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.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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