Force on a rope wrapped around a cylinder: deriving the capstan equation

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Күн бұрын

Here's how to derive the capstan equation for the force needed to cause a rope wrapped around a cylinder to slip.
About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university.
My website: benyelverton.com
#physics #maths #mechanics #statics #forces #resolving #friction #equilibrium #capstan #rope #cylinder #integration #differentialequations

Пікірлер: 9

@nicolasmanopla4584 2 жыл бұрын

Thank you very much for the explanation!.

@DrBenYelverton 2 жыл бұрын

Thanks for watching!

@mxminecraft9410 6 ай бұрын

If (P not )is equal to zero the the required force would be zero so does this mean tha lt in such case looping the rope would be impossible?

@tesgk1 Жыл бұрын

Is it possible to use this principle to replace chain drive and sprocket? How many wraps are optimal? Thank you

@DrBenYelverton Жыл бұрын

In principle yes, but if the main goal is to transfer rotational motion from one place to another then a sprocket would probably be a better choice, as with the capstan you’d need to make sure that the coefficient of friction is large enough to ensure no slippage. The meaning of "large enough" will depend on how much torque will be applied to the system.

@sayanjitb 2 жыл бұрын

Dear sir, while writing the force balance equation along tangential and normal direction why didn't you take the contribution of the weight of the small element?

@DrBenYelverton 2 жыл бұрын

I'm just assuming that we can neglect the weight for modelling purposes. I can't remember whether or not it ends up being possible to solve the resulting differential equation exactly if the weight is included - might be an interesting exercise to give it a try. Also, a quick search suggests that the capstans that are actually used on boats are often oriented such that the rope is wound in the horizontal plane rather than the vertical plane. In this case, the diagram in the video would really be a top-down view and the weight would be acting into the screen, so a full 3D analysis would be required if we wanted to include the effect of weight!