Pendulum calculation

[Fletcher]

Tarsier .. to further clarify my position that Cf's are conservative.

Cf's are generated when an object is forced from its straight line path, say as per this pendulum example - Cf's are a function of Mass having Inertia.

This is where some argue with the conclusions I reach.

Starting from the position of CoE.

If a dual mass radial pendulum [clay's example] falls from 3 o'cl it starts with Joules of Pe - at 6 o'cl it with have Joules of Ke [Rotational & Translational] - this will equal the Pe Joules lost in height, not counting frictional losses to idealize the situation.

If the Cf's developed are allowed to do WORK [F x D in Joules] by letting the masses move radially, then those Joules must be accounted for somewhere to have CoE.

The Work Done using Cf's x distance [Joules] comes off the final Pe of position Joules achieved i.e. Work Done by Cf's = Pe Joules lost, otherwise gravity & Inertia would not be conservative !


CoE is maintained - if Cf's could do Work greater than the Joules of Pe lost then you'd have OU capability - this is what some are arguing is theoretically possible but I've not seen it empirically displayed.

So the reverse must be true - if you add energy to close the distance between the masses against net Cf's then that added energy must be accounted for - it is, closing the separation distance of masses gives a lower MoI & the pendulum swings higher than it started from, without losses as per this hypothetical example.

[Fletcher]

Back to your question Kaine about the MoI NOT changing when one mass moves an equal distance towards the axis as another moves away from it ?

Well, the MoI does change & I explained it as mass being forced to rotate as well as lower its height.

In pure energy terms, if you prefer to think of it that way, a fixed single bob falling from 3 o'cl to 6 o'cl will have Ke made up of Translational Ke [moving across the gravity gradient] & Rotational Ke [rotating movement].

A freely pivoted bob [not fixed connection] has more Translational Ke & lesser Rotational Ke than the equivalent bob attached by a fixed connection i.e. the latter has more Rotational Ke & lesser Translational Ke - a lesser Trans Ke translates to a lesser velocity at 6 o'cl.

This is not the mystery - both pendulums would achieve the same height on the upswing because both their TOTAL Ke's are the same - in the case of where cf's move one mass inwards & another outwards, after the shift to a greater distance apart the masses have greater Rot Ke & lesser Trans Ke but overall TOTAL Ke is the same as before ... except ... the masses must be stopped & this is usually by a physical stop they hit - this is therefore Work Done & accounts for the shortfall in energy seen by the pendulum NOT achieving start height, assuming no frictional losses etc.

CoE !

[clay973]

Thanks for your responses Fletcher, you descriptions seem to match the physical results perfectly.

What are your thoughts on what would happen if the top weight was say 2.5kg and the bottom weight was 2kg?

Or if the 2 weights were joined by a spring so they expand and contract in the same swing?

[Fletcher]

Thanks for your responses Fletcher, you descriptions seem to match the physical results perfectly.

What are your thoughts on what would happen if the top weight was say 2.5kg and the bottom weight was 2kg?

Or if the 2 weights were joined by a spring so they expand and contract in the same swing?

You can easily build a spreadsheet to plug in the figures & variables - there will be a relationship between radius & mass where the Cf's are the same for both masses - at that point of equilibrium no radial force will be apparent & no work can be done by Cf's N.B. the CoM will change according to the relationship & can also be factored into your spreadsheet.

The problem with Cf's [i.e. Cp's] is not that it can't produce a force that can be used, but that mechanics exist in a kinetic world where objects interact & collide - this is an exchange medium for energy - so, as you develop Ke from releasing a mass subject to Cf's [WD = F x D] then in effect the act of using Centrifical Force transfers the energy outside the pendulum system as external work done - this can be done but we can not restore the Pe of the system so that it can repeat.

