Question

A uniform ladder 5.0 m long and weighing 200 N is placed against a very smooth wall so that the lower end of the ladder is 3.0 m from the wall. If the coeficient of friction between the ladder and the ground is 0.50, determine the maximum distance that a 700 N man could climb along the length of the ladder before the ladder slips.

Answer 1

3,4,5 triangle

Vertical forces
200 N down at middle, 1.5 m from foot of ladder
700 N down at (3x/5) from foot of ladder
900 N up at foot of ladder

Horizontal forces
F at top of ladder, 4 m above base
900 mu at base of ladder = F at top

take moments about
base of ladder
700 (3x/5) + 200(1.5) - 4F = 0
but F = .5*900 = 450
so
700(3x/5) +300 = 1800
420 x = 1500
x = 3.57

Answer 2

what about the friction?

Answer 3

where did the 3x/5 come from