Question

An 8.00 m, 201 N uniform ladder rests against a smooth wall. The coefficient of static friction between the ladder and the ground is 0.600, and the ladder makes a 50.0^o angle with the ground. How far up the ladder can an 801N person climb before the ladder begins to slip?

Answer 1

First, you must define a coordinate system.

Choose x to the right as positive and up as thre positive y direction.

Since the wall is smooth it has no friction.

If the ladder is on the verge of slipping, then the force due to friction from the floor will be a maximum:

Summing the force in the y direction

Thus, we can go back and calculate the frictional force

Try summing the forces in the x- direction

Next, Calculating the net torque

Choose the pivot point at the bottom of the ladder (this choice elinimates

Calculate the individual torques for the three remaining forces.

This Plus sign comes from counterclockwise rotation.

This Minus sign comes from clockwise rotation.

This Minus sign comes from clockwise rotation.

Next, on summing the torques and set them equal to zero since it is in equilibrium.

This is the distance that the person climbed up the ladder.