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Author Topic: The pendulum bias paradox experiment  (Read 19380 times)

Offline Tusk

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Re: The pendulum bias paradox experiment
« Reply #15 on: November 12, 2012, 09:34:16 AM »
Quote
Simple.  The kinetic energy of the 2 balls is equal.

Actually the kinetic energy of the small ball = 4 x kinetic energy of the large ball.

The mass of the small ball is 18g and the large ball 72g. The velocity of each ball is determined by the release height and while the apparatus is primitive we can allow that the velocity of the small ball = 4 x the velocity of the large ball (the relevant equations were applied and a fair approximation achieved). Let's allow 1 unit of velocity for the large ball for simplicity and not concern ourselves with labeling units at this stage. Therefore if we compare the kinetic energy of the balls using Ek = ½ mv² we get a value of 36 for the large ball and 144 for the small ball.

However if we compare the momentum of the balls using p=mv we get 72 units for both balls.

As previously stated, you can run the numbers for the entire experiment on the back of an envelope, and the results are in accordance with convention.

What seems unclear here is already known. What is known is not always clear.


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Re: The pendulum bias paradox experiment
« Reply #15 on: November 12, 2012, 09:34:16 AM »

Offline TinselKoala

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Re: The pendulum bias paradox experiment
« Reply #16 on: November 12, 2012, 09:26:53 PM »
What is the problem? If you are not concerned with the behaviour of the wooden block -- since you have stopped mentioning it -- and if you idealize your balls to be perfectly elastic, then momentum is conserved (the balls meet at the same point at every oscillation) and energy is conserved (each ball rebounds back to the same height as it started from, with the same v and dv/dt profile but changed sign.)
Perhaps you could state your "paradox" in such a way as to not create straw men or mislead about what values go into what calculations.

Three travelers stop at an inn. The charboy is minding the till while the keeper is retrieving a fresh keg from the cellars. The travelers ask the price of one room for them all. The charboy says he's not sure, but he'll take 30 drachmas, and bring the change when his boss gets back upstairs with the fresh keg. So the travellers each give the charboy a ten-drachma gold piece, and go on down to their room. A bit later the innkeeper tells the charboy that the room was only 25 drachmas, and gives him 5 one-drachma silver pieces to take back to the travellers. So he does, but on the way he can't figure out how to divide the 5 silver pieces between the three travellers equally. So he simply pockets two of them as his "commission", and gives each traveler one drachma each as change. So each traveller has laid out ten drachmas and received one back... so they've spent twenty seven drachmas. And the two in the charboy's pocket make.... twenty nine drachmas.
Where is the other drachma?

It is in the same place as your "paradox".



Offline Tusk

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Re: The pendulum bias paradox experiment
« Reply #17 on: November 13, 2012, 12:09:27 AM »
Quote
What is the problem?

Why does the ball with greater kinetic energy not dominate?

Quote
If you are not concerned with the behaviour of the wooden block -- since you have stopped mentioning it

The wooden block collisions simply demonstrate more clearly the disparate kinetic energies of the two balls, a condition which is already evident in the original two ball collision.

Quote
if you idealize your balls to be perfectly elastic, then momentum is conserved (the balls meet at the same point at every oscillation) and energy is conserved (each ball rebounds back to the same height as it started from

You appear to grasp the momentum aspect of the experiment yet fall short with the kinetic energy, perhaps due to suspicion of the block collisions?

Quote
state your "paradox" in such a way as to not create straw men or mislead about what values go into what calculations.

These perceptions are your own Sir, and do not adequately reflect my intent or fairly represent my efforts thus far. I shall refrain from comment on your insulting child's riddle and simply restate the single, fundamental question which emerges from this affair and which for all your protestations you appear unable to provide an answer.....

Why does the ball with greater kinetic energy not dominate?


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Re: The pendulum bias paradox experiment
« Reply #17 on: November 13, 2012, 12:09:27 AM »
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Offline TinselKoala

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Re: The pendulum bias paradox experiment
« Reply #18 on: November 13, 2012, 01:31:13 AM »
You have been asked several times by several people to clarify your statement.

Why does the ball with greater kinetic energy not dominate?

Well, anyone can see that it _does_ dominate. It hits the big ball and pushes the big ball back all the way back to where the big ball started from, and it itself bounces back to a higher position than the big ball ever reaches. That's pretty dominating, in my way of interpreting your ambiguous statement. It doesn't let the big ball come into its side of the system at all, it just pushes it back and away.

