A 6.5 m long ladder rests against a vertical wall, reaching a height of 6.0 m . A 60 kg man stands halfway up the ladder. Determine the torque of the force exerted by the man on the ladder about the upper end of the ladder.

Step-by-step solution

Let the length of the ladder be L = 6.5 m and the height of the wall it reaches be h = 6.0 m . The distance of the base of the ladder from the wall is given by the Pythagorean theorem: x = L^2 - h^2 = (6.5)^2 - (6.0)^2 = 42.25 - 36.00 = 6.25 = 2.5 m The man stands halfway up the ladder. The horizontal distance of the man from the vertical wall (which passes through the upper end of the ladder) is: r_ = x 2 = 2.5 2 = 1.25 m The force exerted by the man on the ladder is equal to his weight, acting vertically downward