The pendulum bias paradox experiment

[Tusk]

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.

[TinselKoala]

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".

[Tusk]

What is the problem?

Why does the ball with greater kinetic energy not dominate?

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.

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?

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?

[TinselKoala]

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.

[Tusk]

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.

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.

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.

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.

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.

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?