Why don't you just describe what you think your "paradox" is without using the same statement over and over? I'll tell you why: because there really isn't any paradox unless you define your terms just so.

And I see that you apparently cannot or will not answer the childish riddle, and you cannot see how it applies to your "paradox". There is no paradox. Nobody disputes the fact that kinetic energy is relative to the reference frame, nobody disputes that momentum is conserved in elastic collisions, nobody disputes the fact that the balls rebounding to their original heights (less losses of course) is an expression of conservation of energy and a perfect example of the interplay and interchange between gravitational potential energy and kinetic energy of motion. So just where is your beef, what is the paradox?

Now is your cue to either a) repeat the same phrase, only louder; or b) disappear in a puff of dust.

Offline Tusk

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Re: The pendulum bias paradox experiment
« Reply #19 on: November 13, 2012, 05:41:18 AM »
Quote
anyone can see that it _does_ dominate

How so? Each ball reflects and returns by pendulum action to repeat the collision at exactly the same position.

Quote
It hits the big ball and pushes the big ball back all the way back to where the big ball started from

The same can be said of the larger ball against the smaller.

Quote
it itself bounces back to a higher position than the big ball ever reaches

It does so with far less mass. The momentum on each side of the collision is identical.

Quote
It doesn't let the big ball come into its side of the system at all, it just pushes it back and away

Again, the same can be said of the larger ball.

Quote
Why don't you just describe what you think your "paradox" is

My apologies, I thought it was obvious. At the point of collision, the centre of mass of the system, the balls meet with a bias in kinetic energy. Each ball is returned by contact with the other along a reciprocal path with no loss of kinetic energy (theoretical). Therefore neither ball can be said to dominate the collision. If one were to dominate, any subsequent collision would occur at a different point. The collision/swing cycle of the pendulum system manifests a form of equilibrium. Thus we have a ball on one side of the cycle with 4 x kinetic energy of the other yet each is able to repel the other with no exchange of kinetic energy from one to the other.

Quote
there really isn't any paradox unless you define your terms just so

As I said previously, no paradox can survive it's own solution. However, an inability to perceive a paradox simply due to dogmatic reflex provides no such solution.

Clearly from the tone of the rest of your post this is becoming personal for you, so I'll refrain from responding to those statements. I have no desire to offend, rather my focus is on a clearer perception of reality and likely to be clumsy on an interpersonal level at times, for which I apologise.

Not every drop of water precedes a flood but every flood begins with a single drop. I have seen a hope expressed here in multiple threads that eventually someone will reveal the key to overunity, no patents, no secrecy, just open disclosure in full depth with all significant elements fully explained and capable of replication. Think about what is being asked here; for someone to make a gift of their life's work, freely and without strings attached, possibly at some personal risk, to those who can potentially advance the concept to the next level and in turn perhaps reap the rewards without so much as backward look.

Do you expect such a person to arrive cap in hand, asking permission to bend this law or that, or apologise for doing so? I put it to you that no device capable of overunity is possible unless one or another of the established laws is broken. The heading says 'Mechanical Free Energy Devices'. People have been shoving things around, and into each other in accordance with the laws of conservation of this or that for millenia, without so much as a glimpse of overunity. So it seems quite likely that, at least for a mechanical device, one of those laws will have to go. All the talk in the world about open and closed systems hasn't provided overunity, at least not out in the light of day, here for all to review and evaluate. I see those claiming overunity behind a veil of secrecy, reassuringly stating that no fundamental laws have been broken. Do you really think it's going to be that easy?

When it comes, nothing about it will be familiar. No reference to any text book, no glib response will help shunt your consciousness up to that next level of reality. Only an open mind free of concerns of the ego, a willingness to accept that someone else can see that which you can not yet see, and a burning desire to peer that little bit further out into the darkness. This therefore requires trust and respect on both sides, and not a small amount of patience.

So, a new analogy perhaps; do you not think it strange that a heavily laden slow moving truck with low kinetic energy can be struck head-on by a fast moving lightweight car with high kinetic energy, yet the two crunch together at the point of collision with neither able to push the other along the road? But if we crash each of these vehicles at the same initial speeds into some other obstacle, say a house or a wall, the car would create significantly more damage than the truck. Obviously you accept that this is so, any secondary school physics student already knows it, but can you state clearly why it is so? Unless someone here at least acknowledges the problem there is no advantage in proceeding further. We haven't even got to the hard part yet.

