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Question: A ladder of length L = 2.4 m and mass m = 19.0 kg rests...

Question: A ladder of length L = 2.4 m and mass m = 19.0 kg rests on a floor with coefficient of static friction ?s = 0.50. Assume the wall is frictionless.

a) What is the normal force the floor exerts on the ladder? = 187.4 N
b) What is the minimum angle the ladder must make with the floor to not slip? = 45 degrees
c) A person with mass M = 61.0 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 c and d)
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Answer #1

Part C

we will determine the forces involved, applying Newton's laws:

(1)

(2)

from equation 2 you get

where m has two contributions, the mass of the ladder and the mass of the person

Part D

From the previous equations we can determine that

Now apply to the ladder the second condition for balance and consider the moments of torsion about an axis.

It can be seen that the minimum angle does not depend on the weight

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