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A uniform ladder of length l and mass m1 rests against a frictionless wall. the ladder makes an angle θ with the horizontal.(a) find the horizontal and vertical forces the ground exerts on the base of the ladder when a firefighter of mass m2 is a distance x from the bottom. (answer using m1, m2, θ, gravity g, l, and x as necessary.) horizontal horizontal force= vertical force= (b) if the ladder is just on the verge of slipping when the firefighter is a distance d from the bottom, what is the coefficient of static friction between ladder and ground? μ =

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shinmin
Balancing horizontal and vertical forces, 

N = (m1 + m2)g and 

F = N' 
To find F, taking moments of forces about B, 

N'Lsinθ = m1g*(L/2)cosθ + m2g * xcotθ 

=> N' = [(1/2)m1 + (x/L)m2 cosecθ] gcotθ 

=> F = N' = [(1/2)m1 + (x/L)m2 cosecθ] gcotθ 
When the ladder is on the verge of sliding,

x = d and F = μN = μ(m1 + m2)g 

=> μ(m1 + m2)g = [(1/2)m1 + (d/L)m2 cosecθ] gcotθ 

=> μ = [(1/2)m1 + (d/L)m2 cosecθ] cotθ / (m1 + m2).

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