Law of conservation of energy wrong????????

[Lakshya]

a problem.....pls check..

imagine theres a horizontal planeA bove which the effects of gravity are not felt. any object above the plane just floats and gravity has no influence on it.

now take a chain(for e.g:made of small steel ring) of length hundred metres above the planeA and arrange it so that its in a heap just above the planeA. but take care the chain is not entangled and should be easy to stretch along its length.

 

now pull the lower end of the thread below the planeA and the chain runs down like a single thread and hits the ground and as links pull down on the ones they are linked to , the whole length of the chain will run like a thread and hit the ground in some time. now take planeA is 20metres above the ground surface. the terminal velocity of links when they hit ground will be around 14 metres .

now consider hundred metres of the chain weighs 100 units. the potential energy of the chain just above the planeA will be m*g*h =100 *9.8*20

=19600 units.

 

but kinetic energy recovered would be 1/2 * m * v*v = 0.5 * 100* 14 *14 = 9800 units. so in this method only half the energy is recovered hence violating the law of conservation of energy.

 

SIMPLY PUT, THERES DIFFERANCE IN ENERGY RECOVERED WHEN U TAKE 100 METRES OF CHAIN TO HEIGHT OF 10 METRES AND DROP IT AS WHOLE TOGETHER THAN WHEN YOU ARRANGE IT SO THAT IT RUNS DOWN LIKE A THREAD , EACH LINK PULLING DOWN ON THE OTHER LINK IT IS CONNECTED TO...

 

 

now what will the terminal velocity be when the planeA is above 40 metres...?

i guess its around 19.6m/s instead of 28m/s......

 

ur thoughts pls correct me if im wrong...

[Klaynos]

You've described a non-physical situation so it's not surprising that our laws of physics do not hold true.

[Lakshya]

You've described a non-physical situation so it's not surprising that our laws of physics do not hold true.

 

How is it a non-physical situation. If this is a non-physical situation then SRT which uses Minkowski space is also a non-physical theory.

[Klaynos]

imagine theres a horizontal planeA bove which the effects of gravity are not felt. any object above the plane just floats and gravity has no influence on it.

 

How could you construct such a plane?

[BenTheMan]

Lakshya---

 

There is a discontinuity in the metric. The manifold you are describing is not smooth and differentiable everywhere---it is not a manifold at all.

 

In less technical terms, you can't go from ``gravity'' to ``no gravity'' across a boundary.

 

I think.

[YT2095]

I wonder if a Lagrangian point may qualify?

 

 

but then you`re still left with the problem of the energy consumed to Get It to that point...

 

Oh dear!

[swansont]

I wonder if a Lagrangian point may qualify?

 

 

but then you`re still left with the problem of the energy consumed to Get It to that point...

 

Oh dear!

 

Still a continuous function; it's just the superposition of two other continuous functions.

[foodchain]

What about CP violation?

[BenTheMan]

What about it?

[foodchain]

Well all things being equal in regards to total energy of the universe how does such factor into the big bang in regards to conservation of energy?

[BenTheMan]

It doesn't.

[Lakshya]

Lakshya---

 

There is a discontinuity in the metric. The manifold you are describing is not smooth and differentiable everywhere---it is not a manifold at all.

 

In less technical terms, you can't go from ``gravity'' to ``no gravity'' across a boundary.

 

I think.

You can think of it as that something is accelerating it upward by an acceleration of 9.8 m/s. Then it would stay at its position as the no effects of gravity are felt. How can you say that it is not smooth and differentiable everywhere? It is.

[John Cuthber]

"imagine theres a horizontal planeA bove which the effects of gravity are not felt."

there isn't one.

[swansont]

How can you say that it is not smooth and differentiable everywhere? It is.

 

No, it isn't. Draw the graph; it goes from some value to zero at some point. Discontinuous.

[Severian]

It is not the discontinuity which is a problem. After all, you don't have to imagine this as gravity. You could have some hypothetical potential which was like gravity on one side of the line and zero on the other, and just because we don't know how to make it does not invalidate your argument. It shouldn't be discontinuous, but a very steeply varying function which goes from 0 to your required value within the width of a superstring would do fine.

 

The problem is that you are actually missing an energy in your calculation. Since the field is zero above the plane, the potential energy is also zero. So to move a link of the chain from one side of the plane to the other, you need to apply a force (and put in enough energy to overcome the potential). So your chain is not in free-fall with an acceleration g - you have to remove the acceleration due to the force at the barrier.

 

So it is not very suprising that you energy is not conserved - you have missed a bit.

