Post by: LB7 on 02/09/2018 08:25:08
At start:
c1.png (31.76 kB . 1142x659 - viewed 3020 times)Middle:
f3.png (24.48 kB . 1145x624 - viewed 2988 times)End:
2.png (10.95 kB . 1119x622 - viewed 3000 times)At start, the device is filled with blue spheres with the same size, example radius at 1e-3m. When the device is deformed, the black stem enters inside the container, I do not move out the blue spheres, but I change their diameter, it pass for example at 1e-6m, I do not change the diameter of all spheres just them that are in front the black stem, the others have their diameter unchanged. Like that the green line has the same force on it. The potential energy (of the springs) lost is the same if I consider leak inside the black stem. But I have an extra pressure on the left wall.
The area of the smaller spheres is limited :
dil.png (33.92 kB . 1099x634 - viewed 2929 times)Note: the leaks is to let pass the pressure of the smaller spheres, but NO BLUE SPHERES ESCAPE outside the container.
If I take the middle position
With 'h' the height of the black stem and 'δ' a small angle of rotation around the middle position. Because there is the black stem:
I lost -2*δ*h*√2 from the right wall
I recover +2*δ*h*9/8*√2 because I reduce the size of the blue spheres
The green line sees the same force
The left wall sees a bigger pressure due to the extra pressure from the smaller spheres:
sn.png (51.88 kB . 1206x690 - viewed 2999 times)It is possible to imagine the black stem with leaks/fissures where the smaller blue spheres pass through, like that all the pressure from the smaller spheres will be applied on the left wall. I think I lost more from the left wall like that and the sum of energy must be negative. The volume of blue spheres inside the black shape is maybe 3 % of the volume of the black shape, it could be more or less.
The smaller blue spheres are just around and inside the black stem (leaks/fissures), not everywhere inside the others bigger blue spheres. I think it is necessary to filled the container, I mean with different sizes of blue spheres for example from 1e-3 m to 1e-6 m with the force of the springs in relation with the volume of a sphere, for example 1e-15N/m³. Like that when I reduce the size of the blue spheres, I start with the bigger radius 1e-3 m and I reduce it to 1e-6 m, the force of the spring is the same at 1e-6 m than 1e-3 m, and I prevent the smaller spheres to pass between the bigger spheres. If the volume is filled at 100 % it is not possible for the smaller spheres to pass through the bigger spheres.
strv.png (25.3 kB . 822x318 - viewed 2948 times)Note, the extra pressure on the left wall from the smaller blue spheres depends of the size of the smaller blue sphere, so it is an independent parameter. When I recover the energy from the modification of the volume of the spheres, it pass from V to 0.01 V and I recover the energy +2δh5/4√2*0.99 and I have an extra work on the left wall, I noted W. Now, I pass from V to 0.005 V, I recover +2δh5/4√2*0.995 but the extra work on the left wall is 2*W.
Example with pressures:
dng.png (41.74 kB . 1138x689 - viewed 2914 times)I drew the fissures bigger than they are:
96.png (15.07 kB . 1012x215 - viewed 2953 times)I think if I have no compressible blue spheres it is good. The force from the smaller spheres will be stop with the left wall.
The forces from pressure from the smaller spheres are more like that :
dbv.png (53.56 kB . 1164x590 - viewed 2934 times)The vertical force don't work (negative nor positive) but the horizontal yes. So, if at start, the device is like that:
xwp.png (28.79 kB . 1015x615 - viewed 2957 times)then the vertical forces can work.
I can take the black shape like that:
stnb.png (31.75 kB . 1164x688 - viewed 2924 times)Or better:
dol.png (32.82 kB . 1187x579 - viewed 2955 times)The forces to the left wall are greater.
It is easy to imagine the same device but without the black shape, if I want the same pressure of the orange area, I need attract more with the springs, so the green line will give more energy. The springs don't lost a lot of energy because their length are small. I don't recover an energy because I change the volume of the spheres but I recover an energy from the right wall, near the same. So, with the black shape, I need less force from springs for the same pressure: my device destroys the energy. The only problem is the size of the smaller spheres, it is necessary to prevent they go elsewhere the orange area (around and in the black shape).
Post by: Bored chemist on 02/09/2018 09:16:38
What are you trying to achieve here?
Post by: LB7 on 02/09/2018 19:23:19
drv.png (41.69 kB . 983x562 - viewed 2227 times)I think I recover more energy than I though when I decrease the volume of the spheres. But even here, the volume V1 is lower than the volume V2 so there is a difference of energy. I reduce the volume V2δ and I win that energy, but I need the energy V1δ (with δ a small angle of rotation). IMPORTANT: I don't move out the blue spheres, I reduce their volume by a factor 1000 and I pass them through the black shape, imagine the black shape with holes to let pass inside the smaller spheres. I have an extra pressure from these smaller spheres all around the black shape. The force of the springs is always constant.
dko.png (35.41 kB . 948x490 - viewed 2292 times)When the device is deformed, there is more and more spheres inside the black shape (smaller spheres). I can have like walls inside holes and recover an energy from the holes because the walls of the holes must move to the right in the same time the device is deformed, the surface is less important but the pressure is higher, I think it is compensated. So, maybe the presence of the fixed black shape recover than the right wall lost. So the green line, the right wall, the potential energy don't change because there is the black shape. But I recover an energy from (V2-V1)δP, with P the mean pressure from the smaller spheres.
Maybe there is no energy recovered from the modification of the volume of the spheres, because I need to move the spheres in the same time. So at final, there is only the extra force from pressure from the smaller spheres on the left wall because all the rest doesn't change.
Post by: LB7 on 03/09/2018 18:24:38
The sum of energy from the first pressure (the bigger spheres) is conserved. But the second pressure add a torque on the left wall that is not compensated because the black shape is fixed to the ground.
solg.png (45.22 kB . 910x509 - viewed 2216 times)I exagerate the size of the blue spheres:
dxx.png (69.1 kB . 1015x542 - viewed 2181 times)With the pressures:
syt.png (89.03 kB . 1197x569 - viewed 2163 times)The right wall has less surface because there is the black solid so it works less but when I change the volume of the spheres, I recover the same energy the right wall lost.
The left wall has an extra torque from the force of pressure from the orange area.
Like I said, the only problem is to prevent the orange part to go elsewhere in the container. I think it is only a technological problem not a theoretical.