Rolling balls - winner takes all!

[greendoor]

I can't believe my eyes ... video clip: http://www.hcrs.at/VIDEOS/KUGELA.MPG
In case this link disappears, i'll describe it:

Two identical ball bearings roll down two simple dual wire tracks under the influence of gravity. They are released simultaneously with a special mechanism. The ony difference is that one track has a big dip in it. So the ball rolling down this track has much further to go - it gains energy in dropping further down - but it has to climb back up again too. So the track is longer - more friction - more air resistance ...

But guess which ball wins the race! The one with the dip clearly beats the other - over such a short scale experiment, i'm amazed!

Skeptic at overunity.com says there is no energy gain, because both balls are going the same speed at the end of the race. But the first ball gains in time ... which leads me to my next point ...

[graham]

It could be that the ball that travels the track with the dip accumulates greater kinetic energy because it falls further than the ball on the level track.

Kinetic energy is not directly proportional to speed but doubling the speed produces four times the kinetic energy.

Interesting demo. Makes you think!

Graham

[scott]

It's called the Brachistochrone Problem. It was solved by Johann Bernoulli not long before Bessler demonstrated his first wheel.
http://en.wikipedia.org/wiki/Brachistochrone
http://mathworld.wolfram.com/Brachistoc ... oblem.html
http://www-history.mcs.st-andrews.ac.uk ... hrone.html
-Scott

[graham]

Thanks Scott.
Can someone explain it in "laymans terms"please ?

Math is not my forte.

Graham

[greendoor]

From what i've just read about it - this phenomenon was observed and understood to be true by Newton & the Bernouli brothers and other deep thinkers of the 1700's. Probably Bessler too. The mathematical feat was to calculate the optimum curve that would achieve the greatest speed gain. That basicaly requires the invention of calculus.

I wish maths had been made as exciting as this at school ...

[Fletcher]

Have a read of these Graham.

http://home.ural.ru/~iagsoft/BrachJ2.html

http://www.sewanee.edu/physics/TAAPT/TAAPTTALK.html

[graham]

Thanks Fletcher. The second link of yours was the clearest description.

However, refering to that demo of the two tracks and balls that greendoor posted :-
It would appear that the ball travelling the track with the dip has gained more KE than the one on the level track.

I wonder what would be the result if the end of the tracks were raised so that the ending levels were slightly higher than the starting levels.
Would the ball on the track with the dip manage to climb to the higher level. If so, it would demonstrate over unity.
Fascinating!!

Graham

[Michael]

This is actually an old topic on here. Jim had a hand at designing a machine based on this principle years ago. Greendoor you are correct that both balls have the same velocity at the end. If the ramp with the dip had it so the curve had an equal curvature length in ascent to the descent, so the ball finished at the same height level that it started at, then both balls would have reached the end of their journey at the exact same time. No free energy here.

[Fletcher]

In layman's terms Graham here is how I would show it, but in a wheel situation [ball dropped from 12.01 o'cl] - here we see that one ball/weight is attached to a wheel rim [wheel has no mass] & is forced to follow a curved path where the velocity changes direction continually - the green ball for comparison is dropped vertically [assuming in a vacuum].

If you were to measure the velocities of both balls at any given vertical height they have the same velocity/speed but obviously if both were released at the same time [like the brachistochrone] the ball falling most vertically arrives at its check height much quicker than its mate forced to follow a path that constrains it.

So although you get a time difference there is no additional Ke [as they have the same velocity/speed].

This is actually one good proof I often use to explain why only Potential Energy [i.e. Pe=mgh] is important in a closed system & it matters not a jot what path is taken to go from point A to B & back again.

P.S. obviously in the brachistochrone experiment both balls are released at the same time & arrive at different times & the exact same thing is true for the ball/weight on wheel comparison.

[greendoor]

I can appreciate that the same amount of Work has been done for both balls - because ultimately the same mass is moved over the same distance. However - there has to be more friction over the longer track, so more energy has been extracted from gravity.

To achieve this in less time has to mean more Power has been extracted from gravity. Surely this has to be significant somehow ...

