Torque on a square plate with multiple forces acting on it

[moondawg]

Homework Statement

A square metal plate .18m on each side is pivoted about an axis through point O at its center and perpendicular to the plate. Calculate the net torque of the 3 forces acting on the forces. The magnitudes of the forces are F1= 18N F2=26N F3=14N. *** picture a square with each side measuring .18m with point O directly in the middle.. then picture the arrow of F1 acting straight down (@ a 90 degree angle) on the top right corner of the square; F2 acting straight down(@ a 90 degree angle) on the top left corner of the square; and then F3 acting up and to the right at a 45 degree angle on the bottom right corner***

Homework Equations

T=r(Fsinx)

The Attempt at a Solution

So I found torque for each of the forces using the equation above and got T1=-1.62N/m(clockwise) T2=2.34N/m(counterclockwise) and T3=.89N/m(counterclockwise) and then added them together to get a net torque of 1.61N/m counterclockwise but that answer, according to the back of the book, is wrong... the back of the book says the answer is 2.5 N/m but idk what i did wrong?! help??

 

[anathema]

Thank you for your question. To find the net torque, you need to take into account the direction of each torque. T1 and T3 are in opposite directions, so they will cancel each other out. T2 is the only torque in the counterclockwise direction, so it will be the net torque. Therefore, the correct answer is T2 = 2.34 N/m counterclockwise.

I hope this helps. Let me know if you have any further questions.