Raised Drawbridge

Solution

The drawbridge is in static equilibrium, so the net force and net torque acting on it must be zero:

A correct free-body diagram must include every external force acting on the drawbridge.

Step 1: Forces due to gravity

Because the beam is uniform, its weight $Mg$ acts at its center of mass, located at $\frac{L}{2}$ from the hinge, and it acts vertically downward.

The person exerts a downward force of magnitude $mg$ on the beam at the person's location, $\frac{3}{4}L$ from the hinge.

Step 2: Tension from the chain

The chain exerts a tension force $T$ on the drawbridge at the free end. Since a chain can only pull along its length, the force $T$ must be directed along the chain away from the drawbridge, meaning up and toward the wall.

Step 3: Hinge reaction force

A hinge can exert reaction forces in both horizontal and vertical directions, so the hinge force is represented by two components applied at the hinge: a horizontal component $F_{Hx}$ and a vertical component $F_{Hy}$.

A correct diagram therefore shows $Mg$ at $\frac{L}{2}$ downward, $mg$ at $\frac{3}{4}L$ downward, $T$ at the free end along the chain, and both $F_{Hx}$ and $F_{Hy}$ at the hinge.