The pendulum bias paradox experiment

[TinselKoala]

Ok I'll come back another notch; my previous comment was one of gentle sarcasm, apparently to no avail. Perhaps a direct approach then.

In order to dispel the paradox it is necessary to explain - beyond a simple reference to the disparities of momentum and kinetic energy - why in the two ball collision the small ball (which has the greater kinetic energy) does not dominate the collision. Not recognising the paradox merely indicates an 'off the shelf' perception based on conventional dogma. (hint - statements like 'one collision is inertial while the other is non-inertial' explain nothing)

Why does the ball with greater kinetic energy not dominate?

I was led to believe this was the right place for the examination and discussion of unconventional ideas. There's more where this came from but I'm going to need a little more to work with than indifference.

Is this, then, the statement of your "paradox"?

Either I am not understanding you (along with Mile High and NewtonII) or you are not understanding the full situation you are describing.
I can tell you that I do have somewhat of an EE type background, but I can also tell you that I spent years in the laboratory investigating a set of phenomena involving projectile impacts, transfers of momentum, and kinetic energy (the Graneau water arc experiments) and I believe that my understanding of these phenomena is .... adequate for the present task.
If I am seeing and interpreting your demo correctly, you are saying that the fact that the wooden block moves different distances when struck by each ball, which presumably have the same KE at the point of impact, is a "paradox", since  conservation laws would predict that the block of wood should move the same distance if it is receiving the same "energy" or momentum transfer from the two differently sized balls. I mentioned sticktion, which unlike mere sliding friction, IS related to the initial impact _velocity_, and I mentioned the effects of inelastic collisions on momentum transfer, and I mentioned mechanical impedance mismatch, which is really a description not a reason.

Now... to improve your demo, let's take the trig out of the system, and instead of bringing the two balls out to corresponding _horizontal_ distances, let's bring them (their centers) to corresponding VERTICAL heights.... since this height is what determines the GPE and also the final horizontal velocity of the balls at bottom dead center, where the impact with each other or the wooden block should occur. This vertical height will also be easier to measure; I'm sure I don't have to tell you how to put two ruled sight gauges next to the apparatus and how to indicate the Centers of Mass of the balls against the vertical line gauges.
I'll accept your manual release method as valid, although it would be easy enough for you to rig a simultaneous, mechanical release system.
But let's take the wooden block and put it on some freely-rolling wheels, to reduce the contribution of sticktion, and let's bond a hard striking target to it, and let's be sure to use completely elastic balls... steel ball bearings are a great choice. Now we have better controls on input energy, we have moved towards assuring elastic collisions, and we have reduced the effect of sticktion which is velocity dependent.
Once you've done all of this and repeated the experiment, and you still get a little difference in the distance the block travels... we can see if we can eliminate other causes for the data you see. We may even arrive at the point where we have to consider shock waves travelling through the wooden block as energy dissipative mechanisms. But I doubt if the thread will last that long.

[TinselKoala]

@DTB: thanks for that..... it is indeed an illustration of a mechanical impedance-matching system, whose effect is to maximize the transfer of KE from the driver to the "flyer".... which I'd call a projectile or even a bullet. It certainly is relevant because it illustrates that the energy transfer is dependent on the elasticity of the collision as well as the time over which the force of impact is applied. The "impactor" is like the balls and the "flyer" is like the wooden block. The amount of energy transferred by an impactor with the same initial KE in a given collision depends strongly on the temporal dynamics and the energy dissipated in the collision itself thru deformation, sound, and even spalling of material.

[Tusk]

Interesting that a simple experiment which brings together two known and established outcomes (albeit typically not demonstrated together) causes a focus on the experimental method rather than the results. You can conduct this experiment on the back of an envelope with confidence, the only element requiring attention has already been highlighted.

In the two ball collision, why does the ball with greater kinetic energy not dominate?

I am all out of hints and clues. Try reading my OP. There is nothing new here except what is hidden in plain sight.

[MileHigh]

From what I see the balls have equal kinetic energy.

The slower ball more or less pushes the wooden block along and a lot of the energy is burned of in the dynamic friction between the wooden block and the surface.  The assumption being the slower you move the block the more dynamic friction there is.

The faster ball has a partially elastic collision with the block and the block moves faster over the surface and moves farther.  You can see how the ball keeps moving, so not all of the energy of the ball gets transferred into the wooden block.

I don't see any paradox or anything special.

[Pirate88179]

Interesting that a simple experiment which brings together two known and established outcomes (albeit typically not demonstrated together) causes a focus on the experimental method rather than the results. You can conduct this experiment on the back of an envelope with confidence, the only element requiring attention has already been highlighted.

In the two ball collision, why does the ball with greater kinetic energy not dominate?

I am all out of hints and clues. Try reading my OP. There is nothing new here except what is hidden in plain sight.

Simple.  The kinetic energy of the 2 balls is equal.  F=MA.  I have no idea what you are getting at here.

Bill