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V
24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
April 12, 2017
Solved

One task with 3 bobs - Forces searching

  • April 12, 2017
  • 13 replies
  • 37010 views

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?

3-bobs.jpg

Best answer by vlehner

Great articel!

13 replies

F
Fred_Kohlhepp23-Emerald I
23-Emerald I
April 12, 2017

The horizontal forces at the walls don't have to be equal, and

the force vector has to align with the string

M
MJG1-Visitor
1-Visitor
April 12, 2017

The horizontal forces at the walls don't have to be equal

If they're not equal, then the system is not static.  Those two forces are the only horizontal forces acting on the system, so they must cancel out.  Note that your solution has the two forces very close to each other.  Remove the negative from your RHS (Valery has defined F0x as acting in the opposite direction as F4x) and re-enable evaluation of that region and your final result is pretty much unchanged.

M
MJG1-Visitor
1-Visitor
April 12, 2017

The reactions at 0 and 4 must be in the direction of the string.

For example:

Snip.png

(negative required due to how your variables are defined)

You can write a similar equation for the forces at point 4.

Also, you can balance the forces in the X direction at points 1, 2, & 3, and you can balance the forces in both the X and Y directions at points 0 & 4.  Some of these equations will likely be redundant (what's the mathematical term for this?).

F
Fred_Kohlhepp23-Emerald I
23-Emerald I
April 12, 2017

The horizontal forces at the weights are equal (for static equilibrium.)  The walls are fixed, so there is no requirement that F0x and F4x be equal in magnitude.

Yes, I was sloppy in directions so I needed a negative sign. 

M
MJG1-Visitor
1-Visitor
April 12, 2017

Fred,

I agree the walls are fixed, but look at the string.  It has 5 forces acting on it.  3 of those forces are vertical (points 1, 2, and 3), so the horizontal components of the other two (0 & 4) must be equal and opposite.

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-MFra-21-Topaz II
21-Topaz II
April 12, 2017

Hi Valery Ochkov,

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

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
April 12, 2017

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!

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-MFra-21-Topaz II
21-Topaz II
April 12, 2017

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

V
vlehner1-Visitor
1-Visitor
April 12, 2017

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.

V
vlehner1-Visitor
1-Visitor
April 12, 2017

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

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
April 13, 2017

Ohne die Minimize Funktion?

V
vlehner1-Visitor
1-Visitor
April 13, 2017

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?

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
April 13, 2017

See please mass of bobs and mass of string

Vage.jpg

V
vlehner1-Visitor
1-Visitor
April 13, 2017

there are left 0.21 gramms for the string.

makes 0.65% deviation.

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
April 13, 2017
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

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-MFra-21-Topaz II
21-Topaz II
April 13, 2017

funicular polygon example.jpg

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
April 13, 2017

Point please the book!

Can you solve our task with this method?

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-MFra-21-Topaz II
21-Topaz II
April 14, 2017

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.

copertina meccanica razionale.jpg

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

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
April 15, 2017

What is break - the string (the force was so big) or the function Find?

Can you plot traces points 2 and 3? Слабо?

Video Link : 7739

The last frame

3-bobs-x4.png

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
April 16, 2017

With 2 traces. But better not use spline - to create functions y(x):=Minimize() and y(x):=Find(). Try please!

Video Link : 7740

V
vlehner1-Visitor
1-Visitor
April 16, 2017

Chaos-Pendulum.

wouldn't it be easier to create the DGL-EQN with Lagrangesche's Formalism?

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
April 18, 2017

Is this model true? Can we use the minimize function here?

2-mass-1-boll.jpg

V
vlehner1-Visitor
1-Visitor
April 18, 2017

Valery,

...to be serious

you changed the Geometry: Value x4 from 280mm to 340mm. Why? (better to compare with 280mm to the former problems/situations)

Setting up the 2.nd mass from 2gm to -10gm (now it it a Force upwards) doesn't (may not) corupt the Energy-Laws, so the use of the minimize-Method is in my opinion ok.

The minimal Princip of the potential energys is given by m1, m3.

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
April 18, 2017

The first version of the article in attach.

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