Question

A uniform ladder 5.30  m long rests against a frictionless, vertical wall with its lower end 3.10  m from the wall. The ladder weighs 161  N . The coefficient of static friction between the foot of the ladder and the ground is 0.390. A painter weighing 741  N climbs slowly up the ladder.

a)What is the actual size of the frictional force when the painter has climbed 1.0197  m along the ladder?

b)How far along the ladder can the painter climb before the ladder starts to slip?

completed part

What is the maximum frictional force that the ground can exert on the ladder at its lower end? 352N

Answer 1

The Force diagram of the system can be represented as

To solve the problem we have to find the all variable with the help of free body diagram and Force and Torque balance.

-------------------------------- Solution of Part a --------------------------------------------

Balancing Force in Y direction we can write

Force of friction is given by

Now we also have a relation for torque.

Taking pivot point at base of the ladder. So

So the actual size of frictional force can be calculate by equating force in X direction

So actual frictional force will be 168.7 N when the painter is at height of 1.097 m along the ladder

------------------------------------------------ Solution of Part b ------------------------

To calculate the maximum distance the painter can climb we have to equate maximum frictional force on the ground to the Normal force on the wall that is

replacing F_N2 with max frictional force

So the maximum height the painter can climb is 2.91 m before start to slip.

----------------------- Solution of part c -------------------

Maximum frictional force we have calculated earlier was equal to

which is approx = 352 N