Question

A 12-ft ladder, weighing 40 lb, leans against a frictionless vertical wall. The lower end of the ladder rests on rough ground, 4 ft away from the wall. Determine the reactions at both ends.

a) 20 lb, 40 lb
b) 30 lb, 40 lb
c) 40 lb, 40 lb
d) 40 lb, 80 lb

Answer 1

The normal reaction force from the floor is equal to the weight of the ladder, so the reactions at both ends are 40 lb each. Therefore, the correct answer is option C.

Step-by-step explanation:

First, let's draw a free-body diagram of the ladder:

• The weight of the ladder (40 lb) acts downwards at its center of mass, which is 6 ft from the lower end of the ladder.
• The normal reaction force from the floor acts upwards at the point of contact between the ladder and the floor.
• The reaction force from the wall acts horizontally and away from the wall at the point of contact between the ladder and the wall.

Since the ladder is at rest, the sum of the forces in the vertical direction is zero, which means the normal reaction force from the floor is equal to the weight of the ladder.