Physics of Continuous Objects (Ropes) | Kalda Mechanics Series Ep. 5

In this video, two similar problems are covered, both involving continuous objects, massive ropes. That is, ropes with mass. Because they have gravity acting on them, they won't be straight lines, and some interesting things tend to happen, such as one you notice in everday live, a rope dragging on the ground. The physics of the rope dragging on the ground is analyzed, involving both force and torque balance. The physics of a mass hanging onto a string clamped at two ends is also covered.

[@ak-jo6rp]

Physics lovers gonna love it

[@rabeakhatun2819]

bro u are doing an awesome job please continue this kalda series

[@SlippingHexagons]

Thanks! Yeah I'll continue this series, my uploads might not be that frequent and consistent though because of school :(

[@ak-jo6rp]

Great work bro

[@SlippingHexagons]

Thanks!

[@tujan7598]

smh, i can't believe these small angle approximations. For the second one, you should be able to do dy/ds = lambda*g*s/sqrt((lambda*g*s)^2+(T_x)^2) which is easily integrable via u-sub and then you still get a quadratic in l, right?

[@lovroklobucar4964]

Very good video! I have a question about the second problem. Why is lever arm of torque caused by y-component of tension l instead of l/2? My point is that there is tension in the entire rope so on average lever arm is l/2.

[@SlippingHexagons]

Thanks! On a quick look (it's been 2 months, so forgive me), the value T is just the force that the arm is pulling with, since we only consider external torques, and since that is acting at the end of the rope, the lever arm is l. I'll take a closer look.

[@lovroklobucar4964]

@@SlippingHexagons thank you!

[@SlippingHexagons]

@@lovroklobucar4964 No problem, happy to help!

[@tujan7598]

When are you going to cover some AMC/AIME problems?

[@SlippingHexagons]

I'm not sure, I never really planned to, but maybe I'll do some special videos :)