Solving Friction and Weight Problem: W=75lbs

[Bradracer18]

Homework Statement

A lightweight rope is wrapped around a 100lb drum, passes over a frictionless pulley, and is attached to weight, W. The coefficient of friction is 0.50. Determine the maximum amount of weight that can be supported by this arrangement.

I've drawn a picture, showing what I think are the forces on everything.

I need help solving this, as I'm not sure how to actually do it. The answer, I have(given to me) is W=75lbs.

Homework Equations

The Attempt at a Solution

Forces in x direction = 0 = Fa - Nb + Tw
Forces in y direction = 0 = Na + Fb - 100

Not sure if there is a moment(and if so, where do I take it about)...also, if not...I'm not sure how to solve this next.

Thank you,
Brad
View attachment friction.bmp

 

[Doc Al]

Why not take moments about the center of the drum? Hint: If the drum is just about to turn, what can you say about the friction forces?

 

[AlephZero]

You have 5 unknowns Fa Na Fb Nb and Tw so you need 5 equations.

You have 2 equations already.

When the drum starts to rotate, Coulombs law of friction says
Fa = mu.Na and Fb = mu.Nb That makes 4 equations.

You can get a 5th equation by taking moments. If doesn't matter where you take moments about. Choose a point which several forces pass through, so they have zero moment and you get a simpler equation.

 

[Bradracer18]

Ok...so now, I took the moment about the center.

Counterclockwise

M = 0 = Fb(d/2) + Fa(d/2) - Tw(d)

And the 2 equations above. I'm totally lost as to how I mathematically solve these though, or where I start. Also, I don't know the diameter(d)...so not sure how the moment equation will help...

 

[Doc Al]

Ok...so now, I took the moment about the center.

Good.

Counterclockwise

M = 0 = Fb(d/2) + Fa(d/2) - Tw(d)

Why is one force times d while others are times d/2?

And the 2 equations above. I'm totally lost as to how I mathematically solve these though, or where I start. Also, I don't know the diameter(d)...so not sure how the moment equation will help...

The d drops out, so you don't need the actual value.

If you answer my question/hint about friction, you'll be able to rewrite Fb and Fa in terms of Nb and Na. (Similar to what AlephZero told you to do.) Then you'll have 3 equations and 3 unknowns--solve!

 

[Bradracer18]

Ok...I was saying it was the diameter/2...or the radius. I don't know what I was thinking...I found that mistake, and will try to solve it now...see if I can do it...not sure.

 

[Bradracer18]

yes, I did solve it(it feels good...haha). Thank you for all of your help, I sure appreciate it!