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Question Number 188062 by mr W last updated on 25/Feb/23

Commented by mr W last updated on 25/Feb/23

A and B are connected with a rope of length L. A mouse of mass m moves from A to B along the rope. Find the locus of the mouse, a) if the mass of rope is neglectable. b) if the rope has a mass M.

$${A}\:{and}\:{B}\:{are}\:{connected}\:{with}\:{a}\:{rope} \\ $$$${of}\:{length}\:{L}.\:{A}\:{mouse}\:{of}\:{mass}\:{m} \\ $$$${moves}\:{from}\:{A}\:{to}\:{B}\:{along}\:{the}\:{rope}. \\ $$$${Find}\:{the}\:{locus}\:{of}\:{the}\:{mouse}, \\ $$$$\left.{a}\right)\:{if}\:{the}\:{mass}\:{of}\:{rope}\:{is}\:{neglectable}. \\ $$$$\left.{b}\right)\:{if}\:{the}\:{rope}\:{has}\:{a}\:{mass}\:{M}. \\ $$

Commented by mr W last updated on 25/Feb/23

basically this is the same problem which the suspention bridges like following also have:

$${basically}\:{this}\:{is}\:{the}\:{same}\:{problem} \\ $$$${which}\:{the}\:{suspention}\:{bridges}\:{like}\: \\ $$$${following}\:{also}\:{have}: \\ $$

Commented by mr W last updated on 25/Feb/23

Commented by mr W last updated on 25/Feb/23

Commented by mr W last updated on 25/Feb/23

the difference is: not a mouse, but a lot of people and/or cars are moving.

$${the}\:{difference}\:{is}:\:{not}\:{a}\:{mouse},\:{but}\:{a} \\ $$$${lot}\:{of}\:{people}\:{and}/{or}\:{cars}\:{are}\:{moving}. \\ $$

Commented by 073 last updated on 25/Feb/23

see the R∙C Hibbler structure analysis

$$\mathrm{see}\:\mathrm{the}\:\mathrm{R}\centerdot\mathrm{C}\:\mathrm{Hibbler}\:\mathrm{structure}\:\mathrm{analysis} \\ $$

Commented by mr W last updated on 25/Feb/23

i don′t want to apply complicated structure analysis, but just want to apply simple mathematics.

$${i}\:{don}'{t}\:{want}\:{to}\:{apply}\:{complicated} \\ $$$${structure}\:{analysis},\:{but}\:{just}\:{want}\:{to} \\ $$$${apply}\:{simple}\:{mathematics}. \\ $$

Commented by 073 last updated on 25/Feb/23

ok use hyperbolic function relations

$$\mathrm{ok}\:\mathrm{use}\:\mathrm{hyperbolic}\:\mathrm{function}\:\mathrm{relations} \\ $$

Answered by mr W last updated on 25/Feb/23

Commented by mr W last updated on 25/Feb/23

case a) if the rope is weightless, AC+CB=L ⇒locus of point C, where the mouse is, is a part of an ellipse with focii at A and B.

$$\left.{case}\:{a}\right) \\ $$$${if}\:{the}\:{rope}\:{is}\:{weightless},\: \\ $$$${AC}+{CB}={L} \\ $$$$\Rightarrow{locus}\:{of}\:{point}\:{C},\:{where}\:{the}\:{mouse} \\ $$$${is},\:{is}\:{a}\:{part}\:{of}\:{an}\:{ellipse}\:{with}\:{focii}\: \\ $$$${at}\:{A}\:{and}\:{B}. \\ $$

Commented by mr W last updated on 25/Feb/23

case b) this case is solved in Q187675.

$$\left.{case}\:{b}\right) \\ $$$${this}\:{case}\:{is}\:{solved}\:{in}\:{Q}\mathrm{187675}. \\ $$

Commented by mr W last updated on 25/Feb/23

Commented by mr W last updated on 25/Feb/23

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