IS THIS A REACTIONLESS DRIVE OR A PERPETUAL MOTION MACHINE?

[George1]

To ME.
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Really perfect animation at https://www.besslerwheel.com/forum/down ... p?id=21901
Congratulations! My respect to your skill! Please only make the 7 corrections, if possible.
Looking forward to your answer.
Regards,
George

[ME]

First of all I would like to apologize for being a little more rough than necessary. Please excuse me for my, let's say to some extent, inadequate behaviour. I am really sorry.

That can happen to the best of us.
It only took 22 pages, but it feels like if we can finally start a conversation.
:-)

1) As I interpret this situation, when this sideways motion of the spring is not allowed then no longer that block can slide down the incline;
2) I think that when it starts unattached, the initial forces are more clear;
3) So you don't need a ball, it's just that body 2 is a heavy object that's shaped like having an incline on its top;
4) See 1.;
5a) This somewhat contradicts 2. "Somewhat" because of course you can start with only one corner touching the incline. But why not just start completely unattached?;
5b) When it touches the ramp it will rotate counter-clockwise to match the ramp-angle;
6) Sounds good.

So I firmly attached the planet to the incline. The planet is a heavy block, so it does not have to be spherical/circular.
Because of (1) I added a (north) pole for the box to slide on to prevent that spring from moving sideways.
That green incline weighs almost nothing, and you see that both box and "body" move towards their common center of mass - that's an important observation; hence my remark at (5a).
To state this again, the box no longer slides down that ramp because of this "northpole".
So this mgsinθ of the box is now pushing against the pole at that angle. This force tries to be a torque/turning force at the point of attachment. Thus when this pole would collapse it would drop to the left. But it doesn't, because it's firmly attached.

And now, because of (1) then sure, G=N or G=-G or whatever it was.
The simulation shows that the rotations, as predicted in (5) and (6), do indeed happen and all will have a zero-rotational velocity again because they counter each other again once the box settles motionless on the incline.

Really perfect animation... Please only make the 7 corrections, if possible.

7 ?

Recounting the inventory:
0. Space
1. Block
2. Incline
3. Attractive force;

Well ok, an added (north) pole and other distractions...

[George1]

To ME.
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Perfect! Really perfect second animation at https://www.besslerwheel.com/forum/down ... p?id=21914! Once again my respect to your skill!
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A) Yes, I perfectly agree that the ball can be replaced with a cube. You further develop successfully the basic concept. Good!
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B) I would like to ask you to make again another 7 small corrections however. And here are these 7 small
corrections.
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1) Let us remove the grey rod (which is as if firmly attached to the cube). There must be only four bodies -- the cube, the green ramp, the red block and the sping.
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2) Motion must start where (at the moment in which) the above animation stops. (Where the red block touches the green ramp in the middle of the incline approximately.)
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3) The spring must contract as its longitudinal axis of symmetry must be motionless.
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4) The geometric center of the red block and the geometric center of the cube must approach each other on a straight line, which must coincide with the longitudinal axis of symmetry of the spring.
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5) Except moving on a straght line the red block must rotate clockwise at an angle α. The related center of rotation is the geometric center of the red block.
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6) Except moving on a straght line the green ramp together with the cube (these two forming one united whole as shown in the animation) must rotate at an angle β. The related center of rotation must be geometric center of the cube.
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7) While being in motion the the red block and the green ramp must be always in contact, that is, the sliding contact must never be lost.
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I would like to ask you to make the above 7 small corrections, if possible.
Looking forward to your answer.
Respectfully yours,
George

[George1]

To ME.
=================
Hi there,
Looking forward to your third perfect animation (with the 7 small additional corrections, if possible). Please ask questions, if any.
Best regards,
George

[ME]

1) Let us remove the grey rod (which is as if firmly attached to the cube). There must be only four bodies -- the cube, the green ramp, the red block and the sping.
---------------------------------
2) Motion must start where (at the moment in which) the above animation stops. (Where the red block touches the green ramp in the middle of the incline approximately.)
---------------------------------
3) The spring must contract as its longitudinal axis of symmetry must be motionless.
-------------------------------
4) The geometric center of the red block and the geometric center of the cube must approach each other on a straight line, which must coincide with the longitudinal axis of symmetry of the spring.
---------------------------------
5) Except moving on a straght line the red block must rotate clockwise at an angle α. The related center of rotation is the geometric center of the red block.
-------------------------------
6) Except moving on a straght line the green ramp together with the cube (these two forming one united whole as shown in the animation) must rotate at an angle β. The related center of rotation must be geometric center of the cube.
-------------------------------
7) While being in motion the the red block and the green ramp must be always in contact, that is, the sliding contact must never be lost.

1) I thought you didn't want a sideways motion as was visible in the first animation in space: Hence I added that pole;
2) It already is. You can see in that animation that they get attracted purely vertical before they touch. This indicates that each their Center-of-Mass are aligned vertically;
3) See (1). Perhaps you need to clarify.
4) See (2). That arrangement becomes automatically aligned when we attach the spring at each their Center-of-Mass (CoM)
5) Ok, next time I'll let it bounce at the slope angle. And we already know it will bounce somewhat horizontally to the left. The direction of the Normal-force of the slope forms its mirror line. Like a cue-ball that hits the side cushion of a pool-table.
6) We have to pick an orientation, so either we pick an angle α for one, or an angle β for the other, or an angle α+β for some combination. I don't know what you mean by α or β. So rotating the cube seems most obvious, see (5).
7) Then some things will not be obvious, like I mentioned in (2) and what I predict will happen in (5).

