[Bobolink]

I calculate the energy in/out from start to end. I start at 45° and I stop at 45.001° for example. The conservation of the energy is always true, even for a small movement, even for a small time.

The force on the circle is at 45° relatively to the horizontal so I need to correct it with the cosine function. The movement of the circle is horizontal, the force is at 45°, the work is F*lg*cos(45°). I don't understand why there is a problem there.

One of the problems is that you are not very clear.

So are you saying, that as the end of the red bar moves towards the lower right, a force is applied to the cylinder parallel to the bar and to the top right?  And further the cylinder is not free to roll, however there is also no friction because the cylinder adheres to an elastic material which stretches to accommodate the movement of the cylinder?

[Bobolink]

I think there is a mistake in you drawing.
You have one gray line that goes from the center of the circle to the left to point B.
When the circle is shifted to the right the new gray line is not parallel with the old gray line.  If it was it would intersect point B'.

[LB7 (OP)]

I do my best to be clear.

No, there is no mistake in the drawing. I have the exact movement with the friction. The dot B is ALWAYS at the dot of contact between the circle and the red wall. At start, I studied that device without an elastic but with fricion between the circle and the red wall. Like it is difficult with the friction of 2 objects in movement, I found that example with the elastic. Here, there is no friction: I use the elastic to have the SAME forces than the friction at each time (There is no friction between the elastic and the wall. The circle cannot rotate around itself). Like that, I have the same energy needed to move the circle (compared to the energy with the friction). And I don't need/recover any energy from the rotation of the red wall around A0. At final, I need to measure the modification of the length of the elastic and it is well d2 not d1. It is easy because I have a dot fixed: A. You can compare the drawing with the friction, it is the same.

Years ago, my intuition sees that difference of length but I didn't think at the elastic to measure the distance. You can make the experience to see the trajectories. Here, I have 2 different examples, where the sum of energy is the same, not equal to 0, the example with the elastic is a direct measure.

[Bobolink]

Years ago, my intuition sees that difference of length but I didn't think at the elastic to measure the distance. You can make the experience to see the trajectories. Here, I have 2 different examples, where the sum of energy is the same, not equal to 0, the example with the elastic is a direct measure.

Your intuition was wrong.

No, there is no mistake in the drawing. I have the exact movement with the friction. The dot B is ALWAYS at the dot of contact between the circle and the red wall.

OK

To have the sum of energy at 0 (the energy needed to move the circle equal to the energy from the heating or the elastic) the distance must be d1. But I found d2.

Of course the distance isn't d1!  The elastic is holding the cylinder back!  The 'missing' energy has been converted from kinetic energy to potential energy in the elastic.

[LB7 (OP)]

The 'missing' energy has been converted from kinetic energy to potential energy in the elastic.

I see, the problem comes from the fixed dot, I can't use a fixed dot, so attach the elastic between the circle and the red wall and I change the elastic at each step:


jji.png (164.84 kB . 1563x781 - viewed 4001 times)

[Bobolink]

I see, the problem comes from the fixed dot, I can't use a fixed dot, so attach the elastic between the circle and the red wall and I change the elastic at each step:

Like I said the 'missing' energy is in the elastic.  You guys always crack me up, you think that if you make the scenario complicated enough then some law or other of physics will no longer apply.  You can easily make a scenario I can't figure out, that doesn't mean the laws of physics don't apply it will just mean I can't figure it out.

[evan_au]

energy recovered from the friction

Friction tends to produce heat, which is the lowest form of energy.

It's really hard to recover useful energy from heat (unless it is really hot).

Next time, try generating a more useful form of energy, like electricity.

Lookup: https://en.wikipedia.org/wiki/Thermodynamics
This also tells you that you can't generate energy "for free"

[LB7 (OP)]

Thanks for you advice !

I come back with the method with the elastic, to have the distance 'd2' I need to place the dot A on a needle, and the needle is between the circle and the red wall:

[Bobolink]

What you really need to do stop with the drawings and do some calculations to quantify these thing.  Pictures and arm waving is not going to do it!
What you really really need to do is stop wasting your time trying to beat the conservation of energy.

[LB7 (OP)]

How to calculate the friction between two surfaces in movement without the hypothesis of the conservation of the energy ? I don't see a method on internet, but maybe in books there is, I will find. At least, the name of the method will help me.

I wrote a program:


vfz.png (136.69 kB . 1126x838 - viewed 3796 times)

I used the notation in my first drawing. But I don't know if the calculations are correct. But I have well the energy recover from the friction lower than the energy needed to move the circle.

[Bored chemist]

But I don't know if the calculations are correct.

If they tell you that energy is not conserved, then they are wrong.

[LB7 (OP)]

I'm happy when I understand my mistake ! If I find a method to resolve the energy from friction I could understand. If someone knows I could understand where is my mistake.

