A 100N uniform ladder, 8.0m long, rests against a smooth vertical wall. the coefficient of static friction between ladder and the floor is 0.40. What minimum angle can the ladder make with the floor before it slips?

Question

A 100N uniform ladder, 8.0m long, rests against a smooth vertical wall. the coefficient  of static friction between ladder and the floor is 0.40. What minimum angle can the ladder make with the floor before it slips?

im thinking 100*0.40=40 degrees? can someone tell me if this is right or give me the formula as to how to get it right?

drwls · Accepted Answer

No, that is not right. You can't multiply a force (100 N) by a dimensionless number (0.4) and end up with degrees.

You need to write a moment balance equation for for the ladder an angle of tilt that causes the friction force on the floor to equal the maximum static friction, which is 0.40^100 = 40 N

Write an equation for the total moment about the point where the ladder touches the wall, and set that moment equal to zero. Three terms will contribute: the ladder's mass acting through the center of the ladder, a horizontal friction force of 40 N, and an upward force at the wall of 100 N.