Why does the ball with greater kinetic energy not dominate?

 

 

           





   




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Re: The pendulum bias paradox experiment
« Reply #19 on: November 13, 2012, 05:41:18 AM »
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Offline Fester

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Re: The pendulum bias paradox experiment
« Reply #20 on: November 13, 2012, 08:42:45 AM »
The base plate of this pedulum rig is poor at best. It needs to be done with a single piece of wood. The secondary piece for the block test might not be the same thickness. This will leave gaps and reduce friction. This will mean less friction for the small ball test and not the big ball test. A small lip or even a crack could change the results as well. Also get rid of the elastic rubber balls and get steel balls. Energy transfer for elastic materials is directly effected by their density. Your big ball could have a large air pocket inside of it. It may have the same mass but its may have a bias of density opposite the end your string is on. Which would make the side wall of the ball collapse more than it "should". The spring rate of the ball is going to be how much energy it stores up for the second swing. Hence, part of the kenetic energy is turn back into potential energy. So your rig as a measure of kenetic energy is inadequate because of the rubber balls you use.

You cannot get static results from a non-static environment. The environment in the video is under change from have 2 different base plates and 2 different flexibility rates of the balls. A poor rig giving innacurate results. Ego's do need checked sir, that would be yours. It's one thing to think you have something based on a "shoddy" rig at best, but to plague a students mind with it is not responsible. Your appearant misconception can stick with that student for a long time.

Offline Tusk

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Re: The pendulum bias paradox experiment
« Reply #21 on: November 13, 2012, 10:03:25 AM »
Quote
The base plate of this pedulum rig is poor at best. It needs to be done with a single piece of wood.

Thanks for the advice re increasing experimental rigor Fester. If there was any doubt about the outcome I would certainly have adopted such measures, but since the results as shown are already known and predicted in the literature it seemed acceptable to present an apparatus capable of reproducing those results for demonstration purposes rather than a research grade apparatus. If anyone still has concerns I would refer them to the relevant chapters on momentum and kinetic energy of any decent high school physics book.

There is indeed a noticeable error in the motion of the block when struck by the small ball, it should show a four fold increase over the large ball and block test, but in fact only moves approximately X 3 which really doesn't impact on the spirit of the demonstration. None of the points you mention apparently had any significant effect on the results, which as I have already stated on several occasions are predicted in the literature and furthermore present little difficulty in the calculation.

If the local temperament is more for finding fault in the minutia than checking for authenticity in the main thrust of an idea and attempting to understand the reasoning behind it then perhaps after all I am in the wrong place.





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Re: The pendulum bias paradox experiment
« Reply #21 on: November 13, 2012, 10:03:25 AM »
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Offline Newton II

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Re: The pendulum bias paradox experiment
« Reply #22 on: November 13, 2012, 11:41:08 AM »
Actually the kinetic energy of the small ball = 4 x kinetic energy of the large ball.



If kinetic energy of small ball is 4 times more than that of large ball, then after each collision the energy of both balls should go up and oscillations should become perpetual even after considering losses.  Is it not?

Offline TinselKoala

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Re: The pendulum bias paradox experiment
« Reply #23 on: November 13, 2012, 01:02:01 PM »
@Tusk: I see you have chosen Option A: you repeat the same phrase, only louder.


I explained one interpretation that shows that the smaller ball "does dominate". I could also explain an interpretation of your phrase that shows that the larger ball "dominates", or that neither "dominates".... because you do not specify what you mean by your phrase in a physical (I mean physics, kinematics, dynamics, mathematics) context. You choose to play word games instead of asking a real question that can be answered with vector calculus. You want there to be a paradox where there isn't one, or you want people to see or think there's a paradox, because you have some point that you are going to be making, down the road, and you want people to be trapped into accepting it because of your "logic" at this stage of the matter.

Fine, I'm sure you'll find plenty of people to play your game. Carry on.... but please, you could at least stop being so very predictable.

