Rolling balls - winner takes all!

[ForumNewb]

what is energy? spring produces work through displacement. if energy is that which produces work then is all energy displacement of some kind? what is the meaning of life? will i have enough weed to last the weekend. i don't know!

[ForumNewb]

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

so this little roller coaster trick can turn gravity energy into kinetic energy? kinetic energy is that stuff that like makes those clickity clackers bounce back and forth know what I mean? if there is a race between two balls in a race track the ball on the outside could tie with the ball on the inside know what i mean?

[graham]

Thanks Fletcher for taking the time to explain the this phenomenon. But it seems to me that your explaination doesn't describe what is in the video

Your description of the ball free falling and arriving first at the lowest point makes sense.
The ball following a curved path takes longer because it has further to travel, and gravity is not able to accelerate it freely.

But in the demo video we have level tracks . One has a dip and this ball arrives ahead of the other.
Both balls travel the same horizontal distance but the one that takes the dip arrives first. How unexpected !!

Greendoor wonders:

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

Don't you mean "greater time decrease"?

Good question Greendoor.

Graham

[Michael]

Hi Graham. Fletchers explanation sums it up great. What's important is the potential energy, which is the same for both. The one with the dip is allowed to reach more of its potential faster, that's why it reaches the end first. The curve has nothing to do with it, the curve just makes for a smooth transition between angle changes. Horizontal length is irrelevant unless you were to be talking about a constant velocity, not acceleration, and acceleration is what is happening in this case.

Greendoor one giant dip, in the form of a free fall drop, with a sharp curve at the end sending the ball horizontal would be best.

[graham]

OK, the penny just dropped!!!

Here's what's happening in the video with the two level tracks.
Both balls have the same KE as they begin the journey to the end of the tracks. They are "neck and neck".

When the ball hits the dip it is accelerated by gravity to a higher speed and pulls ahead of the other ball . It continues to pull ahead until it encounters the upslope of the ramp where it gives back the added KE and the speed returns to the original starting velocity.

Because the ball on the track with the dip travelled a portion of the track at a higher speed, it covered the total horizontal distance in less time. There is no net energy gain just a time differential.

I Get it !!!

Graham

[Fletcher]

Yep, & Mike mentioned it before i.e. if you were to curve both tracks upwards to vertical after one of the balls comes out of the dip they would both rise to the exact same vertical height i.e. gain Pe but this is less than the starting Pe [assuming no losses for track friction & windage etc].

The question is can this time difference be used in anyway within a wheel ? Since dropping the ball vertically & then having it follow a curve & dip is probably the best scenario to get to the end point quickest it looks good but anytime we have something roll steeply or drop in free fall it is applying no or less torque on its side of the wheel while in transition which in most cases is counterproductive - a classic catch 22.

[bluesgtr44]

The question is can this time difference be used in anyway within a wheel ? Since dropping the ball vertically & then having it follow a curve & dip is probably the best scenario to get to the end point quickest it looks good but anytime we have something roll steeply or drop in free fall it is applying no or less torque on its side of the wheel while in transition which in most cases is counterproductive - a classic catch 22.

Get it to do this on the ascending side...use the time difference to move it over to the decending side, bunch 'em up a bit. Of course, I have no idea how to physically accomplish this.....;-)


Steve

[graham]

Fletcher poses a question:

The question is can this time difference be used in anyway within a wheel ?

Yes indeed . Just harness the horse in front.
What could be simpler.

Graham

[DrWhat]

"came in pairs, one placed against the other...", "swapping places all the time" :-0)))

[mickegg]

A very interesting topic.

Far from sending us "up the Swanee" <grin>

Fletchers link:
http://www.sewanee.edu/physics/TAAPT/TAAPTTALK.html
is very enlightening.
Thanks Fletcher.

It does show, however, that this cannot be any old dip and rise
in the path, but must be a cycloidal curve in order to provide the
shortest arrival time between the two points.

Interesting that my intuition that a straight line is the shortest path between two points is completely wrong ...

No, you are correct.....but this is about arrival time and not about distance travelled (for a mass under gravitational acceleration)


Oh............and can we leave the debate about straight lines and curved space alone please? <grin>


Regards

Mick

[bluesgtr44]

I'm starting to get a bit of a grip on this stuff now. Here's a part I need help with.....the distance is the same, the actual mileage it would take to get there is not....correct? If we put odometers on the spheres, the one that went through the dip would have traversed more surface contact area than the other? So basically, this sphere used gravity to gain on and actually pass up the other sphere without having to actually work any harder.....gravity did the work?


Steve

[graham]

Steve, the way I see it is that the ball that travels the track with the dip goes a little bit further because if you were to straighten out the track with the dip you would find that the total length of the track is longer than the one without the dip.
You just need more material to accomodate the dip rather than the direct route with no dip.

What I wonder is if the "dip" were to start nearer the beginning of the race and end closer to the finish , would the time difference be even greater?

Since the the ball travels faster once it has passed through the "downslope" it will continue to travel at this higher speed for a greater time until it hits the "upslope" and returns to the original velocity that the other still has.

So I reckon the time difference would be even greater and the ball would get to the end even faster.

Clearly, the dip doesn't have to be a curve since the video demonstrates that equal and opposte ramps do the trick.

If you have the balls, you might experiment with this yourself.

Graham

[Michael]

What I wonder is if the "dip" were to start nearer the beginning of the race and end closer to the finish , would the time difference be even greater?

Yes. Like I said if you let one ball free fall drop to almost the end of the vertical descent right from the beginning and then had a small 90 degree curve that sent the ball moving horizontally, it would get to the end the fastest. ( Edit; within a fixed vertical limit ).

Here's another way to think about all of this. Imagine 2 tracks both the same, no dips. One track has a flipper halfway. Both balls are neck and neck but the one with the flipper on the track has the flipper impart enough energy to the ball so that the ball now has double the speed as the other. Near the end of the track there is a second flipper whos job it is to absorb back the energy the first flipper gave to the ball. Both balls at the end of the journey will have the same velocity even though the one ball got there a lot faster. Both balls will also have the same total energy EXPENDED because the one ball has given its extra energy back to the system.

[Oystein]

The fastet way to get to the end would be to travel far deeper than the track.
A curve falling from the start with about the same diameter as the length of the track... If you let an arm fall from A and end up at B, it will be much faster than those tracks...

Logic :
If you have a flat start surface you will get ------- infinit time
Aproaching infinit deep horisontal fall --------- infinit long time



Best
Øystein

[Michael]

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