A 25-kg 10-m ladder is leaning against a frictionless wall with its base making an angle of 32 $\circ$ to the horizontal.What is the magnitude of the force exerted on the ladder by the ground?
A)314 N
B)675 N
C)245 N
D)462 N
E)543 N

Question

Quizplus · Accepted Answer

The force exerted by the ground on the ladder can be found by considering the equilibrium of forces acting on the ladder. Since the wall is frictionless, the force exerted by the wall is horizontal, and the only vertical force supporting the ladder is the normal force from the ground. The weight of the ladder acts downwards at its center of gravity, which is at the midpoint of the ladder.The weight of the ladder, $W$, is given by $W = mg$, where $m = 25\, \text{kg}$ is the mass of the ladder and $g = 9.8\, \text{m/s}^2$ is the acceleration due to gravity. Thus, $W = 25 \times 9.8 = 245\, \text{N}$.The normal force from the ground must balance this weight to keep the ladder in equilibrium, so the magnitude of the force exerted on the ladder by the ground is equal to the weight of the ladder, which is 245 N.

A 25-Kg 10-M Ladder Is Leaning Against a Frictionless Wall ∘\circ∘

A 25-Kg 10-M Ladder Is Leaning Against a Frictionless Wall $\circ$