Why Can't I Solve This Static Friction Ladder Problem?

AI Thread Summary
The discussion revolves around a static friction problem involving a ladder, where the user is struggling to derive the coefficient of friction (μ) which is expected to equal 0.18. The user has provided a free body diagram (FBD) and attempted to set up equations based on the forces and moments acting on the ladder. Despite multiple substitutions and calculations, they are unable to arrive at the correct value for μ. A key point raised is that the angles in the FBD are incorrectly labeled and should be adjusted to 90 degrees minus theta. The conversation emphasizes the importance of accurate angle representation in solving static friction problems.
jordan35
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Homework Statement


See attachment.


Homework Equations


F = μN

The Attempt at a Solution


I attached the FBD I drew. I then did
ƩFx = FA + FBcosθ - NBsinθ = 0
ƩFy = NA -W + NBcosθ + FBsinθ = 0
ƩMA = 19.5NB - 3.75W = 0
ƩMB = 3.75W - 7.5NA + 18FA = 0
FA = μNA
FB = μNB
θ = arctan(18/7.5) = 67.38°

I know μ is supposed to equal .18, but I can't get it. I've tried substituting different things I don't know how many times now, and I can usually get to an expression of just μ or μ and θ, but I can never get it to equal .18.
 

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The angles at the wall are wrong on your FBD. They should both be 90-theta.
 

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