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Find the length of an endless chain which will hang over a. Circular pulley of radius a so that it is in contact with two thirdsof the. Circumference of the pulley?

I saw this question in a test. I didn't quite understand the question. Can someone give a hint

user69468
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  • Are you familiar with the length of a circumference? –  Feb 13 '16 at 16:24
  • Not sure I understand the question. Are you just asking for $\frac 23$ of the circumference? Surely a real chain (even an endless one) only "covers" half the circumference, no? I mean, it just hangs straight down from the two points on the horizontal diameter. Or am I misunderstanding? – lulu Feb 13 '16 at 16:33
  • I didn't understand the question either.. I know the chain normally covers half the circumference... What is two third doing here.. Still it's a problem from mechanics and I copied it ditto – user69468 Feb 13 '16 at 16:40
  • Well...of course, if one end of the chain is at an angle, then we can make it contact $\frac 23$ of the circumference, but I don't see how to get a "length" out of that observation. Indeed the "length" of an "endless" chain seems a bit paradoxical from the start. Sorry. – lulu Feb 13 '16 at 16:49
  • May be it's s stupid question..may be it's a classic mechanical question...I haven't read the chapter so far. So I don't know – user69468 Feb 13 '16 at 16:52
  • I think. It's something to do with pulley rotates and strings moves so to touch two third you need to have a definite length.. Can anyone solve now – user69468 Feb 13 '16 at 16:55
  • The chain is a loop. – Rick Decker Feb 13 '16 at 20:06
  • You should find out what the question is and state it clearly to make it easier for people to help you. -1 – Ross Millikan Feb 13 '16 at 23:29

2 Answers2

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Find the length of an endless chain which will hang over a circular pulley
of radius a so that it is in contact with two thirds of the circumference
of the pulley?

We have two pulleys (driver and driven).

Pulley "a" is bigger than pulley (say) "b", because has contact angle of 240 degrees (two thirds of the circumference = two thirds of 360 degrees).

We don't know :

a radius

b radius

center to center distance

For the formulas involved see "The pulley problem" in: https://en.wikipedia.org/wiki/Belt_problem

Formulas are the same for belts and chains.

So you can express total length as a function of both radii and center to center distance.

cgiovanardi
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Here the endless chain means a chain whose ends are united by a link.

That should help you to understand the question.

This is a common catenary problem.

Read the proof from here http://mysite.du.edu/~jcalvert/math/catenary.htm

Venkat
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  • While the meaning of "endless chain" you provide is apt and helpful to solving this problem, it doesn't answer the question posed here. The link you provide might include an answer, but merely providing a link is considered a low quality post. Please provided (at a minimum) a quote or paraphrase of the most relevant information to be found at the cited link, so that your Readers will have a sensible basis to decide whether to follow the link. This will also help in reconstructing the link should it become inoperative in the future. – hardmath Apr 22 '16 at 02:50