If at the end of both ramps we replaced the basket with a ramp.  Which ball would climb higher? 

Omnibus,  If there is a great energy gain than the ball should be able to climb higher than it's starting point.  This won't happen.

The ramp experiment has to be carried out and then we'll know the answer. However, even if there is no gain at the end point the fact remains that the kinetic energy of one ball differs from the kinetic energy of the other ball--these balls travel through actual physical paths of differing lengths and one of them covers the longer distance for a shorter time. That's an undeniable fact. Thus, if indeed there's no gain at the end point one should explain what energy that extra kinetic energy has been converted into (if it isn't converted into extra potential energy at the end point).

Further, if there's no potential energy gain at the end point the ball indeed won't be able to climb higher than its starting point. That doesn't mean, however, that there hasn't been energy gain (kinetic energy gain)--we see with our own eyes that one ball despite the longer path, reaches the end point sooner. Whether or not that extra kinetic energy can be used to lift the ball at the end point above the starting point in no way erases the fact that there is an energy gain.

One thing we should establish firmly because it is obvious from the videos--the ball on the curved path has extra kinetic energy independent of how that extra kinetic energy can be used for practical purposes. To deny this is to fly in the face of experimental facts and the basic concepts in physics.

@ramset,

While my eyes are telling me that one is faster[more KE],I know this can not be true

On the contrary, it is true that one is faster and therefore has more KE. Your eyes see that correctly and you should believe what you see rather than believe @Fletcher's ramblings.

@Low-Q,

I'm thinking friction vs. "steepness" of the track. The ball on the straight track suffer from more friction than the other ball in the steeper part of the track. So that ball can accelerate with less friction and gain more speed even if it is going uphill at the final part of the track. This uphill might also be less friction.

That's correct and I agree also with @Fletcher's similar explanation:

the track pushes with a more horizontal component than vertical unlike a constant slope track.

This is what's called constructive opportunity for a conservative force field to induce spontaneous displacement which is tantamount to violation of CoE or production of energy "out of nothing".

How is this obvious violation of CoE to be used in a practical device is yet to be seen.

Fletcher,  Do you have to factor in the friction of the ramps?
For instance if both ramps have considerable friction, the ball on a slight incline will be slowed more so than one on a very steep incline.  Am I correct?

Yes, you do - imagine a frictionless ramp for the thought experiment - the same way as we imagined a friction less bearing on a wheel or disk which a weight rode - friction is a force & can be represented by vectors - that means the track is pushing at right angles to the track - this impedes the acceleration of the ball if the track is flattish compared to steep - this is why tracks with initial steepness allow the ball to accelerate up quickly & ultimately arrive at destination quicker, carrying a faster average velocity.

A metaphor might be a parachutist reaching terminal velocity in free fall - two parachutists equal in every way except one weighs twice the other - both will be affected by air drag & will stabilise at terminal velocity but the terminal velocity of the more massive parachutist [all else being equal] will be considerably higher than the light one - proportionately the percentage of air drag is higher for the lighter parachutist [like a feather falls slowly on earth but everything falls the same rate on the moon] - hope that helps.

Chet .. 3 o'cl isn't time but vertical distance - no matter what track the rolling mass takes i.e. around the rim of a disk, down a flat incline, undulating incline, concave, convex, dipping below final height track etc etc as long as the velocity is measured at the same vertical heights [V1;V2:V3;V4;V5] the velocities will be the same [no allowance for small amount of friction on track difference].

As a graphic example  - attach a mass to a frictionless & massless wheel [no inertia] - let it fall from 12 o'cl to 6 o'cl & measure its velocity at 6 o'cl - let an identical mass fall vertically in free fall from 12 o'cl to 6 o'cl & measure its velocity - one will have velocity in the vertical while the other has velocity in the horizontal - but both have the same speed & hence Kinetic Energy - they both took considerably differing amounts of time to get there with different average velocities - no one but omnibus is suggesting that the path a mass takes increases the Ke - as already explained AT ANY HORIZONTAL HEIGHT COMPARISON the velocities/speeds are the same - since physical contact is required in mechanics to turn that Ke into work done then it matters not what the average velocity is but only its contact speed [across the finish line speed].

