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Question-46430




Question Number 46430 by MrW3 last updated on 26/Oct/18
Commented by MrW3 last updated on 27/Oct/18
maybe we should at first forget the  length of the rope ring. the question  is just if the rope can rest in a inclined  position on the surface of cone.
$${maybe}\:{we}\:{should}\:{at}\:{first}\:{forget}\:{the} \\ $$$${length}\:{of}\:{the}\:{rope}\:{ring}.\:{the}\:{question} \\ $$$${is}\:{just}\:{if}\:{the}\:{rope}\:{can}\:{rest}\:{in}\:{a}\:{inclined} \\ $$$${position}\:{on}\:{the}\:{surface}\:{of}\:{cone}. \\ $$
Commented by MrW3 last updated on 26/Oct/18
a rope ring of length L is placed on  the surface of a cone and rests on it. all  surfaces are frictionless. the mass  of rope is ρ per unit length.  we know the ring can rest in a horizontal  position (red). but are there any other  positions possible like the blue one?  what is the max. tension in rope?
$${a}\:{rope}\:{ring}\:{of}\:{length}\:{L}\:{is}\:{placed}\:{on} \\ $$$${the}\:{surface}\:{of}\:{a}\:{cone}\:{and}\:{rests}\:{on}\:{it}.\:{all} \\ $$$${surfaces}\:{are}\:{frictionless}.\:{the}\:{mass} \\ $$$${of}\:{rope}\:{is}\:\rho\:{per}\:{unit}\:{length}. \\ $$$${we}\:{know}\:{the}\:{ring}\:{can}\:{rest}\:{in}\:{a}\:{horizontal} \\ $$$${position}\:\left({red}\right).\:{but}\:{are}\:{there}\:{any}\:{other} \\ $$$${positions}\:{possible}\:{like}\:{the}\:{blue}\:{one}? \\ $$$${what}\:{is}\:{the}\:{max}.\:{tension}\:{in}\:{rope}? \\ $$
Commented by ajfour last updated on 26/Oct/18
Isn′t the blue one an ellipse, Sir?  tough question Sir!
$${Isn}'{t}\:{the}\:{blue}\:{one}\:{an}\:{ellipse},\:{Sir}? \\ $$$${tough}\:{question}\:{Sir}! \\ $$
Commented by MrW3 last updated on 26/Oct/18
yes. I think it must be an ellipse.
$${yes}.\:{I}\:{think}\:{it}\:{must}\:{be}\:{an}\:{ellipse}. \\ $$
Commented by MJS last updated on 26/Oct/18
we can′t exactly calculate the perimeter of  an ellipse...
$$\mathrm{we}\:\mathrm{can}'\mathrm{t}\:\mathrm{exactly}\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of} \\ $$$$\mathrm{an}\:\mathrm{ellipse}… \\ $$

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