Question

A ladder of length L = 2.1 m and mass m = 18 kg rests on a floor with coefficient of static friction μs = 0.57. Assume the wall is frictionless.


a. What is the normal force the floor exerts on the ladder?

b. What is the minimum angle the ladder must make with the floor to not slip?

c. A person with mass M = 66 kg now stands at the very top of the ladder.
What is the normal force the floor exerts on the ladder?

d. What is the minimum angle to keep the ladder from sliding?

Answer 1

a. Fn = M*g = 18 * 9.8 = 176.4 N. = Normal force.

b. Fs = u * Fn = 0.57 * 176.4 = 100.5 N. = force of static friction.
Fp - Fs = M*a.
Fp - 100.5 = 18 * 0,
Fp = 100.5 N. = force parallel with plane to overcome Fs.
Fp = Fn*sinA = 100.5.
176.4*sinA = 100.5,
A = 34.75o = max. angle.