The only proof IMO that energy can be created by using Cf's [N.B. not by developing them] is to apply the Work Done relationship of Cf's x distance via a mechanical linkage to accelerate the pendulum forward, this giving it velocity & momentum - IF it can achieve a higher vertical position [Pe] than it started with [this takes account of the CoM] then that will be proof conclusively that Cf's can be used to restore Pe & that an extra energy gain can be had to do external work - in effect a solid proof of an energy gain from the effects of inertia & rotation in a gravity field thus proving one or both are not conservative, aka OU from Cf's.

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Connecting the masses by springs so that they first expand part then contract in the same swing will not result in restoration of Pe !

The reason is this, but before I go into it - first, we all tend to think of the example of the spinning ice skater straightening & curling his arms to increase or decrease angular velocity/momentum etc - this seems conservative in that no extra energy is gained from the exercise & we'd all probably agree with that - so we might think the same applies for your example of masses moving apart & together thru the interaction of Cf's & springs [which store Ke as Pe] - we might reasonably expect that since the masses moved out & back the same distance or even further e.g together, that no work was done & that the pendulum would achieve the same vertical height [Pe] that it started with [assuming no losses etc].

The reality is that it doesn't though it can come close - partly this is because of the method usually applied to move the weights along the radials e.g. slides etc - this keeps things in alignment but can also reduce angular velocity as I'll explain later.

Anyway, as per your spring connected example - the masses move apart then back towards each other - if they move the same distance out & back the pendulum will still loose Pe - if they start quite far apart & the spring is allowed to bring them all the way together e.g 1 unit distance apart & 2 unit distances until together then this is analogous to the ice skater - but still full Pe will not be restored though it may come close - never will there be a gain in Pe using only inertia & gravity.

Lastly, as a member here [broli] once demonstrated with a sim program, if you have a spinning disk & release a weight to move outwards along an infinite radial due to Cf's [or Cf's & gravity fall], the weights inertia & friction against the slide will eventually halt the disks rotation, stopping it dead - in effect the two inertia's are leveraging against each other.

[Tarsier79]

Thanks Fletcher. I think I will take some time to get my head around logically why the COM isn't the only factor in the MOI of the rotating double pendulum.

I did as you suggested and played with WM2d.... compared to a single weight at 1M, to get the same velocity with 2 weights spread apart to .5 and 1.5 I had to make it so the inner weight was 3X the outer. (Confirming it is proportional.)

[Fletcher]

http://en.wikipedia.org/wiki/Radius_of_gyration

Perhaps a search on gyration [center of] might make more sense to you than what I write.

Consider what happens to an inverted 'T' pendulum in terms of CoM & Center of Gyration, especially if you lengthen the top of the T & add weights at the end ?!

This is easy to model in WM2D.

Then extrapolate to disk bobs of various diameters & 'X's as I mentioned to view the bob as a package of discrete atoms which combine in the term MoI.

[pequaide]

When a one kilogram mass is dropped in freefall 10 meters it will have a velocity of 14.0047 m/sec ; and that velocity will allow it to rise 10 meters. One hundred percent of the energy; the momentum and the motion is accounted for in the fact that the mass has a velocity of 14.0047 m/sec.

When a one kilogram mass is dropped in a pendulum 10 meters it will have a velocity of 14.0047 m/sec ; and that velocity will allow it to rise 10 meters. One hundred percent of the energy and momentum and motion is accounted for in the fact that the mass has a velocity of 14.0047 m/sec. No other information is necessary. There are no other stored forms of energy; momentum; or motion.

For every centrifugal force there is an equal and opposite centripetal force. These forces are balanced and have no effect upon the quantity of motion held in the system. Any particular interest in them is in my opinion a red herring. These forces (CP and CF) do not increase or decrease the motion in the system: they are simply there. They do not mysteriously hide energy away from us or store mystic quantities of energy; they are simply there, and they are balanced. The fact that the final velocity of freefall and pendulum motion are exactly the same proves that there is no centripetal/centrifugal stored energy in pendulum motion. It is all up front; it is all there, (14.0047 m/sec for a pendulum = 14.0047 m/sec for freefall)

Forces can be, and often are, balanced. Force does not necessarily cause motion. A five kilogram mass can exert 49.003 newtons on the science lab table all summer but it does not move the table. Trying to make an energy pump out of these two forces (CP and CF) would be like fitting a suit for a ghost.

