Effective Friction Related to Pulley Radius (Atwood Machine)

[Turkus2]

First time posting on the forum - I've been coming here a lot the past year or so to seek answers. This one is concerning a lab. I think I've already done the legwork but am sort of looking for either something I'm missing or a confirmation of sorts. It's pretty messy and wordsy but if you have an answer, cool. If not, tell me to scram and I probably will.

So the lab involves an Atwood machine. We are using a constant mass throughout the experiment on a graduated pulley. We put together our equation for effective friction and calculate it for each setup. Shocking, the effective friction drops precipitously (some might say... exponentially) as the radius of the pulley increases.

A question that's hinted at but only just (quite common in this class) is the relationship between the two. I'm fairly certain I've boiled the equation down to:

Ffriction = a(mass1 + mass2) + g(mass2 - mass1) - (2*i*d)/r²t²

We haven't covered inertia yet - so the i above is a given constant and the d value is the distance the heavier mass drops (which if plugged into the position equation and solved for, produces 1/2at²)

Now... I think I have worked out that if the mass is constant throughout and one assumes the acceleration can be made to be constant throughout (by maneuvering some mass from one side to the other - but keeping the total mass of the system constant), and by plugging in the position equation value for d - the equation simplifies to Ffriction = k(1/r²). Or, the radius and friction are inversely proportional.

Christ, that was a long way to walk to ask... are the square of the radius and the effective friction of the system inversely proportional?

Thank you for reading. This was practically a blog post.

 

[anorlunda]

I'm not sure I understand your question. It sounds like you did experiments, and then used curve fitting to match the data to a function. Now you ask if that is the right function; is that your question? Also if you ask about inertia, then the experiments involve speed, nut just static friction; correct?

I always thought that the thing that dominated pulley friction versus radius was the resistance of the rope or cable to bending/unbending. A steel cable has more bending resistance than a rope, and a twisted rope more resistance than a braided rope. Did you include that in your experiments?

 

[Turkus2]

I'm not sure I understand your question. It sounds like you did experiments, and then used curve fitting to match the data to a function. Now you ask if that is the right function; is that your question? Also if you ask about inertia, then the experiments involve speed, nut just static friction; correct?

I always thought that the thing that dominated pulley friction versus radius was the resistance of the rope or cable to bending/unbending. A steel cable has more bending resistance than a rope, and a twisted rope more resistance than a braided rope. Did you include that in your experiments?

Thanks for the response. The class is a little unorthodox (i think) in that we are given a vaguely written lab manual and then we design it ourselves. We are basically asked to have everything prepared to perform the experiment and pump out the report in a 2.5hour class. The process of conceptualizing the data deduction and formatting the presentation is the tedious part.

All that said - we are really measuring the effective friction of the pulley on its axle. The inertia is given and while we can move weights from one pulley to the other, the system's entire mass remains constant. I conclude that based on that and the availability of small enough masses, we could make the acceleration constant - which would develop the relationship between the two - inverse square law.

But I'm rambling now. Hope that helps.

 

[anorlunda]

OK, I understand your approach. Do you have a question for PF?

 

[Turkus2]

OK, I understand your approach. Do you have a question for PF?

I think I'm just verifying that my reasoning is sound, specifically related to how I'm considering the constants.