Question

Problem 89

Answer 1

Given information

We are given that:-

Climber weight.

static friction coefficient between wall and shoes    

static friction coefficient between wall and shoes    

Step-by-step explanation

Step 1.

Since the walls are vertical, the normal forces work horizontal, perpendicularly away from the wall faces. We assume that the frictional forces are at their maximum value.

 

The FBD of the problem is as below:

Let the normal force left wall be and the normal force from the right wall be .

Since there is no motion in horizontal direction, both these forces must be balanced:

 

Now, since the weight of the person is a force directed downward, the frictional forces on both the walls must be directed upward and their sum must be equal and opposite to the weight so that the person does not fall.

Let the frictional force acting on the left wall be and the frictional force acting on the right wall be .

Now, the equation of motion in the vertical direction becomes:

 

 

since