Thanks for watching! That's exactly right, the tension ends up higher on the side with the greater mass. Also, for a smooth pulley, there is only equilibrium if the mass ratio m₂/m₁ is exactly 1, but if it's not smooth then the system can remain in equilibrium when the mass ratio is within some range determined by the coefficient of friction. I actually have a video going into detail on this if you're interested: kzfaq.info/get/bejne/rtBhgc1nxLHWd58.html And for completeness, the derivation of an equation I use in that video: kzfaq.info/get/bejne/ipqnic-AvqzTeGw.html

@@DrBenYelverton thanks so much Ben for replying to me. I appreciate the thoughtfulness of your response, and how quickly you got back to me. I hope to watch the suggested videos if I make it further into my mechanics studies (understanding the concepts I find very challenging). The videos may answer my question, though incase not I want to ask for some extra detail here. Why does the side of the pulley with greater mass supply the extra tension, and not the side with the lower mass? What I said in my initial comment was just a guess really, and it seems I got lucky.

​@@GabrielConstantinides It's probably easiest to understand this by first considering the case where both masses are stationary. Then it follows (by considering the free body diagram of each particle) that the tension on each side is equal to the weight of the particle on that side, and hence the tension is larger on the side with a larger mass. If you then keep the lighter mass fixed but gradually increase the heavier mass, then the tension on the heavier side continues to increase, while the tension on the lighter side remains fixed. There's now a difference in tension between the two sides, which means the system wants to start accelerating, but friction can prevent this up to a certain point. Once the tension difference is large enough (the exact meaning of "large enough" depends on the coefficient of friction) then it will start accelerating, with the tension on the heavier side still being larger. I think this all sounds quite complicated but essentially it just comes down to the fact that the heavier mass is pulling harder, so produces more tension in the rope!

@@DrBenYelverton thanks so much Ben, the last part you said about the heavier mass pulling harder is a really good way to summarise it. I hope I will manage to make more sense of all this stuff if I put the work in. Do you have a tip jar or anything so I can pay tribute? It won't be much, but I'd like to show my appreciation

@@GabrielConstantinides No problem - it takes time to build up intuition about these things. Thanks for your kind thought - I don't have anything like that set up at the moment though, so the best way to support the channel would be to share my videos with anyone who you think might find them interesting!