# 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?

Mar 21, 2016

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 =$\mu R$
2. R (normal reaction of ladder with ground= 200N+80N =280N

Hence $F r = 0.6 \times 280 = 168 N$

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:
$200.4 \cos 50 \cdot + 80 x \cos 50 = 168 \cdot 8 \sin 50$
solving for $x$ we find x = 10m which suggest he can climb to the top of the ladder
Might need checking!