Presumably the deafening silence indicates a healthy skepticism and rightly so. Time to cross the I's and dot the T's then.

Let's define the large ball as ball A with mass 72g and the small ball as ball B with mass 18g (I can't 'prove' the mass of the balls but all of this can be easily replicated, which I recommend you do).

Since the velocities must be at 1:4 ratio in order to produce the kinetic energy bias claimed let's allow V(ball A)=10cm/sec and V(ball B)=40cm/sec

p=mv therefore p(ball A)=72x10=720

also p(ball B)=18x40=720

Thus we have balls A & B with the same momentum.

Ek = ½ mv² therefore Ek(ball A)=3600

and Ek(ball B)=14400

so as described Ek(ball B)= 4xEk(ball A)

i.e. the kinetic energy of ball B is greater than that of ball A by a factor of 4
 
Since measuring the duration of the collision from first contact to all motion stopped would require sophisticated apparatus, so that provided we apply the same value throughout, we can allow an arbitrary t(collision)=0.01sec

As stated previously, for simplicity we can also allow that the force applied by each ball to the other is constant throughout t(collision)

We know from Newton's 3rd law that F(ball A)=F(ball B)

We require a value for one more variable, again difficult to measure but since we are bound by mathematical certainty we can allow that the distance traveled by ball A centre of mass during t(collision) denoted by S(ball A)=0.1cm and let the mathematics provide a true respective value for S(ball B)(centre of mass).

Since S=ut+½ at² so a(ball A)=2000cm/sec²

and since F=ma therefore F(ball A)=144000 (dynes)

As F(ball A)=F(ball B) so using F=ma therefore a(ball B)=8000cm/sec²

and since S=ut+½ at² we get S(ball B)=0.4cm or 4xS(ball A)
 
Once you allow that ball B has 4x kinetic energy of ball A an explanation is required for the apparent complete absence of the typical effects of a kinetic energy bias in the collision. Since apparently the exact mechanism or even the circumstance was not commonly understood the term 'paradox' seems to have been appropriate. If this discussion is to progress from the unusual to the mind blowing we will require a little less skepticism and a willingness to look twice, or thrice, when a first glance suggests some error or subterfuge. Like anyone my work may be subject to errors but there is no subterfuge, and I intend to present it openly in good faith for anyone to replicate, assuming a fair hearing.







 

 
 

Hi Kator01, thanks for posting. As you inferred it's been quite some time since this thread was of any interest to anyone. Also I should make it clear that this was simply a case of putting a toe in the water for me, since I was looking for a suitable place to post the PE thread. In other words the thread was intended more for gauging the general mood and receptiveness, although I think there is a fair point to be made regarding perceptions. A good argument could be made for entering the room with somewhat less of a confrontational manner, but considering the likely resistance to the main task ahead (a concern justified by subsequent events) I felt it was preferable to signal a certain level of confidence. I know of few significant achievements, if any, that were accomplished without it. 

you are stating that the little ball has 4 times the velocity of the bigger ball. This seems to be a wrong assumption taking into consideration of what I can see
in your vid.

The larger ball was displaced by such a small amount that it's height changed only imperceptibly. While the experiment was an approximation due to the nature of the apparatus, the literature will confirm the data gathered and the observations made. I was not intending to question the literature, merely confirm it; and the experiment (of my own design) nicely demonstrates what is generally accepted in physics, yet perhaps not so generally understood.

In order to judge this in a correct way the true value of velocities, one needs to know
the exact heights the two masses were lifted.

Actually v at the equilibrium position may be determined by max angle of swing; but since the outcome of the collisions is already known, and the intended focus lay elsewhere, it seemed sufficient to estimate initial parameters providing the outcome concurred with the literature, which it did. I was not proposing a breach of any laws in this thread, simply attempting to reach out to anyone open to new perspectives.

Surprisingly there was more than a little concern regarding the minutia, and even challenges to the results, whereas the reason for the results were apparently not widely known. And while I am quite certain an explanation exists in the literature somewhere, my own conclusions are just that, arrived at by deduction. It seems far too easy to flick a metaphorical switch in our head and proclaim 'this is momentum' and 'this is kinetic energy'. Not possessing a classical physics education I simply asked myself where the kinetic energy had gone (in 'the momentum collision') and set about finding a plausible answer, along with a clear understanding.

if you raise the small mass 4 times the height of that of the big mass you will just double the speed.

That seems reasonable, although I was using an approximation of the angular method. Using height I would have needed x16 and having just dusted off the apparatus it appears this was in fact the case. In any event the aim was to produce a collision where the first object had x4 KE of the second, and the behaviour of the objects post collision concurred with expectations gleaned from the literature. An acceptable alternative experiment might have been ball bearings launched from different heights from ramps, or many other designs, but I chose the pendulum for ease of use in the matter of timing and simplicity.

So sorry, but kinetic energy of both masses can not be clearyfied in this experiment. The displacement-test of the wood-piece suffers
a failure because there is no even underground, You extended the ground by another piece of wood, so I would be happy if you could
give better detailed data of the exact heigths.

The KE bias is supported by the results and the various applicable laws and equations which govern such matters. As for the rudimentary equipment, as previously stated this was not intended as a proof, rather a demonstration of a known phenomenon for the purpose of further discussion. If you are suggesting that something in the literature is awry regarding the assertions made regarding the experiment, or that my conclusions are incorrect I will welcome your additional input.

Anyway your paradox-engine-thread is almost very interesting.

Almost..... lol thanks