# Friction and weight

1. Apr 10, 2007

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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,
View attachment friction.bmp

2. Apr 10, 2007

### Staff: Mentor

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?

3. Apr 10, 2007

### AlephZero

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

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.

4. Apr 10, 2007

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.....

5. Apr 10, 2007

### Staff: Mentor

Good.

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

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!

6. Apr 10, 2007