For each of these points: Hence the need for you to provide a picture yourself...
A new animation may take a while, currently I have other things to do.

[George1]

To ME.
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Hi ME,
Thank you for your reply.
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Let us firstly clarify the geometry of the motion (the kinematics) of a certain particular case. And just after that we could consider what happens with forces.
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1) The spring must only contract and must not move sideways, that is, its longitudinal axis of symmetry must be motionless.
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2) The geometric center of the red block and the geometric center of the cube must approach each other moving on a straight line, which must coincide with the motionless longitudinal axis of symmetry of the spring.
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3) Except moving on a straight line the red block must rotate clockwise at an angle α. The related center of rotation is the geometric center of the red block.
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4) Except moving on a straight line the green ramp together with the cube (these two forming one united whole as shown in the previous animations) must rotate clockwise at an angle β. The related center of rotation must be the geometric center of the cube.
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5) While being in motion the red block and the green ramp must be always in contact, that is, the sliding contact must never be lost.
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6) There must be only four bodies -- the cube, the green ramp, the red block and the spring.
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Note. Actually we have to design the point of view of an observer, who accepts motionless the straight line, on which move the geometric center of the red block and the geometric center of the cube, and which is the longitudinal axis of symmetry of the spring.
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Now it seems to me that everything is clear. But please ask questions, if any.
Looking forward to your answer.
Best regards,
George

[George1]

To ME.
-------------------------
Looking eagerly forward to your third perfect animation. Please ask questions, if any.
Best regards,
George

[George1]

To ME.
----------------------
Where did you disappear, dear colleague? What happens?

[ME]

A new animation may take a while, currently I have other things to do.

Currently I have no access to the simulator.

But be prepared that the result is very likely similar to the first in-space simulation.
Especially when the 'Earth' is relative very small compared to the incline.

[George1]

Hi ME,
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Thank you for your reply.
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1) The two most important requirements for the third animation are that (1) the longtudinal axis of symmetry of the contracting spring must be motionless (that is, the contracting spring must not move sideways; the spring must solely and only contract!) and (2) the sliding contact must never be lost.
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2) Waiting for your access to the simulator.
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Looking for ward to your answer.
Regards,
George

[ME]

But that's precisely why I created that northpole!
1. Either that box slides along that incline so the spring traces an arc while contracting;
2. Or that box does not move at all;

You can't have it both ways.

On the Earth's surface things move along a very large radius, yet the same happens there.
The radius is as such that it only seems like gravity is always vertically down on a flat plane, but actually a sideways motion traces an arc too.
Say a box slides 1 meter sideways, then it traces an arc of γ≈ 32 milli-arc-seconds ≈ 9·10⁻⁶ degrees.
Because this angle is so immensely small, the definition of Earth-level has a different meaning than a pure geometric level*
Per meter sideways the Earth remains level according to gravitational attraction while it drops an immeasurable amount of about 80 nano-meter on a very smooth Earth surface compare to that geometric level.
* Fun fact is that while due to Earth's gravitational distortion a horizontal laser beam is deflected a tiny bit down it is actually that the curvature of the Earth is still stronger so that a horizontal laser beam is deflected upwards relative to the Earth's surface.

There is actually another way to utilize that spring for it to conform with your requirement. That's simulation #4 put in queue...

[George1]

To ME.
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But we are talking again about different things.
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Let me explain again.
1) An observer assumes that the line, which connects the geometric center of the red block to the geometric center of the cube is MOTIONLESSS AND DOES NOT MOVE SIDEWAYS AT ANY ANGLE. What would see such an observer? He/she would see the following 3 things.
1-1) The spring contracts.
1-2) The geometric center of red block and the geometric center of the cube approach each other moving on a straight line, which is the longitudinal axis of symmetry of the spring.
1-3) The red block and the cube rotate clockwise at angles α and β, respetively.
2) We can always choose such sizes of the bodies for which angles α and β to be measurable and big enough to be seen.
3) The red block and the green ramp must be always in touch.
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Clear enough now?

[ME]

Clear enough now?

You repeat the same thing...and it's obviously very clear to you.
But it's not clear to me.
It's the reason I ask for a diagram that comes from your hand.

[George1]

To ME.
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Ok, I see.
1) Please look at the link https://www.researchgate.net/figure/Fol ... _311099116
2) Please look at the second rectangle from left to right. A vertical dashed line divides the area of the rectangle into two equal parts.
3) The rectangle is the screen, in which takes place the animation.
4) The dashed line is the straight line on which move the geometric center of the red block and the geometric center of the cube.
5) The dashed line and the rectangle form one inited whole, that is, the rectangle and the dashed line do not move relative to one another.
6) The dashed line is axis of symmetry of the contracting spring.
7) The motions of all other bodies are adjusted accordingly.
Seems to be clear now, doesn't it?
Looking forward to your answer.

[George1]

To ME.
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And one more as if clearer example.
1) Please look at the link https://ssddproblems.com/a-rectangle-ma ... es-part-2/
2) Please look at the rectangle ABCD. The straight line (the segment) MNdivides the area of the rectangle into two equal parts.
3) The rectangle is the screen, in which takes place the animation.
4) The line (segment) MN is the straight line on which move the geometric center of the red block and the geometric center of the cube.
5) The line (segment) MN and the rectangle form one inited whole, that is, the rectangle and the line (segment) MN do not move relative to one another.
6) The line (segment) MN is the axis of symmetry of the contracting spring.
7) The motions of all other bodies are adjusted accordingly.
Seems to be clear now, doesn't it?
Looking forward to your answer.