Exercise 10.3 A square metal plate 0.180 m on each side is pivoted about an axis

Question

Exercise 10.3

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 (Figure 1) .

Part A

Calculate the net torque about this axis due to the three forces shown in the figure if the magnitudes of the forces are F1 = 23.0 N , F2 = 17.0 N , andF3 = 16.7 N . The plate and all forces are in the plane of the page. Take positive torques to be counterclockwise.

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Figure 1 of 1

Exercise 10.3

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 (Figure 1) .

Part A

Calculate the net torque about this axis due to the three forces shown in the figure if the magnitudes of the forces are F1 = 23.0 N , F2 = 17.0 N , andF3 = 16.7 N . The plate and all forces are in the plane of the page. Take positive torques to be counterclockwise.

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Figure 1 of 1

Explanation / Answer

given:

side=0.180m18cm
radius=9cm=0.09m
F1=23N
F2=17N
F3=16.7N

Torque for F1: =rxF=(23)(.09)=2.07
Torque for F2: rxF= (17)(.09)=1.53

Torque for F3 = (16.7)(0.09) / (sin 45) = 2.12

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

the net torque by....
-F1+F2+F3=-2.07+1.53+2.12=1.58 N-m

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