What if the rope has mass? (Atwood machine)

[@Lukasz.Skowron]

For elegance, you can transform the last equation with the cosh() function :)

[@DrBenYelverton]

Indeed, I did mention this briefly towards the end (around 16:15) but wanted to keep it in exponential form for the purposes of explaining the physical intuition behind the result. But you're right, that would certainly be a more concise way to write the answer!

[@learnscience1250]

thank you so much...

[@DrBenYelverton]

You're welcome, thanks for watching!

[@PhysicsFANatic]

Why when writing potential energy it's -λxgx, isn't it -λxgx/2 + λxgx/2 = 0, since one side moves up and the other goes down?

[@DrBenYelverton]

It would be zero if we ignored the mass of the rope and had particles of equal mass, for the reason that you described. However, it works differently with the rope because the part of the rope that moves up on one side is transferred over to the other side, so that overall there is a loss in potential energy.

[@Titorites]

👍👍