Orbits... / General Science and Electronics / Forums

Forums

4hv.org :: Forums :: General Science and Electronics

« Previous topic | Next topic »

Orbits...

1 2 next

Move Thread

LAN_403

Slava

Sun Nov 29 2015, 06:24PM

Registered Member #518 Joined: Tue Feb 13 2007, 05:20AM
Location: New York
Posts: 168

My friend and I are debating for 2 days now...

There is a science demonstration where you drop a coin or ball into a funnel and it goes in circles, then eventually falls into a hole in the middle

argument #1) if there was no energy loss from friction and sound, it would orbit forever (like the orbit of planets around the sun)

argument #2) gravity will eventually pull the coin/ball into the center regardless of energy loss

Please help!

...

Mon Nov 30 2015, 01:17AM

Registered Member #56 Joined: Thu Feb 09 2006, 05:02AM
Location: Southern Califorina, USA
Posts: 2445

Depends on the angle you start it at. Consider the limiting case of shooting the coin strait down into the hole - clearly all of the coins energy would be converted to kinetic energy and it would fall into the hole.

In the case of a lossless system where you started the trajectory exactly such that the centrifugal upward force balances the downward force from gravity then the coin would 'orbit' forever. I point out however that this is an unstable equilibrium (unlike planetary orbits), so practically the coin is always going to climb up the ramp (and slow down) or fall down the ramp (and speed up).

I would have to think about it, but it is conceivable that with a carefully designed cone shape you could make make the system stable, but then you would loose the entertaining bit where the coin slowly speeds up as it falls down toward the hole.

BigBad

Mon Nov 30 2015, 02:36AM

Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
Location:
Posts: 600

The correct answer is 1) but with caveats.

The caveat is that the surface must be perfectly smooth. If it isn't, even if you assume no losses, it can change the angular momentum, and the eccentricity will change over time and it will be virtually certain to either fall into the middle or get flung out the top of the funnel.

Slava

Mon Nov 30 2015, 03:07AM

Registered Member #518 Joined: Tue Feb 13 2007, 05:20AM
Location: New York
Posts: 168

Can someone do a 3D physics simulation? Best way to settle this...

BigBad

Mon Nov 30 2015, 07:59PM

Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
Location:
Posts: 600

yes, but I'm not going to, I've already told you the answer.

Slava

Mon Nov 30 2015, 08:04PM

Registered Member #518 Joined: Tue Feb 13 2007, 05:20AM
Location: New York
Posts: 168

I got your answer and its actually the one i proposed... I just need to prove it to a friend of mine. Best way to prove it is a simulation.

2Spoons

Mon Nov 30 2015, 09:03PM

Registered Member #2939 Joined: Fri Jun 25 2010, 04:25AM
Location:
Posts: 615

No, the best way to prove it is with an analytical solution. Simulations are often not "lossless" as they are inevitably numerical solutions, with rounding errors and discrete steps in the simulation. It is entirely possible for a discrete step simulation to be unstable when the continuous system is not.

+1 to Big Bad's answer.

Slava

Tue Dec 01 2015, 03:25AM

Registered Member #518 Joined: Tue Feb 13 2007, 05:20AM
Location: New York
Posts: 168

The best comparison I came up with is a pendulum swinging in a circle or ellipse...

It will spin forever at the same amplitude... the only way for it to drop to a lower orbit is if it loses energy.

Signification

Tue Dec 01 2015, 04:20AM

Registered Member #54278 Joined: Sat Jan 17 2015, 04:42AM
Location: Amite, La.
Posts: 367

2Spoons wrote ...

No, the best way to prove it is with an analytical solution. Simulations are often not "lossless" as they are inevitably numerical solutions, with rounding errors and discrete steps in the simulation. It is entirely possible for a discrete step simulation to be unstable when the continuous system is not.

I agree totally with this...SO MUCH!!!

I work almost exclusively with this method (ever since it was the --only-- method)---the work may be VERY difficult--and even sometimes simple (if you know and properly apply the *basic* laws), but the outcome is uniquely satisfying and virtually always includes a bonus or two!...IMHO

Uspring

Tue Dec 01 2015, 10:00AM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
Location:
Posts: 711

Consider a rotationally symmetric funnel with the symmetry axis vertical. Place a mass m on it with a circumferential (i.e. tangential) speed component v. Then the centrifugal force will be:

Fc = m * v^2 / r

when it rotates at radius r. The angular momentum J is given by

J = m * v * r

and it is a constant of motion, since the funnel is rotationally symmetric. We can then write Fc as:

Fc = 1/m * J^2 / r^3

The downward slope of the funnel causes an inward force. If that is smaller than the centrifugal force, the mass will be driven upward else it will continue down. The shape of the funnel defines a "force law", i.e. the inward force as a function of r. If e.g. it is an inverse square law such as the one in gravity, the centrifugal force will always become larger at low r since it rises a 1/r^3 as compared to the attractional force, which rises a 1/r^2. That prevents planets from falling into the sun.
For funnels the force law can be different, so for some shapes the mass can spiral infinitely down into the funnel.

1 2 next

Moderator(s): Chris Russell, Noelle, Alex, Tesladownunder, Dave Marshall, Dave Billington, Bjørn, Steve Conner, Wolfram, Kizmo, Mads Barnkob