A ladder of mass 39.4 kg and length 2.88 m is leaning against a wall at an angle θ. The coefficient of static friction between ladder and floor is 0.282; assume that the friction force between ladder and wall is zero. What is the maximum value that θ can have before the ladder starts slipping?
The answer is 29.4 degree. How do I get this answer?
Draw the figure.
Put the ladder weight W as a downwrard force at the center of the ladder.
The force at the top of the latter is Normal to the wall, Fh, pushing against the ladder.
At the bottom of the ladder, a normal force, Fv, and a horizontal force Fh2
So immediately you know Fh2=mu*Fv
Now, sum moments about the the base of the ladder.
W*1.44*cosTheta-Fh*2.88*sinTheta=0
Now sum horizontal forces: Fh+Fh2=0
Sum vertical forces: Fv+W=0
You have three unknowns, Fv, Fh, Theta
Happy solving.