A uniform ladder stands on a rough floor and rests against a frictionless wall a

Question

A uniform ladder stands on a rough floor and rests against a frictionless wall as shown in the figure. Since the floor is rough, it exerts both a normal force f_1 and a frictional force on the ladder. However, since the wall is frictionless. It exerts only a normal force N_2 on the ladder. The ladder has a length of L = 4.9 m, a weight of w_L = 61.0 N, and rests against the wall a distance d = 3.75 m above the floor. If a person with a mass of m = 90 kg is standing on the ladder, determine the following. the forces exerted on the ladder when the person Is halfway up the ladder (Enter the magnitude only.) N_1 = N N_2 = N f_1 = N the forces exerted on the ladder when the person is three-fourths of the way up the ladder (Enter the magnitude only.) N_1 = N N_2 = N f_1 = N

Explanation / Answer

through the balance of vertical force

N1 = mg + WL = 61+90*9.8 = 943 N

d = 3.75 m (given)

length of ladder, l = 4.9 m

b = sqrt( l^2 - d^2) = 3.154

from the horizontal balance of force

N2 = f1

from the balance of torque along the point of floor contact:

Case 1:

f1 = N2 = (943*3.154/2)/3.75 = 396.56N

Case 2:

f1 = N2 = (61*3.154/2 +882*3.154*3/4)/3.75 = 582N

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