Question

A body with a mass of 1 ton is attached to a rod with a hinge, the rod is 12 meters long and the hinge is 2 meters from the body.

If a force of 120 Newtons is applied to the rod at the far end of the body, find the force exerted on the body.

What force should be applied to lift the body at a torn speed?

Answer 1

Explanations & Calculations

• Distance to the applied force is 10m from the hinge & 2m from to the body.
• When a force is applied on the far end, an equal torques are generated about the hinge. Therefore,

$\qquad\qquad \begin{aligned} \small \Tau_{left}&=\small \Tau_{right}\\ \small 120N\times10m&=\small f\times2m\\ \small f&=\small 600N \end{aligned}$

• Since the weight of the body is approximately $\small (1000kg\times10ms^{-2}=)$ $\small 10^4N$, this generated force is insufficient.
• To lift the weight, a force which capable of generating an equal torque around the hinge to the torque generated by the body is needed.
• Therefore, if that force is F,

$\qquad\qquad \begin{aligned} \small \Tau_{left}&=\small \Tau_{right}\\ \small F\times10m&=\small 1000kg\times9.8ms^{-2}\times2m\\ \small F&=\small 1960\,N \end{aligned}$

• This force is needed to just lift the weight, and any greater force will impose a greater force than mg on the body. If the body is not capable of tolerating it, body would tear off.