In the following, a ladder of length L = 15.0 m and weight FWl = 725 N leans aga

Question

In the following, a ladder of length L = 15.0 m and weight FWl = 725 N leans against a frictionless wall. The angle the ladder makes with the rough ground is 53 degree. The ladder's center of weight is 0.45 L from the lower end. A firefighter of weight Fw2 = 955 N climbs the ladder until his center of mass is 0.65 1, from the lower end. Find the height h of the ladder's upper end above the ground; Find the magnitude of the force on the ladder from the wall; Find the magnitude of the static frictional force on the ladder from the rough ground; and Find the magnitude of the support force on the ladder from the rough ground.

Explanation / Answer

(a) Height, H = Lsin = 15 * sin53o = 11.98 m

(b) Let Nw be the force on the ladder by the wall.

Torque about the lower end of the ladder is zero.

NwLsin - Fwl(0.45L)cos - Fw2(0.65L)cos = 0

=> Nw = (0.45Fwl + 0.65Fw2)/ tan = [(0.45 * 725) + (0.65 * 955)] / tan53o = 713.6 N

(c) Static frictional force on the ground, f = Nw = 713.6 N

(d) Support force from the ground, Ng = Fwl + Fw2 = 725 + 955 = 1680 N

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