A good analogy would be a moving puck floating on dry ice. The experimenter is interested in measuring the horizontal velocity of the puck. But while he is making these measurements there is a large force from the puck pushing down on the table and the table is pushing back. The experimenter totally ignores these forces as you should ignore CF and CP. Many times knowing what to leave out is an important part of achievement.

[Tarsier79]

Peq

I believe a simple newtons arrangement that should prove your theory. If you have two dissimilar weights and drop the larger to hit the smaller stationary weight, the larger will keep going.

1. You could measure the height the larger achieves, and by that calculate the momentum lost vs the momentum transferred and the height gain of the small ball.

2. By starting both balls at a calculated height with a repeatable release mechanism, you should be able to get the heavier ball to come to a complete halt, which would be your complete transfer.

According to your and Kirks theory, there should be a COM lift in both cases.

The findings of this thread render my prev. experiment somewhat invalid due to the weight distribution of the two pendulums. I suspect the results will be similar though.

[pequaide]

The cylinder and spheres experiment works as a proof; why not just repeat that?

[Tarsier79]

Does the cylinder and spheres experiment show conclusive proof of a gain in energy? If there was, then we would already have a working wheel. Having an excess of energy would mean that the rest is just a case of engineering problems.

I did a search on cylinder and spheres, and haven't found exactly how that experiment works. I did find a number of videos that I have put on my to-do list to watch.

Why do this experiment? We are looking for repeatable, measurable and conclusive proof of a gain of energy.

[clay973]

Tarsier, read this epic thread for the details of the cylinder and spheres http://besslerwheel.com/forum/viewtopic ... highlight=

The tests were not conclusive as no input or output were ever measured.

[Fletcher]

Peq

I believe a simple newtons arrangement that should prove your theory. If you have two dissimilar weights and drop the larger to hit the smaller stationary weight, the larger will keep going.

1. You could measure the height the larger achieves, and by that calculate the momentum lost vs the momentum transferred and the height gain of the small ball.

2. By starting both balls at a calculated height with a repeatable release mechanism, you should be able to get the heavier ball to come to a complete halt, which would be your complete transfer.

According to your and Kirks theory, there should be a COM lift in both cases.

The findings of this thread render my prev. experiment somewhat invalid due to the weight distribution of the two pendulums. I suspect the results will be similar though.

Does the cylinder and spheres experiment show conclusive proof of a gain in energy? If there was, then we would already have a working wheel. Having an excess of energy would mean that the rest is just a case of engineering problems.

I did a search on cylinder and spheres, and haven't found exactly how that experiment works. I did find a number of videos that I have put on my to-do list to watch.

Why do this experiment? We are looking for repeatable, measurable and conclusive proof of a gain of energy.

See below the Trasier-Newton Cradle analogue & also a Pequaide cylinder & tethered sphere analogue [N.B. controlled rotation speed driven by a rim mass falling under gravity as per Nick's thread].

Follow the sims & note at any frame the summed Pe & the Ke's - in sim world at no time does the Ke exceed the Pe losses etc - some will argue that a sim cannot show OU because it is programmed based on Energy calculations - I'd probably agree with that - the point is that either could be easily made in the real world to compare against the sim predictions to end this argument.

N.B. in the modified Newtons Cradle [your option 2] I made all elements steel with an elasticity of 1.00 [steel is 0.95] - this reflects the perfectly elastic collision of the satellite slingshot effect where there is no physical collision - this is the best result possible with the sim program.

