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Classical Mechanics

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Climbing a Ladder

CLMECH-QL11PS

If a ladder leans against a smooth wall and makes a $60^\circ$ angle with the floor, how far up the ladder, X, can a person climb before the ladder begins to slip?

Take the mass of the person to be 10 times the mass of the ladder, and the coefficient of friction $\mu_s =0.5$ between the ladder and the floor. The ladder has a uniform mass density and has length $\ell$.

What is the maximum distance X that a person can climb before the ladder will slip? Created for Albert.io. Copyright 2016. All rights reserved.

A

$$\frac{X}{\ell}=0.90$$

B

$$\frac{X}{\ell}=\frac{\sqrt{2}}{2}$$

C

$$\frac{X}{\ell}=\frac{\sqrt{3}}{2}$$

D

$$\frac{X}{\ell}=0.55$$