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Re: The pendulum bias paradox experiment
« Reply #23 on: November 13, 2012, 01:02:01 PM »
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Offline Tusk

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Re: The pendulum bias paradox experiment
« Reply #24 on: November 14, 2012, 03:54:49 AM »
I'm sorry you see it that way TK, I was merely attempting to avoid obfuscation of the fundamental principles in play here by getting bogged down in the maths. We really don't need to dot all the I's and cross all the T's at this stage of reviewing established material - the simple fact that we can arrange a collision between two bodies with different kinetic energy which results in the total mass of the system being brought to a complete state of motionlessness at the very centre of mass of the system is not even in question, it is already known. We can see this happening clearly in the experiment, and already know that the small ball has higher kinetic energy than the large ball (if not from the ball on block tests then by simple observation of relative mass and velocity).

The issue of dominance in the collision seems to me self explanatory, but perhaps I can state this another way for clarity; let's assume a totally non-elastic collision between two balls of clay with the same mass and velocity as in the experiment. Since in the elastic collision the balls cease all motion then reciprocate at the bottom of the pendulum (as it happens this is also the location of the centre of mass of the two balls) we can assume with confidence that the clay balls will come together and remain motionless at this same point.

If the balls represented sumo wrestlers then it would be fair to say that neither ball dominated. If we allowed the balls to represent an arm wrestling bout then again, neither ball dominated. If the balls represented two bulls rushing headlong at each other during combat then again, neither could be said to dominate.

Only if the balls in this inelastic collision were still in motion post collision could we then say that one ball had dominated. Going back to our elastic collision we would say that if the point of collision moved in subsequent collisions, then one ball had dominated.

But I find it hard to believe that someone of your experience could repeatedly fail to see the blindingly obvious. More likely you are simply unable to answer the question, in which case you are now too heavily invested in 'winning' this exchange to admit that a genuine phenomena is in play here which requires explanation. No doubt you would prefer the discussion to deteriorate into a dry mathematical analysis, but I refuse that challenge and for good reason. If the discovery of overunity was possible by mathematics alone we would have it already. Only by an open minded re-examination of known phenomena using careful observation and the gift of logic can we hope to uncover those aspects of the phenomena which will lead us to a full understanding of reality yet which have to this point in time eluded us. So I ask yet again...

Why does the ball with greater kinetic energy not dominate?

(and for TinselKoala, by special request)

Why does the ball with greater kinetic energy not disturb the centre of mass of the system, which is static throughout the experiment?





Offline TinselKoala

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Re: The pendulum bias paradox experiment
« Reply #25 on: November 14, 2012, 07:08:34 AM »
Because momentum is conserved. You apparently want to look for conservation of energy in the wrong place. I have told you already that CofM accounts for the center of mass remaining in the same place, and that CofE accounts for each ball rebounding to its original height. Assuming perfectly elastic collisions of course. There is no paradox, simply a misapplication, apparently, by you, of the correct laws in the correct place. Again, I believe that this is deliberate and that you have some agenda down the line and you are leading up to something. So get to it.

It would be a neat trick to get your "perfectly inelastic" clay balls to stop dead when they hit; this would require the _total_ kinetic energy of the two balls to be completely dissipated as deformation, heating, etc. perfectly symmetrically throughout the resulting mass. In a thought experiment, maybe. In the real world, I doubt it. The internet is full of examples of partially damped "inertial thrusters" that  "work" by partitioning kinetic energy unequally this way and thus, moving their centers of mass, in a manner that you apparently might call a paradox. I've made a few myself.

If you want me to explain to you why momentum is conserved, or why _total_ energy is conserved..... the best I can do for you there is to appeal to an anthropic principle of sorts: because if the Universe were otherwise, it would not look like it does now and we wouldn't be here to view it. Or I could refer you to God ... but he's not talking, at least not to me.

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Re: The pendulum bias paradox experiment
« Reply #25 on: November 14, 2012, 07:08:34 AM »
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Offline Pirate88179

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Re: The pendulum bias paradox experiment
« Reply #26 on: November 14, 2012, 07:13:16 AM »



Why does the ball with greater kinetic energy not disturb the centre of mass of the system, which is static throughout the experiment?

I take exception to this conclusion.  The center of mass does indeed move, just enough to obtain equalibrium  which, nature seems to like.  If studied closely using a rigid test device, this would become obvious.

Bill

Offline TinselKoala

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Re: The pendulum bias paradox experiment
« Reply #27 on: November 14, 2012, 07:17:45 AM »
I take exception to this conclusion.  The center of mass does indeed move, just enough to obtain equalibrium  which, nature seems to like.  If studied closely using a rigid test device, this would become obvious.

