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Newtonian mechanics, Work from centripetal acceleration?
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Newtonian mechanics, Work from centripetal acceleration?
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einsteinium252
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Newtonian mechanics, Work from centripetal acceleration?
«
on:
25/07/2008 05:52:01 »
greetings,
A while ago I came across an abstract on a web page that claimed to extract work from centripetal acceleration. It initially sounded like a misunderstanding of the math involved (and fun to poke holes in), but as I read further it sounded like it made a little sense. Can anyone tell me if I'm overlooking anything? Or am I on a mathematical goose chase.
Summed up: Two weights placed opposite each other are spun in a circle around a center point.
1. As the angular velocity increases the centripetal acceleration increases, such that a=v/r^2.
2. Then a*M=F, to create force Fc vectored perpendicular to the direction of motion.
3. As the centripetal acceleration increases the weights are allowed to move, thus creating the distance in the D*F=Work equation.
4. The weights move out, draining energy out of the system as the weights are forced to move at a higher velocity while remaining at the same RPM. This creates a force Fa opposite the direction of motion. However, Fc=r^2*k whereas Fa=r*k
5. As the weights spin down, the energy used to accelerate them to their angular velocity is recollected.
6. Work is extracted?
BIG problem, Energy cannot be created nor destroyed.
If nothing else, it is a novel concept.
«
Last Edit: 25/07/2008 06:05:31 by einsteinium252
»
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graham.d
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Newtonian mechanics, Work from centripetal acceleration?
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Reply #1 on:
25/07/2008 09:39:58 »
As the weights move out the energy stays the same. Their velocity does not change but the rate of rotation slows. You can calculate it also from the conservation of angular momentum. Ballet dancers use this in reverse: they spin around on their toes, then bring their arms in, which increases their rate of rotation. You can try it on an office swiveling chair too. There is no change in energy.
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lyner
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Newtonian mechanics, Work from centripetal acceleration?
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Reply #2 on:
25/07/2008 11:37:05 »
The description of the model is incomplete, I think.
Are they driven by a central shaft? Is there a spring connecting them? What is the Law of the Spring - is it proportional to applied force?
Or is there friction involved as the masses are allowed to move in and out?
We would really need to agree on the above before we could have a meaningful discussion about what would actually happen.
The only thing you can definitely say, at this stage, is that angular momentum would be conserved. (And that there will be no anomaly if we work it out right!)
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einsteinium252
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Newtonian mechanics, Work from centripetal acceleration?
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Reply #3 on:
25/07/2008 15:19:46 »
Sophiecentaur,
Forgive me for the lack of description in the model, and I failed to communicate the concept of the machine concisely. The very work done by the machine comes from the force provided by the centripetal acceleration. I only mentioned the changing moment of the weight as something that would slow the velocity of the weights(thus reducing the centripetal acceleration of the weights, like if you put your arms out while spinning on an office chair). To straighten out the complete mechanical model, the weights are opposite eachother on a single metal beam, that is driven by a central shaft. Each weight is attached to an expansion spring, which is connected to a point on the bar between the shaft and the weight. The spring can be a gas shock, or any other energy storage device.
The Work comes from the weight being driven out by centripetal acceleration by a force F and latched at distance D from the point at which it began. After the shaft "spins down" and all the energy used to "spin it up" is collected, the centripetal acceleration is gone and the weights are released from the latch. The weights fly back to home with +Joules, because the acceleration acted on a vector that is perpendicular to the direction of motion and the angular velocity is unaffected.
Again, the law of energy conservation kicks in. Disproving it instantly. But where the problem lies has eluded me.
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Last Edit: 25/07/2008 15:22:22 by einsteinium252
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lyner
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Newtonian mechanics, Work from centripetal acceleration?
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Reply #4 on:
26/07/2008 11:30:07 »
OK- this is not difficult.
As the masses move out, work is done (K.E. is lost) but Angular Momentum remains the same.
This means that, effectively, the velocity, v, of the masses is proportional to 1/r.
The work done by each mass as it moves out can be shown, fairly easily, to be the difference between Kinetic Energy before and after:
E
_{1}
- E
_{2}
= L
^{2}
(1/r
_{1}
^{2}
-1/r
_{2}
^{2}
)/2m
^{2}
where m is the value of each mass, L is the Angular Momentum and r is the radius.
This work could be expended in overcoming friction or stored in compressing a spring etc.
The rotational energy is, by now, less. If you 'spin down' the shaft you will extract less energy than you put in, initially. The remaining energy is in your spring or just lost to friction.
The Energy has all been accounted for and no Laws have been violated.
I think that is a full enough explanation but feel free to take me to task about anything you're not happy with.
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einsteinium252
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Newtonian mechanics, Work from centripetal acceleration?
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Reply #5 on:
27/07/2008 01:08:57 »
Wow, thanks Sophiecentaur and graham. d for clearing all this up for me. I see now that when r increases the kinetic energy is lower, but the angular momentum remains the same! So, just like the person on the office chair pulling in their arms, the rpms change but total energy stays the same. The person can keep changing the weight, but only the rpm's change.
Major Kudos on the mathematical proof for the true work done by the weight, I appreciate it.
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lyner
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Newtonian mechanics, Work from centripetal acceleration?
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Reply #6 on:
27/07/2008 16:23:42 »
And I appreciate your appreciation!!!
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Newtonian mechanics, Work from centripetal acceleration?
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Reply #6 on:
27/07/2008 16:23:42 »
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