Question

A thin rod of lengh L lies on the +x-axis with its left end at the origin. A string pulls on the rod with a force f directed toward P point a distance is above the rod should you attach the string to det the greatest torque about the origin if point P is above the right end of the rod.

Answer 1

Explanations & Calculations

• Assume the force being applied is located as shown in the picture.
• Tension in the string is equal to the magnitude of the applied force.

• Torque around a pivotal point is defined as the force $\times$ perpendicular distance to it from the pivot. $\tau = f \times d$

• Therefore, torque due to the applied force f can be written as $f\cos\theta \times l$
• Now, maximize the product, $\cos\theta$ should be maximum. $-1 \eqslantless \cos\theta \eqslantless1$
• $\cos\theta_{maximum} = 1$

• Therefore, $\tau_{max} = f \times l$

• Maximum torque is obtained when the force is applied on the far end from the pivotal & perpendicular to the rod.