Physics, 05.05.2020 17:06 tiggyandrep2dbee

A square metal plate 2.5m on each side is pivoted about an axis though point O at its center and perpendicular to the plate. Calculate the net torque due to the three forces if the magnitudes of the forces are F1=18N, F2=20N, and F3=11N..

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Answer from: cocobelle

Complete Question

The diagram for this question is shown on the first uploaded image

The net torque $\tau = 21.95N \cdot m$

Explanation:

From the question we are told that

The length of each side is L = 2.5 m

The first force is F_1 = 18N

The second force is F_2 = 20 N

The third force is F_3 = 11N

The free body diagram for the question is shown on the second uploaded image

Generally torque is mathematically represented as

$\tau = r * F$

Where $\tau$ is the torque

r is the length from the rotating point to the point the force is applied, this is also the radius of the circular path made

F is the force causing the rotation.

looking at the free body diagram we can deduce that L is the diameter of the circular path made as a result of toque

Now for the torque due to force F_1

$\tau_1 = - F_1 * r_1$

The negative sign is because the direction of F_1 is clockwise

=> $\tau_1 = - F_1 * \frac{L}{2}$

Substituting value

$\tau_1 = - 18 * \frac{2.5}{2 }$

$\tau_1 = - 22.5 N \cdot m$

The torque as a result of the second force is mathematically evaluated as

$\tau_2 = F_2 * r_2$

$\tau_2 = F_2 * \frac{L}{2}$

$= 20 * \frac{2.5}{2}$

$\tau_ 2 = 25 \ N \cdot m$

The torque as a result of the third force is mathematically evaluated as

$\tau_3 =r_3 (F_3 sin \theta + F_3 cos \theta )$

$\tau_3 = \frac{L}{2} (F_3 sin \theta + F_3 cos \theta )$

Where the free body diagram $\theta = 45^o$

$\tau_3 = \frac{2.5}{2} (11 * sin (45) +11 cos (45) )$

$\tau_ 3 = 19.45 \ N \cdot m$

The net torque the mathematically

$\tau = \tau_1 + \tau_2 + \tau_3$

substituting value

$\tau = -22.5 + 25 + 19.45$

$\tau = 21.95N \cdot m$

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