Atwood Machine Inertia Friction and directional forces

[Raju1972]

I have an Atwood Machine. I have an aluminium Pulley of radius 4 inch. A gym cable running over it. Not sure coefficient of friction but smooth movement. One end of rope, I attach wt. of 0.5 kg. I had to attach weight of 1 kg for acceleration to start. If I attach 2 kg, I had to attach 3.1 kg, for the system to start acceleration. If I attach 4 kg, I had to attach 6.1 kg to other end. Now if I take 2 pulleys and run rope over them and repeat experiment, I need even more weight differential for system to accelerate. Thus there are some forces acting which need to overcome to start system acceleration. I think apart from inertia of pulley and static frictional force, probably some x and y directional force components are coming into play. All Atwood problems talk about equation for acceleration but not able to find equation for "weight differential" required for the system to start accelerating. Also any suggestions on ways to reduce this weight differential to start system acceleration shall help.

 

[Nugatory]

Because you have measurements, it sounds as if you're describing the behavior of an Atwood machine that you've actually built. If so, that's pretty cool... and the construction details will matter. What did you use for bearings for each pulley?

 

[Raju1972]

Because you have measurements, it sounds as if you're describing the behavior of an Atwood machine that you've actually built. If so, that's pretty cool... and the construction details will matter. What did you use for bearings for each pulley?

As I am doing a prototype, to cut on cost, I used very simple pulleys. Hence my pulleys have no bearings. Now when I use wt of 0.5 kg, I had to put 1 kg. So I am assuming I had to put extra 0.5 kg to accommodate all the deficiencies of cheap materials used. So next time when I take 2 kg, I would be fine if I get acceleration when I attach 2.5 kg at other end (extra 0.5 kg for pulley/rope friction, rotational inertia of cheap material) But I had to put 3 kg to start acceleration. Similarly when I use 4 kg, I would be fine to see acceleration at 4.5 kg. But I had to put 6 kg. Things get worse when I use Atwood Machine with 2 pulleys. Do you still think this huge difference is only because I am using pulleys with no bearings? If yes, please suggest what kind of bearings/pulleys I should use.. I suspect that the so called inertia I am observing before acceleration is a function of masses attached probably due to vector forces. But I am unable to prove it. I am attaching images of my setup. One set of images is for "2 pulley Atwood machine with small pulleys" and other set of images is with big pulleys and 1 and 2 pulley Atwood machine. [Even though I did experiments for all combinations]

 

[Nugatory]

I was right - what you are doing is pretty cool! :)

As I am doing a prototype, to cut on cost, I used very simple pulleys. Hence my pulleys have no bearings.

That is a reasonable tradeoff to make, but the downside is that the physics of a rotating shaft in a sleeve is fairly complicated: You have to consider static friction, dynamic friction, and the way that the sideways loads on the pulleys will tend to jam the shafts against the sides and change the resistance of the pulleys - any or all of these may be large enough to overwhelm the effects that you're trying to measure.

You can try smoothing the shafts, using shafts that are as round as possible (a lathe would be great, but just chucking them in a power drill and turning them against sandpaper works), try for the smoothest possible tight fit in the holes, lubricate the shafts... Try to get as close as possible to the ideal frictionless rotation that a theoretical Atwood machine depends on.

But you'll probably be happiest if you can find some bearings in the trash somewhere. The wheel bearings in a scrapped bicycle would be good for the weights and sizes you're working with, and old hard disk drives contain extremely high-quality ball bearings but may be a bit small for your current design.

 

[Raju1972]

I was right - what you are doing is pretty cool! :)
the sideways loads on the pulleys will tend to jam the shafts against the sides and change the resistance of the pulleys - any or all of these may be large enough to overwhelm the effects that you're trying to measure.
But you'll probably be happiest if you can find some bearings in the trash somewhere. The wheel bearings in a scrapped bicycle would be good for the weights and sizes you're working with, and old hard disk drives contain extremely high-quality ball bearings but may be a bit small for your current design.

As I think more, I tend to agree with you. Initially I neglected bearings but bearings are probably must. As I increase weight, there is more tension in the rope and that in turn adversely affecting load on shaft. Having bearings shall probably help convert this load into rotational force, which is what is required. I am out of town this weekend but will try inserting bearings into my pulley and check the results. Thanks for your help.

 

[Raju1972]

I did few more experiments with bearings in the pulley. But not much of a difference. With latest experiments using 2 pulleys, I am seeing that wt. required on other side of pulley to start acceleration, is close to twice the wt. on one side. So if wt. is x kg on one side then I need to put ~2x on other side before acceleration starts.