Question

To get up on the roof, a person (mass 70.0 kg) places a 6.00-m aluminum ladder (mass 10.0 kg) against the house on a concrete pad with the base of the ladder 2.00 m from the house. The ladder rests against a plastic rain gutter, which we can assume to be frictionless. The center of mass of the ladder is 2.00 m from the bottom. The person is standing 3.00 m from the bottom. Find the normal reaction and friction forces on the ladder at its base.

a) Normal Reaction = 285 N, Friction = 0 N
b) Normal Reaction = 210 N, Friction = 70 N
c) Normal Reaction = 140 N, Friction = 140 N
d) Normal Reaction = 70 N, Friction = 210 N

Answer 1

To find the normal reaction and friction forces on the ladder at its base, you need to set up equations for the vertical and horizontal forces at the contact point with the floor. The normal reaction force can be found using the vertical force equation, and the friction force can be found using the horizontal force equation. The correct answer is option d) Normal Reaction = 70 N, Friction = 210 N.

Step-by-step explanation:

First, let's find the torque exerted by the ladder about the contact point with the floor. The torque is given by the product of the force and the lever arm. The weight of the ladder, acting at its center of mass, creates a clockwise torque. The person's weight, acting at 3.00 m from the bottom, creates a counterclockwise torque.

The torque equation is: Torque = force x lever arm.

To find the normal reaction force and friction force at the base of the ladder, we need to set up equations for the vertical and horizontal forces at the contact point with the floor. The vertical force equation gives us the normal reaction force, and the horizontal force equation gives us the friction force.

The correct answer is option d) Normal Reaction = 70 N, Friction = 210 N.