Uphill roller and conservation of energy

In summary, there is a cone that can roll uphill by shifting its center of gravity, which may seem to break the laws of conservation of energy. However, the analysis on the website linked in the conversation shows that the center of gravity actually moves downhill as the cone goes up the incline, thus conserving energy. The idea of using this as a perpetual motion system is not possible due to the asymmetry of the rails and the need to do work to lift the cone back to its starting position. Additionally, there is a "shoot the moon" toy that demonstrates the concept of using angular momentum to add energy to a system, allowing a steel ball to roll upwards.
  • #1
K29
108
0
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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  • #2
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!
 
  • #3
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?
 
  • #4
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.)
 
  • #5
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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  • #6
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.
 
  • #7
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.
 
  • #8
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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1. What is an uphill roller?

An uphill roller is a type of roller coaster or amusement park ride that features a track with an incline, which allows the train or cart to travel upwards against gravity. This creates a thrilling experience for riders as they feel like they are defying the laws of physics.

2. How does an uphill roller conserve energy?

An uphill roller uses the principle of conservation of energy to maintain its speed and momentum. When the train or cart reaches the base of the incline, it has a certain amount of kinetic energy. As it travels uphill, this energy is transformed into potential energy, which is then converted back into kinetic energy as the train or cart moves down the other side of the incline.

3. Why is conservation of energy important for an uphill roller?

Conservation of energy is important for an uphill roller because it ensures that the ride will continue to operate smoothly and safely. Without the conservation of energy, the train or cart would not have enough speed and momentum to make it up and over the incline, and the ride would come to a halt.

4. How does the track design affect the conservation of energy in an uphill roller?

The track design of an uphill roller is crucial for maintaining the conservation of energy. The incline must be carefully calculated to ensure that the train or cart has enough kinetic energy to make it over the top. Additionally, the track must be smooth and free of any obstructions to minimize friction and maintain the energy of the ride.

5. Are there any safety concerns with an uphill roller and conservation of energy?

While conservation of energy is important for the operation of an uphill roller, there are safety concerns that must be addressed. If the incline is too steep or the track is not designed properly, the ride may not have enough energy to make it over the top, potentially causing a dangerous situation for riders. It is important for engineers and designers to carefully consider these factors when creating an uphill roller.

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