Question

A uniform ladder of length L and mass m leans against a frictionless vertical wall, making an angle of 56° with the horizontal. The coefficient of static friction between the ladder and the ground is 0.36. If your mass is four times that of the ladder, how high can you climb before the ladder begins to slip?

Answer 1

msFn = Fw; Fn = 5mg; Fw = 2.25mg
FwL sin 60
o
= (mgL/2 + 4mgx)cos 60
o
= 2.25mgL sin 60
o
x = 0.85L; you can go 85% of the way to the top

Answer 2

LOL, I got the wrong picture out the solutions manual. That's how you solve it though, just substitute the values.