

Yes, that's a better response, thankyou.

Got it, thanks!