-A 40 kg uniform ladder,5.0 m long,is placed against a smooth wall at a height of h = 4.0 m.The base of the ladder rests on a rough horizontal surface whose coefficient of static friction is 0.40.An 80 kg block is suspended from the top rung of the ladder,just at the wall.In the figure,the force exerted on the wall by the ladder is closest to:
A)740 N
B)1300 N
C)980 N
D)900 N
E)1100 N

Question

-A 40 kg uniform ladder,5.0 m long,is placed against a smooth wall at a height of h = 4.0 m.The base of the ladder rests on a rough horizontal surface whose coefficient of static friction is 0.40.An 80 kg block is suspended from the top rung of the ladder,just at the wall.In the figure,the force exerted on the wall by the ladder is closest to:
A)740 N 
B)1300 N 
C)980 N 
D)900 N 
E)1100 N

Quizplus · Accepted Answer

The force exerted on the wall by the ladder is equal to the weight of the ladder plus the weight of the block, minus the force of friction between the ladder and the ground. The force of friction is equal to the coefficient of static friction times the normal force between the ladder and the ground. The normal force is equal to the weight of the ladder plus the weight of the block, minus the force exerted on the wall by the ladder. Therefore, the force exerted on the wall by the ladder is:$$F_w = W_l + W_b - F_f$$$$F_w = (40 kg)(9.8 m/s^2) + (80 kg)(9.8 m/s^2) - (0.40)(40 kg + 80 kg)(9.8 m/s^2)$$$$F_w = 740 N$$

-A 40 Kg Uniform Ladder,5