Uphill roller and conservation of energy

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Discussion Overview

The discussion revolves around the mechanics of a cone that rolls uphill by shifting its center of gravity, raising questions about conservation of energy and the possibility of perpetual motion systems. Participants explore theoretical implications, practical observations, and the underlying physics concepts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants question how a self-sustaining system like the rolling cone could seemingly violate conservation of energy, noting that the center of gravity moves down while the cone moves up.
  • Others argue that the analysis shows no violation of conservation of energy, as the center of gravity indeed travels downhill as the cone ascends.
  • One participant expresses confusion about energy loss and gain during the cone's movement, seeking clarification on the fundamental principles involved.
  • Another participant suggests that a perpetual motion system could be created by allowing the rails to pivot, although this idea is met with skepticism and correction regarding the feasibility of such a system.
  • A participant references a toy that demonstrates similar principles, where the center of mass moves upwards while the object appears to gain energy through manipulation.

Areas of Agreement / Disagreement

Participants generally disagree on the feasibility of creating a perpetual motion system from the described mechanics, with some asserting that conservation of energy principles are upheld, while others challenge the assumptions and implications of such a system.

Contextual Notes

There are unresolved questions regarding the assumptions made about energy as a scalar and the specific mechanics of the cone's movement. The discussion also touches on the limitations of the proposed perpetual motion system, which relies on the symmetry of the rails.

Who May Find This Useful

This discussion may be of interest to those studying mechanics, energy conservation, and the principles of motion, as well as individuals curious about the implications of theoretical physics in practical applications.

K29
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There is this cone that rolls uphill by itself, by shifting its centre of gravity.

http://plus.maths.org/issue40/features/uphill/index-gifd.html"

I wouldn't have looked up the mathematics of the issue if I hadn't seen it working with my own 2 eyes at a friend of mine's university physics museum.

2 questions:

1.) Thus "self-sustaining" system seems to break the laws of conservation of energy. How is this possible? The fact that the centre of gravity moves down the hill while the actual cone moves up doesn't seem to result in a conservative energy equation. Even thinking about imaginary forces such as centrifugal, coriolis etc does not help.

2.) I handled the double-cone and as far as I could tell its a legit piece of wood. So why hasn't anyone taken 1 000 000 of them and set them up with some dynamos in a smart way to make energy?
 
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K29 said:
1.) Thus "self-sustaining" system seems to break the laws of conservation of energy. How is this possible? The fact that the centre of gravity moves down the hill while the actual cone moves up doesn't seem to result in a conservative energy equation. Even thinking about imaginary forces such as centrifugal, coriolis etc does not help.
The analysis on the site that you linked demonstrates that the center of gravity actually travels downhill as the double-cone goes 'up' the incline. No violation of conservation of energy.

Pretty cool, nonetheless!
 
I'm understanding that as it moves up the hill it would lose potential energy. As it rolls back down it gains the potential back. Is that correct? If so don't you think that is a problem :p

I think I'm missing something fundamental here. Could you elaborate?
 
K29 said:
I'm understanding that as it moves up the hill it would lose potential energy. As it rolls back down it gains the potential back. Is that correct? If so don't you think that is a problem :p
Why would that be a problem? Note that as the center of gravity lowers (as it goes 'up' the hill), the gravitational PE decreases while KE increases. Energy is conserved.
I think I'm missing something fundamental here. Could you elaborate?
I suspect you don't appreciate the fact that while it appears that the cone is moving uphill, the center of mass of the cone actually moves downhill. (Otherwise conservation of energy would be violated.)
 
Yeah I'm ok with that. . I drew up a co-ordinate system. Let's say the cone starts at (0,0) it rolls up the track to a position say (1,4). The position of the centre of mass would be at (-1,-4). My energies gave me a problem because I wasn't considering energy as a scalar.
But I'm comfortable with the energy conservation now. Thanks...

A perpetual motion system can be constructed from this if we simply allow the rails to pivot in the centre. When the cone reaches one end, it will tilt the rails and then roll in the opposite direction. This system could power a clock, in which case I am going to crunch some numbers and attempt to construct it :P. If anyone is interested in "perpetual motion" check this out http://www.kilty.com/pmotion.htm"
 
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K29 said:
A perpetual motion system can be constructed from this if we simply allow the rails to pivot in the centre. When the cone reaches one end, it will tilt the rails and then roll in the opposite direction.
Why would you think that? Note that the rails are not symmetric.
This system could power a clock, in which case I am going to crunch some numbers and attempt to construct it :P.
Don't count on it.
 
K29,

Discussion of perpetual motion is not permitted here. Your analysis is wrong as Doc Al pointed out. Whenever you think you have found perpetual motion you know that you made a mistake in your analysis. In this case you will have to do work to lift the cone in order to put the system back in the original configuration.
 
The link doesn't work with IE8, but I was able to see a photo of the device. As pointed out the object's center of mass is moving downwards as it rolls forwards on the supports.

There is a "shoot the moon" toy, that has a steel ball resting on two hinged rods that the user can move:

shootthemoon.jpg


The rods are initially held together, with the ball at the far end of the toy. The rods are then spread apart so the ball starts rolling downwards and forwards, generating angular momentum. Then with a learned timing, the rods are then smoothly brought back together at a decreasing pace, which apparently adds energy to the system by "squeezing" the ball, which moves it forwards and upwards, and the ball's center of mass does actually move upwards.
 
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