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?

1 Answer
Mar 21, 2016

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


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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!