A person using a ladder supported on vertical wall is 3/4 of the way up the ladder. If the person climbing the ladder has a weight of 980 newtons and the ladder is 4.89 meters long, how far from the wall can the base of the ladder be placed, and not slip? The coefficient of friction between the base of the ladder and the ground is 0.34. Assume that there is no friction between the ladder and the wall and that the ladder is effectively weightless.

Answer 1

Set the moment about the ladder/wall contact point equal to zero. Assume the ladder has no mass. (That is probably not a good assumption, but they did not provide a value). Let the ladder length be L, and the distance of the ladder bottom from the wall be x. The person's weight (980 N)cancels out. 0.34 is the STATIC friction coefficient. The normal force of the ground on the bottom of the ladder is 980 N.

(x/4)*980 + sqrt(L^2 -x^2)*0.34*980 = x*980
3x/(4L) = 0.34*sqrt[1 - (x/L)^2]
0.5625*(x/L)^2 = 0.1156[1 - (x/L)^2]
0.6781*(x/L)^2 = 0.1156
x/L = 0.413

Answer 2

thanks for your timely help.