An 800-N man stands halfway up a 5.0 m ladder of negligible weight. The base of the ladder is 3.0 m from the wall as shown. Assuming that the wall-ladder contact is frictionless, the wall pushes against the ladder with a force of:
A) 150 N
B) 300 N
C) 400 N
D) 600 N
E) 800 N

Question

An 800-N man stands halfway up a 5.0 m ladder of negligible weight. The base of the ladder is 3.0 m from the wall as shown. Assuming that the wall-ladder contact is frictionless, the wall pushes against the ladder with a force of: 
A) 150 N 
B) 300 N 
C) 400 N 
D) 600 N 
E) 800 N

Quizplus · Accepted Answer

Using the principle of moments, we can determine the force exerted by the wall on the ladder. Taking moments about the base of the ladder, we have:

(800 N)(2.5 m) = Fw(3.0 m)

where Fw is the force exerted by the wall on the ladder. Solving for Fw, we get:

Fw = (800 N)(2.5 m)/(3.0 m) = 667 N

Note that this force is acting perpendicular to the wall. To get the component of this force that is parallel to the wall, we need to multiply it by sin(θ), where θ is the angle between the ladder and the wall. Since the ladder is halfway up the wall, we have:

θ = arctan(2.5 m/3.0 m) = 39.8°

So the force parallel to the wall is:

Fparallel = Fw sin(θ) = (667 N)(sin 39.8°) = 400 N

Therefore, the answer is B) 300 N.

An 800-N Man Stands Halfway Up a 5