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Uphill roller and conservation of energy

  1. Feb 25, 2010 #1

    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" [Broken]

    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?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Feb 25, 2010 #2

    Doc Al

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    Staff: Mentor

    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!
     
  4. Feb 25, 2010 #3

    K29

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    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?
     
  5. Feb 25, 2010 #4

    Doc Al

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    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 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.)
     
  6. Feb 25, 2010 #5

    K29

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    Yeah I'm ok with that. . I drew up a co-ordinate system. Lets 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" [Broken]
     
    Last edited by a moderator: May 4, 2017
  7. Feb 25, 2010 #6

    Doc Al

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    Why would you think that? Note that the rails are not symmetric.
    Don't count on it.
     
  8. Feb 26, 2010 #7

    Dale

    Staff: Mentor

    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.
     
  9. Feb 26, 2010 #8

    rcgldr

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    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.
     
    Last edited: Feb 26, 2010
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