## College Physics (4th Edition)

We can rank the situations in order of the magnitude of the torque applied to the handle, from smallest to largest: $e \lt a = b = d \lt c$
The magnitude of the torque can be expressed as $\tau = r~F~sin~\theta$, where $r$ is the displacement between the rotation axis and the point where the force is applied, $F$ is the force, and $\theta$ is the angle between the force vector and the displacement vector $r$. We can find the magnitude of the torque for each situation: (a) $\tau = r~ F~sin~\theta$ $\tau = (0.50~m)(20~N)~sin~90^{\circ}$ $\tau = 10~N\cdot m$ (b) $\tau = r~ F~sin~\theta$ $\tau = (0.25~m)(40~N)~sin~90^{\circ}$ $\tau = 10~N\cdot m$ (c) $\tau = r~ F~sin~\theta$ $\tau = (0.25~m)(80~N)~sin~60^{\circ}$ $\tau = 17.3~N\cdot m$ (d) $\tau = r~ F~sin~\theta$ $\tau = (0.25~m)(80~N)~sin~30^{\circ}$ $\tau = 10~N\cdot m$ (e) $\tau = r~ F~sin~\theta$ $\tau = (0.50~m)(40~N)~sin~0^{\circ}$ $\tau = 0$ We can rank the situations in order of the magnitude of the torque applied to the handle, from smallest to largest: $e \lt a = b = d \lt c$