Bill
I think you are right too, Bill. I think if you idealize the masses to points and have their suspensions at the same point, ideally the center of mass wouldn't move. But this is impossible to achieve in reality with balls of different diameters and suspensions separated by a finite distance.

Offline MileHigh

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Re: The pendulum bias paradox experiment
« Reply #28 on: November 14, 2012, 09:17:21 AM »
I haven't read the last few days but just skimmed the last few postings.

Some comments that may help:

Conservation of momentum typically is discussed in cases of an inelastic collision.  Momentum is conserved and energy is lost, but often energy is not even being considered in cases like this, just momentum.

When the balls are about to hit, and after the hit,  it would appear the center of mass for the two balls does not change, and the center of mass is not moving.  You observe a nearly perfectly elastic collision.  It's like each individual ball hit a hard wall and bounced off.  They must have equal kinetic energy when they hit for that to happen.  If there was an imbalance in kinetic energy then the center of mass between the two balls would have to be moving after the collision and it doesn't.  You would notice an asymmetry in the the behaviour of the balls with the first few successive hits and you don't see any.

So you are left with both the small and the large ball hitting the block of wood with the same kinetic energy, but different masses and velocities.  The block of wood reacts appropriately for each type of hit as was previously explained.

Offline Tusk

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Re: The pendulum bias paradox experiment
« Reply #29 on: November 14, 2012, 10:36:27 AM »
A fair attempt TK.

Quote
Because momentum is conserved

Quote
CofM accounts for the center of mass remaining in the same place

Quote
CofE accounts for each ball rebounding to its original height

As I stated earlier, not recognising the paradox merely indicates an 'off the shelf' perception based in convention.

Quote
If you want me to explain to you why momentum is conserved, or why _total_ energy is conserved.....

Clearly you cannot, neither the vast majority. But your perception of the phenomena is based completely on established laws with no real understanding of the 'how' or 'why'. No shame in that but since you seem unlikely to acknowledge the difference, turning over new ground will be all but impossible, not unlike investigating gravity with someone completely comfortable with the idea of things somehow magically 'pulling at each other' across the void (Mr Einstein's warped fishnet of space-time notwithstanding). This with no rancour, we are at odds merely due to disparate perspectives.

So, I will give you the answer, although at this point for what purpose I am not certain. Why does the ball with greater kinetic energy not dominate?

As a first step let's examine How:

Throughout the collision the forces applied by each ball to the other must be equal, and while these forces vary throughout the collision we can for the sake of clarity treat them as constant. Since kinetic energy is a function of velocity it is also a function of distance. The centre of mass of the ball with the greater kinetic energy must therefore travel a greater distance during the collision because the period during which the collision takes place is the same for both balls (the acceleration of the balls cannot be equal as this would produce unequal forces). Thus both balls come to a state of rest each having applied an equal force to the other for an equal period of time.

Why?

Since all motion (and every collision) is governed by momentum therefore kinetic energy is simply an artifact of the frame of reference in which it is observed. If our frame of reference were the centre of mass of the large ball (pre-collision) we would observe that the small ball had high kinetic energy and post collision results would be in accordance with that observation. If our frame of reference were the centre of mass of the small ball then it would have no kinetic energy. But since our frame of reference for the experiment is the centre of mass of the system we observe the true nature of the phenomena, determined solely by momentum with the kinetic energy of the balls seemingly unequal yet in fact simply not relevant. Kinetic energy only manifests when measured against a 'static' point in our frame of reference, or in other words when we place ourselves in the same frame of reference as 'the large ball'. The reality and determination of every collision resides in the domain of momentum.

Conclusions

The experiment demonstrates what is already known; kinetic energy is not invariant. I use the double negative here just as it often appears in the literature. If you want to say something without anyone really hearing it use a double negative. So we could also say that kinetic energy is variable (depending on frame of reference). It follows that conservation of energy, at least with reference to kinetic energy, is also frame of reference dependent.

As a result, anyone interested in mechanical overunity might want to think seriously about the mechanical manipulation of frames of reference, without which conservation of (kinetic) energy dictates that there can be no advantage.

As stated previously there is more, but perhaps this material is a tad too spicy for the local palate.
 







 


 

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