A uniform \(3.0\,\mathrm{m}\) beam of weight \(120\,\mathrm{N}\) is hinged at one end and held horizontal by a vertical cable at the far end. Find the cable tension.

In the pin-hinge model, how many force components can a hinge exert on a planar rigid body?

A \(5.0\,\mathrm{m}\) horizontal beam is supported at its ends. A \(200\,\mathrm{N}\) load is at the midpoint and the beam weight is negligible. Find each support reaction.

A \(6.0\,\mathrm{m}\) light beam is supported at both ends. A \(240\,\mathrm{N}\) load is \(1.5\,\mathrm{m}\) from the left support. Find the support reactions.

A uniform \(3.0\,\mathrm{m}\) beam weighs \(90\,\mathrm{N}\) and is supported at both ends. Find each support reaction.

A \(2.0\,\mathrm{m}\) beam is hinged at the left and held horizontal by a cable at the right. The cable is vertical. A \(60\,\mathrm{N}\) load hangs \(0.50\,\mathrm{m}\) from the hinge. The beam weight is \(40\,\mathrm{N}\). Find the cable tension.

Why is it often useful to take torques about a hinge or support before writing force-balance equations?

A uniform \(5.0\,\mathrm{m}\) ladder of weight \(180\,\mathrm{N}\) leans against a smooth wall at \(60^\circ\) above the floor. Find the horizontal wall force and the floor friction force.

A uniform beam of length \(L\) and weight \(W_b\) is hinged at the left. A sign of weight \(W_s\) hangs from the right end. A cable attached to the right end pulls up and left at angle \(\theta\) above the beam. Derive the cable tension and hinge reactions, state assumptions, and interpret why one hinge reaction is independent of \(W_s\).

A uniform ladder of length \(L\) and weight \(W\) leans at angle \(\theta\) against a smooth vertical wall on a rough floor. Derive the minimum coefficient of static friction needed for equilibrium, state assumptions, and interpret the limits \(\theta\to90^\circ\) and \(\theta\to0\).