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Classical Mechanics

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Moderate

Ladder Against the Wall

CLMECH-BDNXCJ

A ladder is leaning against the wall. Treat the ladder as having a uniform mass density ( the center of gravity is in the center of the ladder), the wall is smooth and therefore exerts only a normal force, whereas the floor is rough with a coefficient of static friction, $\mu_s$.

What is the minimum angle, $\theta$, such that the ladder does not slide on the floor and fall down?

The ladder leans against a smooth wall and is kept from slipping by a rough floor. Find the minimum angle between the floor and the ladder. Created for Albert.io. Copyright 2016. All rights reserved.

A

$$\theta=2\,\mu_s$$

B

$$\theta=\frac{1}{2\,\mu_s}$$

C

$$\\\theta=tan^{-1}(\frac{1}{2\,\mu_s})$$

D

Without knowing the mass this question cannot be answered.