One task with 3 bobs - Forces searching

[ValeryOchkov]

I try to find forces in this task. The Mathcad 15 sheet is in attach. Are equations in the Given-Find block right?

What is the 8-th equation?

[ValeryOchkov]

F.M. написал(а):

Hi Valery Ochkov,

This is the well known case of Funicular Polygon, extensively studied in rational mechanics.

Thanks, F.M. It Is веревочный многоугольник!

I try to solve this task in Mathcad! With Animation!

[-MFra-]

...verevochnyy mnogougol'nik?!?!....I like much more funicolar polygon....

[ValeryOchkov]

F.M. написал(а):

...verevochnyy mnogougol'nik?!?!....I like much more funicular polygon....

How it in Italian?

Poligono funicolare! Полигоно фуниколаре? Sembra una Dolce vita!

[-MFra-]

I like... "chernaya ikra"....russkiye salaty.......Rossiyskiye zhenshchiny.....+.....+.....

[ValeryOchkov]

F.M. написал(а):

I like... "chernaya ikra"....russkiye salaty.......Rossiyskiye zhenshchiny.....+.....+.....

Sorry, Черная икра отдельно, но это уж слишком пышно!

[ValeryOchkov]

Ко мне как-то давно приезжал один профессор из Италии. Он спросил, почему ваши студентки одеваются как наши проститутки - мини-юбки, туфли на шпильках, яркая косметика... Я сказал, что это ваши проститутки одеваются как наши студентки.

[-MFra-]

... ... here we dress as we please ... students then .... do not talk about...are absurd !!! .... They dress in the traditional way only in the graduation ceremony ... and it is not always said that happen.

[-MFra-]

How wonderful!

[ValeryOchkov]

Our task and... женщины - ladies

[-MFra-]

... is too visible a finger ... ... which contains a message for those who are doing some strange thoughts ... and that disfigures so fascinating Sofia.

[ValeryOchkov]

Good!

Other Sofia without the finger and with our chain!

[-MFra-]

Valery ... what a wonderful girl ... but ... we're coming off the rails ...

[ValeryOchkov]

Some time it is useful! Седина в бороду - бес в ребро! We say in this cases!

[-MFra-]

The only things that can vary are the forces and consequently the angles and not the wire lenghts, assuming that the two constraints at the ends are fixed.

[Fred_Kohlhepp]

If the wire lengths don't change, and the positions of the ends and the weights don't change, how do the forces change?

I think Val held three length constant and shortened #4 to allow the forces to change in his animation.  The original problem is static.

[-MFra-]

Certainly in my sentence there is a certain ambiguity. I was referring to the possibility of change, in an animation, only the forces in play and keep constant the wire lengths. Or, in the calculation, only by varying the forces, to obtain the various equilibrium configurations.

[vlehner]

What about bringing the geometrical relationships (Phytagoras) into account like that:

My problem is: I'm missing 2 Equations for the complete solution.

10 unknown and only 8 EQ.

btw.: The Force F4x should be positive.

[vlehner]

...It seems to be that there is a solution:

[ValeryOchkov]

Ohne die Minimize Funktion?

[vlehner]

Do we really need a minimize function if we have 10 conditions and 10 Equations?

If yes, how does it works in a solve block?

[ValeryOchkov]

Better so put initial date

[vlehner]

good Idea!

THX

[ValeryOchkov]

See please mass of bobs and mass of string

[vlehner]

there are left 0.21 gramms for the string.

makes 0.65% deviation.

[ValeryOchkov]

Volker Lehner написал(а):

there are left 0.21 gramms for the string.
makes 0.65% deviation.

One new task - we have not a string with mass 0.2 g, but a (gold) chain with mass 10 g for example

See please pictures here

Этюд 7. Цепная функция Или Пятый элемент

[-MFra-]

[ValeryOchkov]

Point please the book!

Can you solve our task with this method?

[-MFra-]

Hi,

The book, in two volumes, is written in Italian and was published in the middle of the last century. I bought it when I was a  student in the preparation of the relative rational mechanics exam. The above image is my own translation.

since it was given an answer to the problem, I do not continued in the calculation. Go on those who want it.

[-MFra-]

previous draft correction:

[ValeryOchkov]

One book in Russian

§ 5. РАВНОВЕСИЕ ВЕРЕВОЧНОГО МНОГОУГОЛЬНИКА