Omnibus .. try to understand the reasoning underlying physical principles & the math rather than relying on shallow use of numbers & bluff - if that doesn't sink in then go & do some experiments with your hot wheels & come back & tell us how you were able to harness all that extra energy in a useful way - duh!

@Fletcher,

since physical contact is required in mechanics to turn that Ke into work done then it matters not what the average velocity is but only its contact speed [across the finish line speed].

Wrong. It is not true that a body traveling in vacuum along a trajectory with no physical contact with other bodies doesn't have kinetic energy. The kinetic energy of a body is only determined by the mass and the velocity of that body and depends on nothing else. Learn physics.

Invoking brachistochrone curve in this discussion only muddles it. That mathematical problem does not overthrow what physics defines as kinetic energy (see above) but only helps to determine the optimum path for a body of a given mass and potential energy to convert it into kinetic energy. Mathematics isn't physics. Mathematics only helps physics to obtain its solutions easier. To understand a physical phenomenon, however, you have to know physics and its basic notions which you obviously don't.

Omnibus .. try to understand the reasoning underlying physical principles & the math rather than relying on shallow use of numbers & bluff - if that doesn't sink in then go & do some experiments with your hot wheels & come back & tell us how you were able to harness all that extra energy in a useful way - duh!

Don't teach me what to understand. Instead, you try to understand that "all that extra energy" not being harnessed "in a useful way" is not at all an argument against the reality of that extra energy. Your utilitarian approach only shows that you're not comfortable with the elementary notions of physics.

Hear it again because, obviously, it is not getting across to you. Kinetic energy is only a function of velocity and mass. A ball of mass m which travels along a longer distance for a shorter time has a greater velocity and therefore has greater kinetic energy than a ball of the same mass m that travels along a shorter distance for a longer time. This is the only way physics defines kinetic energy. In the definition of kinetic energy physics implies no interaction, no impact, no transfer, no anything else you are imagining. You are inventing Fletcherphysics which isn't an object of discussion here. Educate yourself first about what physics, not Fletcherphysics is and then join this discussion. What you're doing now is only wasting bandwidth.

@ramset,

You posted too soon [should have waited till you got home to test].

I would've posted too soon if what the videos show is a scam, say, the two balls are of different mass. I don't believe that's the case, do you?

Therefore, it is an established fact that the videos demonstrate two balls of the same m turning the same gravitational potential energy into different amounts of kinetic energy.

Now having established that fact it's a completely different story how we would use that fact for the continuous production of that extra kinetic energy.

The ball on the longer track moves faster.  But at each horizontal location where it is moving faster the ball on the longer track is LOWER than the ball on the straight, gently sloping track.  So it has dropped further, and that additional change in PE resulted in greater KE and thus more velocity.

But at the end of the tracks, both balls are at the same height again.  How did the ball on the longer track get back to this height?  It had to go back UP at some point(s) along the track.  At each point it was going up it was slowing down.

At the end of the tracks, both balls are going the same velocity, if friction is to be ignored.

Seems like all the "ups" should cancel all the "downs ",[on the longer steeper course]
and every one should finish at the same time?

Not at all Chet.  The average speed on the longer track can be faster, so that ball will reach the end of it's track quicker.

Think of it like this:

1)  Straight track:  Ball smoothly accelerates from 0 to 10 mph from beginning to end of the track.  Average speed is 5 mph.
2)  Long track:  Ball accelerates from 0 to 20 mph (steep drop), then decelerates to 15 mph (slight rise), then accelerates to 20 mph (slight drop), then decelerates to 10 mph (steep rise) at the end.  The overall average speed is greater than 5 mph, right?  And the ball gets to the end faster, but with the same exact final velocity as track #1.

For the speed of the ball on the longer track to ever drop below the 10 mph maximum of the ball on the straight track, the long track would need to have hills that take the ball higher than the straight track.

M.