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