The method I used with the needle: it is just to prove my intuition is right. But it is worst than I think: the method of the needle is an amplificator of the energy, it destroys more energy. More the diameter of the needle is small more the forces aside the walls is bigger and like the distance moved by the red wall is lower than the distance of the circle: I lost more and more energy !

[Bobolink]

But it is worst than I think: the method of the needle is an amplificator of the energy, it destroys more energy.

So if you have a certain amount of energy in a closed system some of the energy can just disappear?  If you could do the opposite and make energy appear out of nowhere, you would be a rich person.  Good luck.

[LB7 (OP)]

I'm not certain, I'm looking for a method independant of the conservation of the energy to verify. Very strange, that there is no mehtod for a so basic function, I mean the friction.

[LB7 (OP)]

The example:


fr3.png (63.98 kB . 752x698 - viewed 3306 times)

I control in position the circle and the wall, I need 2 external devices, but I count all the energies I give or recover. There is always the contact between the 2 walls.

To have the friction between the walls I consider a spring presses the two walls at the dot of contact, only at that dot:


hhg3.png (34.19 kB . 357x340 - viewed 3201 times)

With the wall fixed at 45° (reference) I translate the circle but not rotate it. The dot '1' is fixed on the wall and the dot '2' is fixed on the circle. I just move a little to the right the grey circle because it is at the same place than the blue circle. I have:


f5.png (47.06 kB . 903x683 - viewed 3320 times)

Now, I rotate and don't translate the wall (the wall is always fixed at 45°, it is the reference):


fds.png (41.83 kB . 941x814 - viewed 3303 times)

At final the distance moved is the sum of the two last: it is d2 not d1 in the global drawing.

The circle need the energy d1*F but the friction lost d2*F. With F the force of the friction.

That device destroys the energy but it is possible to use the example with the needle and the elastic for example to create it.

[LB7 (OP)]

I found the method that works in every cases to measure the distance of the friction between two surfaces in movement::

1/ Before start: place a fixed dot on each object at the dot of contact.
2/ The dot of contact is fixed to the ground: fixed in position but also fixed in orientation.
3/ After end: measure the distance from the dot of contact to the fixed dot along the path of the object1: the line or the circle. Measure the distance moved by the dot of contact from start to end from the end of the dot of contact: be careful, the dot of contact is fixed ALSO in orientation.
4/ The algebric sum is the distance of the 2 distances.

For the following example :


vzd.png (115.64 kB . 1091x837 - viewed 3227 times)

The energy to move the circle is lg*cos(44.5°)*F = d1*F. The distance of friction is d2, so the energy from heating is d2*F. The energy is not conserved. With a line and a circle ... I like !!!!

[Bobolink]

The energy to move the circle is lg*cos(44.5°)*F = d1*F. The distance of friction is d2, so the energy from heating is d2*F. The energy is not conserved. With a line and a circle ... I like !!!!

That is wrong energy was conserved.  If there was no friction then d1 would equal d2.  But there was friction so d2 is shorter than d1.  So the friction contribution is d1- d2, not d2. 
The only way to prove your idea is to do the math, your drawings are not enough.

[LB7 (OP)]

The only way to prove your idea is to do the math, your drawings are not enough.

Logic, geometry, measure, etc. it is math. Elementary math (primary school), for an elementary example. Even I think before math, geometry, measure, logic existed, but math had taken all of theses matters for it.

If there was no friction then d1 would equal d2.  But there was friction so d2 is shorter than d1.  So the friction contribution is d1- d2, not d2.

The energy to move the circle is d1*F, so I need to have d1*F from the friction but I have d2*F.

[LB7 (OP)]

I understood the mistake physicists maked: it is important to watch the orientation of the dot of contact. If the dot of contact doesn't change its orientation, there is no relative rotation between the 2 objects. So, the geometrical method is false and the integral too because the 2 methods sees a rotation of the wall relatively to circle and count that. In fact, when I rotate all the objects  at the final position to be at the start position, I need to rotate the circle back. It is because physicists see a relative rotation of the wall relatively to the wall that creates a mistake in the integral. If the method take in account the orientation of the dot of contact then these two methods can be applied. In the drawings it is possible to watch the dot of contact fixed when I fixed the wall. If the dot of contact is fixed there is no rotation (or modification of its orientation), so the graphical method is:

1/ draw the start and final position
2/ group the all objects in the final position
3/ rotate the group of the final position back to have the same orientation for one object (the wall for example)
4/ rotate one object forward (the circle for example) of : the relative rotation of one object to the other less the difference of the  orientation of the dot of contact
5/ measure the distance of friction.

[LB7 (OP)]

It is easier to think with the dot of contact fixed on the ground and move the others object. But fixed in position  AND IN ORIENTATION.