In the flywheel & flung mass scenario the tether rope absorbs much of the energy as tension & strain as Cf's stopped the flywheel, IMO.

P.S. shafts are effectively mass_less.

These sims show the heavier object being stopped in its tracks - they alo show an almost 100% energy transfer but they don't show a gain in energy.

The momentumists would have you believe they also show 100% transference of momentum & therefore there must be a gain in energy ???

[Tarsier79]

Thanks Fletcher. I have done a number of Newtons cradle tests in WM2D, although your skill in the program is obviously far superior to mine. I would like to do the tests in the real world, but my efforts are supposed to be directed towards renovating my house to sell before the property market dies any further.

Notice in the WM2D of the impact with dissimilar pendulum lengths, the 1KG pendulum should be 2x the length of the 2KG, but the ratio you have is 3 : 4.18. Is the ratio you used calculated with the inertial properties in mind, or was it trial and error to make the simulation act in this way? In my real world build of this test, the 1/2mass COM at 2x the distance seemed to bring the heavier weight to a near complete stop upon impact, which seemed to me to say this was the correct length in real world. Again my mass was distributed in 3 places, so the inertial properties would not act exactly like the sim. I understand now that the 1/2 mass will have more inertia at double the distance, so will never achieve the 2x speed it needs to have in this type of impact.

My latest suggestion above is to remove the leverage factor from the newtons arrangement, and just have 2 simple ball masses... In sim this also doesn't show a lift in COM. My point is this real world test would IMO logically be fairly conclusive, as far as elastic collisions are concerned.

I did have a quick read of Peq's thread this morning, but for some reason didn't deduce the "cylinder and sphere" experiment was a flinging mass experiment. I was trying to access the pictures without success. I have also previously done some flinging mass sims, without any gain in PE, but a real world build of this type is low on my list.

[Fletcher]

Thanks Fletcher. I have done a number of Newtons cradle tests in WM2D, although your skill in the program is obviously far superior to mine. I would like to do the tests in the real world, but my efforts are supposed to be directed towards renovating my house to sell before the property market dies any further.

I understand the pressures for time & mental energy we all face, so priorities are essential - there are others capable builders here that could build to add flavour to the pie.

Notice in the WM2D of the impact with dissimilar pendulum lengths, the 1KG pendulum should be 2x the length of the 2KG, but the ratio you have is 3 : 4.18. Is the ratio you used calculated with the inertial properties in mind, or was it trial and error to make the simulation act in this way?

In my real world build of this test, the 1/2mass COM at 2x the distance seemed to bring the heavier weight to a near complete stop upon impact, which seemed to me to say this was the correct length in real world. Again my mass was distributed in 3 places, so the inertial properties would not act exactly like the sim. I understand now that the 1/2 mass will have more inertia at double the distance, so will never achieve the 2x speed it needs to have in this type of impact.

My priority was to alter the second pendulum shaft length until the first falling pendulum had NO kick back or follow-thru [trial & error method, 100% momentum transfer] - IOW's it stopped dead in the shortest distance - I had to keep in mind that the elasticity of the materials affects this, so I started from a position with 100% elasticity [akin to the gravitational slingshot results] - that pendulum length gave those results in sim world - if I had of used ordinary materials with lesser elasticity the Ke was way less & the Pe recovery shortfall far greater.

My latest suggestion above is to remove the leverage factor from the newtons arrangement, and just have 2 simple ball masses... In sim this also doesn't show a lift in COM. My point is this real world test would IMO logically be fairly conclusive, as far as elastic collisions are concerned.

If the two masses are dissimilar i.e. the first colliding bob more massive than the second [but both at the same radius length] then there is always follow-thru of the first mass - that would not be a complete 100% transfer of momentum - if an elasticity of less than 100% is used in the materials you also don't get near the 100% transfer of energy - if I have misunderstood your description put up a drawing & I'll try & sim it for you.

