The pendulum bias paradox experiment

[Newton II]

Why does the ball with greater kinetic energy not dominate?

I didnot understand your question.   What I see from that expereiment is that,  the bigger ball will rise to lesser height because of its weight hence it moves through lesser distance in arc path.  The smaller ball rises to higher height because of its lesser weight hence moves through longer distance in arc path.   

The potential energy gained by both the balls will  be equal  m1*g*h1  = m2 *g*h2.      If you use both the balls of same size,  they will be displaced to equal distance.

[TinselKoala]

Momentum, mv, is conserved.
There is also a difference between elastic and inelastic collisions in the demonstration, as well as the matter of the stiction of the block being a function of impact velocity. These complications may be considered similarly to the issue of impedance matching in electrical transmission lines. In fact, there is a mechanical impedance mismatch between the swinging ball and the resting block, and the magnitude of this mismatch is different for the two different balls, which hit the block with the same _momentum_ but with different velocities.
I guess.

[MileHigh]

Thanks for your reply MileHigh. Perception is everything. Someone (presumably like yourself) with a good grasp of basic physics would certainly understand why the small ball (having significantly more kinetic energy than the large ball) does not dominate in the collision. To the untrained eye however, the balls appear to have equal energy in the two ball collision, yet the ball and block collisions demonstrate that this is certainly not the case.

No paradox can survive it's own solution. To those familiar with the phenomena I offer my apologies.

When the balls are first released, they in fact do have approximately the same amount of kinetic energy.   So you are making an incorrect assumption.  So perhaps the illusion of the paradox is a bit more complicated than you thought?

[Tusk]

Good effort TK, hopefully you won't object to me doing an analysis of your response:

Momentum, mv, is conserved.

As it should be, under all circumstances. I will be breaking a law of physics later, but not this one.

There is also a difference between elastic and inelastic collisions

True but this doesn't affect the outcome in terms of the paradox. Substituting another ball suspended by pendulum (in place of the block) gives a similar result.

there is a mechanical impedance mismatch between the swinging ball and the resting block, and the magnitude of this mismatch is different for the two different balls

Am I correct in assuming you have an electrical or electronic engineering background? Anyway it's a fair comment but again, we can just substitute a ball for the block.

It might be helpful to run a little thought experiment at this point. Allow that a ball is struck hard with a bat (cricket or baseball) next to a railway line as a train goes past. Allow that both the ball and the train are moving at the same velocity and in almost the same direction, but the ball converges with the train and enters a carriage through an open window. Inside the carriage the occupants observe the ball seemingly float in mid air as it reaches it's apogee then drop to the floor where it remains at rest.

Disregarding air resistance (for simplicity) quantify the kinetic energy of the ball. Not literally, just consider the problem and how it relates to the pendulum result.





 

[DreamThinkBuild]

Hi Tusk,

Welcome to the forum. Thanks for sharing your experiment.

Hi TinselKoala,

Something you said about impedance matching bought up this paper I read recently.

AN ALGORITHM FOR THE HYPERVELOCITY LAUNCHER SIMULATION OF HIGH-LOW DENSITY FLYER PLATES

http://jeacfm.cse.polyu.edu.hk/download/download.php?dirname=vol3no4&act=d&f=vol3no4-4_BaiJS.pdf

A rubber ball is essentially a graded surface as you go to the core the material density/impedance changes. I do not know if this is relevant to this pendulum experiment but it's an interesting effect.