A square metal plate 0.180 m on each side is pivoted about an axis through point

Question

A square metal plate 0.180 m on each side is pivoted about an axis through point O at its center and perpendicular to the plate.

Calculate the net torque about this axis due to the three forces shown in the figure if the magnitudes of the forces are F1= 21 N, F2= 15.5N, F3= 15.8 N. The plate and all forces are in the plane of the page. Take positive torques to be counterclockwise.

A square metal plate 0.180 m on each side is pivoted about an axis through point O at its center and perpendicular to the plate. Calculate the net torque about this axis due to the three forces shown in the figure if the magnitudes of the forces are F1= 21 N, F2= 15.5N, F3= 15.8 N. The plate and all forces are in the plane of the page. Take positive torques to be counterclockwise.

Explanation / Answer

Torque for F1: (21.0)(.09)=1.89
Torque for F2: (26.0)(.09)=2.34
Torque for F3: (53.8)(.09)/sin45=.5.6904

Then I find the net torque by....
-F1+F2+F3=6.14

it should be divided by sin 45 because your perpendicular distance of force from pivot point will be half of diagonal of the square. It you check by trigonometry, it will be

half of side of square * cosine (45)

or

half of side of square / sin (45)

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