Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 10 - Rotation - Questions - Page 286: 6

Answer

We can rank the forces according to the magnitude of the torque they create about point $P$: $F_5 \gt F_4 \gt F_2 \gt F_1 \gt F_3$

Work Step by Step

We can write a general expression for the torque: $\tau = r \times F$ $r$ is the displacement vector from the axis of rotation to the point where the force is applied $F$ is the force vector The torque increases as the magnitude of $r$ and $F$ increase. The torque is a maximum when the angle between these two vectors is $90^{\circ}$ and the torque decreases to zero as the angle $\theta$ decreases to zero. The angle between $r_3$ and $F_3$ is zero. Therefore, the torque due to $F_3$ is zero. The angle between $r_1$ and $F_1$ is slightly more than zero. Therefore, the torque due to $F_1$ is slightly more than zero. The angle between $r_2$ and $F_2$ is slightly more than the case with $F_1$. Therefore, the torque due to $F_2$ is slightly more than the torque due to $F_1$ If $F_4$ is extended to where it makes a $90^{\circ}$ with the displacement vector from point P, we can see that the torque due to $F_4$ is greater than the torque due to $F_2$ The torque due to $F_5$ is clearly greater than the torque due to $F_4$. We can rank the forces according to the magnitude of the torque they create about point $P$: $F_5 \gt F_4 \gt F_2 \gt F_1 \gt F_3$
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