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 =

Question

Physics

Quintin

14 June, 09:40

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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Chasity Pena · Answer 1

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).