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. Assuming the weight of the ladder to be negligible as compared to the man and assuming the wall to be smooth, determine the force exerted by the ground on 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 x = L^2 - h^2 = 6.5^2 - 6.0^2 = 2.5 m . The forces acting on the ladder are the weight of the man W = mg = 60 9.8 = 588 N 590 N , the normal reaction from the ground N_V , the horizontal friction from the ground N_H , and the normal reaction from the smooth wall N_W . For vertical equilibrium, the vertical force exerted by the ground is: N_V = W 590 N For horizontal