Sally wants to hang up some decorations on the side of her house, so she props up a ladder of length L = 3m against a wall at an angle of θ = 50° with respect to the horizontal. The ground is somewhat icy, where the coefficient of static friction between the ground and the ladder’s feet is µ = 0.55; while the wall of her house can be considered frictionless. If Sally has a mass of 60kg and the ladder has a mass of 80kg, what is the max distance that she can climb up the length of the ladder without it slipping? You may assume the ground is perfectly flat, and the wall is perpendicular to the ground.

The max distance is  

Explanation:

A sketch of this question is shown on the first uploaded image

 From the question we are told that

           The length of the ladder is

           The angle with respect to the horizontal is

           The coefficient of static friction is

           The mass of  sally is  

           The mass of ladder is  

The frictional force acting between the ladder and the ground is mathematically represented as

Where g is the acceleration due to gravity

Substituting values

For the ladder not to slipping the frictional force must be equal to the Normal force

 Which implies that the normal force

Let assume that sally is at a distance z from point B as shown in the diagram

Form the ladder to slip then the net torque about must be equal to zero

The net torque is mathematically represented as

Making z the subject

amplitude

hope this

access to city

explanation: