What if there's friction between the rope and the pulley? (Atwood machine)

[@jebsong5908]

Really clear explanation. It's criminal that you don't have more subscribers!

[@DrBenYelverton]

Thanks for your kind words!

[@ayushprasad1197]

Thanks for a great explanation. I had searched out the topic on friction between pulley and string out of curiosity and found out this video. Thanks once again.

[@DrBenYelverton]

Happy to hear that the video helped! It's an interesting problem and not one that seems to get discussed often.

[@DaTopDJ]

Quite an elegant explanation. Nice video! 👍

[@DrBenYelverton]

Thanks. I enjoyed making this one as I hadn't seen the frictional case discussed before!

[@jawspeak]

Very helpful explanation as the simplistic other videos leave out so much interesting and relevant factors. I am subscribing!

[@suryakantabehera5599]

Thank you sir ,well explained 😊

[@rashmitabiswal1389]

Thank you sir these videos are amazing for JEE advance

[@DrBenYelverton]

Happy to help, thanks for watching!

[@snehashisnayakgugu3796]

best sir….please make some vdo for olympiad physics questions

[@chawnneal3103]

Thanks so much, like some of the others my first question out of curiosity was, okay T1 = T2 w/o friction, but what if we wanted to solve with T1 and T2 and what justification lead to the initial T1 = T2! Specifically what mathematical model lead to T1 = T2 as I understood their (frictionless pulley) statement was telling us they were simplifying some model! Anyways thanks so much for this video! I'm going to checkout your other video, you allude to, about the derivation!

[@DrBenYelverton]

Thanks for watching - yes, always good to question where these assumptions come from!

[@tasneemkt4797]

Nice problem! Can you do a similar problem where the pulley can rotate meaning it has a mass m and some radius r and the rope has mass too? 😅 And what's the condition for the pulley doesn't slip?

[@DrBenYelverton]

Thanks. It gets a lot more complicated if you want to include all three effects (friction, massive rope, and pulley rotation) as you need to set up an equation of motion for each element of the string. I think I tried this a few years ago and ended up with a differential equation that couldn't be solved analytically!

[@arunkumarmamidala5685]

​@@DrBenYelvertoncan we do in matlab

[@shafin3365]

Respect from Bangladesh 👍

[@Jay-hh4ul]

Sir as we've already considered m2 > m1 the inequality should be 1≤ m2/m1 ≤ e^πu

[@DrBenYelverton]

We assumed m₂ > m₁ at the beginning for simplicity, but for the final result we need to take into account the case where m₁ is larger. In fact, m₂/m₁ can be less than 1 with the system still in equilibrium, and by symmetry you'll only get slippage in the opposite direction if the mass ratio falls below the reciprocal of e^πμ.

[@rtheben]

Good exercise, but that is a strange pulley, normally one would thing that the pulley has a moment of inertia and can freely rotate and also you have no slippage of the rope to the pulley. In that setup one can calculate all dynamics and when you eventually get slippage or not

[@LuizPoublan]

What's the condition for the system to be moving with a constant velocity? Or that's impossible to happen?

[@zdiac3255]

Interesting problem! But don't we assume system to be at equilibrium while deriving capstan equation? but clearly here rope is not at equilibrium, so is the equation still valid?

[@DrBenYelverton]

Well, it depends on our modelling assumptions. If we can neglect the mass of the rope, ΣF = ma becomes ΣF = 0 and the derivation of the capstan equation still applies. If not, then you're right and you need to apply Newton's second law to each element of the rope to come up with a new, and more complicated, equation of motion.

[@aadih.n3438]

hello why isn't t1>t2?

[@innovativeskyline9946]

It's a very good video

[@DrBenYelverton]

Many thanks!

[@nacicelik1954]

Does the system slipping or not slipping , does pulley turning?

[@DrBenYelverton]

In this example the pulley isn't turning and the rope is slipping over it.