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Eclair_de_XII

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## Homework Statement

"To get up on the roof, a person (mass 70.0 kg) places a 6.00-m aluminum ladder (mass 10.0 kg) against the house on a concrete pad with the base of the ladder 2.00 m from the house. The ladder rests against a plastic rain gutter, which we can assume to be friction-less. The center of mass of the ladder is 2.00 m from the bottom. The person is standing 3.00 m from the bottom. Find the normal reaction and friction forces on the ladder at its base."

## Homework Equations

##\theta=cos^{-1}(\frac{1}{3})=tan^{-1}(2\sqrt{2})##

##m_0=10kg##

##s_0=\frac{2 m}{tan\theta}##

##m_1=70kg##

##s_1=\frac{3 m}{tan\theta}##

##||s||=6m##

## The Attempt at a Solution

I'm choosing my lever arm to be the point at which the ladder touches the ground.

##∑|τ|=-g(m_0s_0+m_1s_1)+||s||cos\theta⋅F_r=0##

##∑F_x=-gcos\theta(m_0+m_1)-F_r+f_s=0##

##F_r=f_s-gcos\theta(m_0+m_1)##

##F_r⋅||s||⋅cos\theta=g(m_0s_0+m_1s_1)##

##F_r=\frac{g}{||s||}sec\theta(m_0s_0+m_1s_1)##

##f_s-gcos\theta(m_0+m_1)=\frac{g}{||s||}sec\theta(m_0s_0+m_1s_1)##

##f_s=gcos\theta(m_0+m_1)+\frac{g}{||s||}sec\theta(m_0s_0+m_1s_1)##

Can anyone tell me if I'm going in the right direction? Thanks.

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