Question

8m, 200N uniform ladder rests against a smooth wall. μs beetween the ladder and the ground is 0.6 and the ladder makes a 50° angle with the ground.how far up the ladder can an 80N person climb before the ladder begins to slip?

Answer 1

We need to consider the moment of the forces about a point (see diagram)

Explanation:

For the system to be in equilibrium in the diagram:

1. the horizontal forces must be in balance

2. the vertical forces must be in balance; and

3. the clockwise moments about a point must equal the anticlockwise moments

Hence for

1. Fr (reaction force with wall) = Friction force =`muR`
2. R (normal reaction of ladder with ground= 200N+80N =280N

Hence `Fr= 0.6times280=168N`

We will define the man as being `x` up the ladder. The centre of gravity of the ladder will be 4m along

If we take moments about the point where the ladder touches the ground:
`200.4cos50* + 80xcos50=168*8sin50`
solving for `x` we find x = 10m which suggest he can climb to the top of the ladder
Might need checking!