Question

5) A 5.0-m long, 12-kg, ladder rests against a smooth vertical wall with the bottom of the ladder 3.0 m from the wall. The coefficient of static friction between the floor and the ladder is 0.28. What distance measured along the ladder from the bottom, can a 60-kg person climb before the ladder starts to slip? Ans: 1.7 m

Answer 1

let theta is the angle made by the ladder with horizontal.

theta = cos^-1(3/5)

= 53.1 degrees

let m = 12 kg, M = 60 kg

let x is the distance measured from the bottom of the ladder where the person can climb.

let Fw is the force exerted by the wall

Apply net torque abot the bottom = 0

Fw*5*sin(53.1) - M*g*x*sin(90-53.1) - m*g*(5/2)*sin(90-53.1) = 0

Fw*4 - 60*9.8*x*cos(36.9) - 12*9.8*2.5*cos(36.9) = 0

Fw - 15*9.8*x*cos(36.9) - 3*9.8*2.5*cos(36.9) = 0

Fw = 117.5*x + 58.78

now apply, Fnety = 0

N - M*g - m*g = 0

N = (M+m)*g

= (60 + 12)*9.8

= 705.6 N

now apply, Fnetx = 0

Fw - Fs = 0

Fw - N*mue_s = 0

117.5*x + 58.78 - 705.6*0.28 = 0

==> x = 1.18 m <<<<<<<<-----------------Answer