 

However, you may be thinking instead of the potential not being zero above the plane, but just flat (so there is still no apparent force). Then you don't need to expand much energy pushing the links of the chain over the edge. Physically you could think of this as the chain being on a high up shelf of ice. One link falls off (blown by the wind or something) and the rest follows. But that is a perfectly normal scenario and I have even seen it used as an exam question. There is no conservation of energy problem there. Neglecting air resistance, each link will hit the ground with a speed [math]v=\sqrt{2gh}=\sqrt{2 \times 9.81 {\rm ms}^{-2} \times 20 {\rm m}} = 19.8 {\rm ms}^{-1}[/math] just like usual, conserving energy.

[alan2here]

The anti-graverty box that you are using will probably (when it is invented) require huge amounts of electricity continuously to keep it working, or there will be some other reason why this would not work.

 

Ive thought that wormholes\portals must need a cube law amount of power to move something increasing distances to keep in line with CoE (remeber the obvious CoE violation in valves portal footage, the same must apply to if they are real, worm holes unless they had such a rule for distance)

 

Why not just use the earth as an example and put the platform that your chain starts on in orbit where there is as close to no gravitational field as matters.

[Lakshya]

It is not the discontinuity which is a problem. After all, you don't have to imagine this as gravity. You could have some hypothetical potential which was like gravity on one side of the line and zero on the other, and just because we don't know how to make it does not invalidate your argument. It shouldn't be discontinuous, but a very steeply varying function which goes from 0 to your required value within the width of a superstring would do fine.

 

The problem is that you are actually missing an energy in your calculation. Since the field is zero above the plane, the potential energy is also zero. So to move a link of the chain from one side of the plane to the other, you need to apply a force (and put in enough energy to overcome the potential). So your chain is not in free-fall with an acceleration g - you have to remove the acceleration due to the force at the barrier.

 

So it is not very suprising that you energy is not conserved - you have missed a bit.

 

However, you may be thinking instead of the potential not being zero above the plane, but just flat (so there is still no apparent force). Then you don't need to expand much energy pushing the links of the chain over the edge. Physically you could think of this as the chain being on a high up shelf of ice. One link falls off (blown by the wind or something) and the rest follows. But that is a perfectly normal scenario and I have even seen it used as an exam question. There is no conservation of energy problem there. Neglecting air resistance, each link will hit the ground with a speed [math]v=\sqrt{2gh}=\sqrt{2 \times 9.81 {\rm ms}^{-2} \times 20 {\rm m}} = 19.8 {\rm ms}^{-1}[/math] just like usual, conserving energy.

 

Please explain yourtself as I am unable to understand you.

[Severian]

er... which bit did you not understand?

[BenTheMan]

It is not the discontinuity which is a problem.

 

I will defer to your expertise:) I thought that (s)he had a field discontinuity, which is a problem for GR, if I'm not mistaken. Certainly discontinuities in the potential are ok.

[Mag]

Please explain yourtself as I am unable to understand you.

 

I think the main idea is that you need a force to bump part of the chain into the gravitational field below the plane.(?)

[CPL.Luke]

its far simpler than that, unless the entire chain is dropped simultaneously its not going to be free fall, hus the "missing energy was really from assuming freefall.

 

for instanc if you were to have a case of free fall its simple to prove conservation of energy.

 

I may be able to pst this tomorrow but I have a road trip to get ready for.

[Rocket Man]

the point is easier to defend if the chain slides off a frictionless platform.

 

CPL.Luke is right, the OP assumed freefall, however, each link's accelleration is retared by the intertia of the link at the top which is initially stationary.

if you factor everything in, conservation of energy is not violated.

[Mr Skeptic]

a problem.....pls check..

imagine theres a horizontal planeA bove which the effects of gravity are not felt. any object above the plane just floats and gravity has no influence on it.

now take a chain(for e.g:made of small steel ring) of length hundred metres above the planeA and arrange it so that its in a heap just above the planeA. but take care the chain is not entangled and should be easy to stretch along its length.

 

Uh, would it be ok if we replace your construction with a chain of length L and density 1 resting on a frictionless surface a distance d above the ground, with constant acceleration g? Then the gravitational force on the chain will be canceled by the normal force (the same force that prevents you from falling through the floor). That way we don't need to imagine an impossible gravitational field that is constant g and suddenly disappears.

 

Anyhow, the problem you are having is that you assume both that the chain is in free fall (by your use of the equations for terminal velocity of an object in free fall), and that it is not in free fall (by stating that it moves off like a thread)

 

If you know some calculus, I can cook up some equations for you. Otherwise, consider that only a portion of the chain has gravitational attraction, but it has to pull the mass of the entire chain. You can calculate the terminal velocity of the chain by using the law of conservation of energy: (1/2) m v^2 = m g h so v = square root (2 m g h /m) = square root (2 g h). This is why you should learn to love the law of conservation of energy; it will let you calculate things you wouldn't know how to do otherwise.

 

Cheers,

Mr Skeptic