Does the opposite work - is there a faster way to raise a weight? Perhaps vertically straight up, or rolling up a slope, is not the most efficient way to raise a weight? Maybe a cycloidal track is the best way, which means wheel & levers are already on the right track ...

Interesting that my intuition that a straight line is the shortest path between two points is completely wrong ... and that something so simple can be so complicated. I just wonder what else we have missed ...

[ovyyus]

To achieve this in less time has to mean more Power has been extracted from gravity...

Power isn't extracted from gravity. The energy released by the falling ball is the energy invested in lifting it against gravity.

A longer track will obviously mean more loss to track friction and windage, but those losses are usually very small and hardly noticable in such an experiment.

[Fletcher]

Here it is in vector format - gravity force [i.e. acceleartion due to gravity] is the same for both balls as they are the same weight.

When rolling down the track [doesn't include friction or windage losses] the gravity force [g] is opposed by the resultant force [R ... N.B. at right angles (normal) to the track slope] - but the resultant force is made up of a horizontal component [h] & a vertical component [v] - so after the same time on the track from release, the ball on the steeper track has more horizontal vector [track pushing it sideways] & less gravity opposing vertical vector than the other ball on the shallower less steep track.

What this means is that the ball on the steep track gets more force/thrust shifting it sideways & less force opposing gravity .. so it accelerates faster than the other ball in the same time interval - the ball on the less steep track has less sideways thrust & more vertical vector opposing gravity which acts to slow its acceleration down, by comparison.


P.S. feel free to do a calculus intergration for different slopes or curves if you want to ;)

[greendoor]

Power isn't extracted from gravity. The energy released by the falling ball is the energy invested in lifting it against gravity.

A longer track will obviously mean more loss to track friction and windage, but those losses are usually very small and hardly noticable in such an experiment.

Semantics. Hydroelectric dams provide power by the fall of water. Without gravity, the water wouldn't fall. I don't think it's wrong to say that gravity can provide power. If it applies Force that moves Mass over a Distance for a length of Time, that's Power by my understanding. Sure - solar radiation provided the energy to raise the water in the first place. But if you insist on going back to the source of all energy, it becomes a bizarre chicken vs egg debate. Back to the big bang - if there ever was one.

Other forms of energy could provide work in zero G. These devices only work if there is a gravity field. So I will insist on saying that it's possible to extract power from gravity. Surely this is the point of giving Bessler any serious consideration.

Two identical masses fall the same height and travel the same distance under the same source of power - gravity - and yet one arrives before the other. That means to me that one used more power than the other.

If these masses were identical large trucks in a mountain truck race, and took a longer route and still arrived ahead of the other, I don't think anyone would dispute which truck used the most fuel.

The balls had the same potential energy when the started.
They had the same potential energy when they stopped.
You agree that friction losses are negligable.
But the time difference is palpable even on a small scale.

A curve beating a straight line - surprised me but seems fair enough.
A sharp dip down, followed by a sharp rise upwards - that's what surprises me. A smooth curve I could have understood ...

This makes me wonder if a series of sharp dips and rises - an oscillating path - could give an even greater time increase...

I'm wondering if a time increase could be exploited in an overbalancing system where one extra ball is kept in the air at any one time ..

And i'm wondering if the reverse situation applies ... can we raise a weight the same distance with less power if we use an oscillating path ...

[ovyyus]

Semantics. Hydroelectric dams provide power by the fall of water. Without gravity, the water wouldn't fall. I don't think it's wrong to say that gravity can provide power...

I'm not sure it is a matter of semantics. Wouldn't it be more accurate to say that hydroelectric dams provide power from lifted water? Without lifting (by whatever means) the water can't fall.

I can not extract power from a clock spring, but I can extract power from a wound clock spring. You might agree there is no power in the spring itself?

[Oystein]

Have aybody thought about exactly where the energy is stored when compressing or stretching a spring ? is it in the magnetic binding between the atoms ? And where do the energy go if you let the loaded spring just disolve in some liquid etc..

Best Oystein