I did have a quick read of Peq's thread this morning, but for some reason didn't deduce the "cylinder and sphere" experiment was a flinging mass experiment. I was trying to access the pictures without success. I have also previously done some flinging mass sims, without any gain in PE, but a real world build of this type is low on my list.

Pequaide's cylinder & sphere's experiments was where he took a section of pvc pipe around which he had wrapped opposing lengths of nylon cord with a small bob at each end held loosely against the pvc exterior - the cylinder was more massive than the bobs.

He held the pvc cylinder vertically & using his wrists spun the cylinder whilst letting go so that it fell vertically - due to the rotational energy imparted to the cylinder the bob's did not have an equilibrium of forces & so deployed outwards due to Cf's - their inertia dragged on the cylinder slowing its rotational speed as the tethers unwound - then both bobs were fully deployed still trying to increase their radius so that their tethers were at right angles [thereabouts] to the pvc cylinder rim.

This halted the rotation of the pvc cylinder as it fell & was concluded by peq. that this was 100% momentum transfer - also that if you knew the velocity of the bobs then you would see a gain in energy [Ke].

The argument was that there was never any controlled & repeatable measure of the INPUT Energy to set the pvc cylinder & sphere's rotating - it was unmeasured muscle energy therefore a claim of increases in energy was unjustified & unwise until Input Energy was measured - also the velocity of the bob's was never established accurately i.e. Output Energy.

This led to an independent experiment by Nick, at around the same time, where he reduced the essence of pequaide's cylinder & sphere's experiment to the simple basics, but in a controlled & measurable way.

He turned the pvc cylinder into a vertical arrangement able to be accelerated by gravity & a known drive mass to give the cylinder rotational velocity [aka energy] & angular momentum - he reduced two opposing tethered sphere's to just one.

The result was it acted as pequaides dropped pvc cylinder & sphere's had done - the bob & tether unwound due to Cf's - when equilibrium of forces was established [i.e. Cp's = Cf's] then the inertia of the bob [at its velocity] stopped the heavy flywheel & its drive mass dead in its tracks, thus if the theory was correct, transferring all momentum to the bob, which according to the theory should have seen a gain in Energy i.e. creation of energy as claimed by the theorist.

Nick, Wubbly & ovyyus built real world versions of Nick's setup that encapsulated the essence closely - I built a sim reproduction - none showed a gain in energy because none could even restore original Pe much less achieve a gain in Pe from start conditions - as per my sim yesterday, here on this thread, the Ke [aka velocities achieved] never exceed the Pe losses at any time in the cycle - I could have graphed it but I thought you'd understand more if you followed it thru yourself.

P.S. there is no argument from me that a cylinder given rotational velocity & energy can be stopped by a tethered bola deploying - but I disagree that there is an energy gain, when gravity is the only cause of motion.

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Later today along the lines a clay's original pendulum thread, if I get time, I will build a simple Cf's pendulum that attempts to use the Cf's generated in swing [via a mechanical linkage] to accelerate the pendulum forward thus giving it extra velocity, Ke & momentum, hopefully to fully restore starting Pe - that should prove that once again, when gravity is the only cause of motion, that energy cannot be created & that gravity & inertial forces are conservative - at least in energy equation based sim world ;7)

[Tarsier79]

If the two masses are dissimilar i.e. the first colliding bob more massive than the second [but both at the same radius length] then there is always follow-thru of the first mass - that would not be a complete 100% transfer of momentum - if an elasticity of less than 100% is used in the materials you also don't get near the 100% transfer of energy

Agreed, see above for my suggestion on how to account for this: http://www.besslerwheel.com/forum/viewt ... 7897#87897

You don't need a complete momentum transfer, because if the smaller weight takes say half the momentum from the larger, and momentum is conserved, you will still have a gain in PE at the highest point in the swing of both weights combined.


Clay sorry to hijack your thread, but its relevance ties in well with, and is an important factor in all pendulum models.