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"Veritasium" (YT) - "The Big Misconception About Electricity" ?

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adx:

--- Quote from: Sredni on January 14, 2022, 01:10:01 am ---Lets have two slides with almost no friction and with the same slope. One is at one meter above ground level (plus the minimum height to get the minimum slope to compensate for friction), the other is at 100 meters above ground. We make two one ton stones slide for 1 km to their destination: a machine that will make the block fall and turn all gravitational potential energy into heat (eat your heart out, Carnot!).

The block falling one meter generates m g (1 meter) J of energy. The block falling 100 meters generates one hundred times that energy.
Has the energy travelled along the slide?
Both slides are identical, both stone blocks are identical, and the both moved at the same speed on the slide.

Has one slope really carried 100 times the energy of the other one? ...

--- End quote ---

It has to carry the same, and it has to be the absolute amount of energy, so any expenditure of energy comes off what it was sent with, solving the paradox of unknown potential or unrealisable energy. If the block is returned over the direction of "travel" then relative energy is easy to define.

SilverSolder:

--- Quote from: adx on January 18, 2022, 12:10:32 pm ---
--- Quote from: Sredni on January 14, 2022, 01:10:01 am ---Lets have two slides with almost no friction and with the same slope. One is at one meter above ground level (plus the minimum height to get the minimum slope to compensate for friction), the other is at 100 meters above ground. We make two one ton stones slide for 1 km to their destination: a machine that will make the block fall and turn all gravitational potential energy into heat (eat your heart out, Carnot!).

The block falling one meter generates m g (1 meter) J of energy. The block falling 100 meters generates one hundred times that energy.
Has the energy travelled along the slide?
Both slides are identical, both stone blocks are identical, and the both moved at the same speed on the slide.

Has one slope really carried 100 times the energy of the other one? ...

--- End quote ---

It has to carry the same, and it has to be the absolute amount of energy, so any expenditure of energy comes off what it was sent with, solving the paradox of unknown potential or unrealisable energy. If the block is returned over the direction of "travel" then relative energy is easy to define.

--- End quote ---

If we ignore that G varies with altitude....   :D

The gravitational potential energy of the blocks is converted to kinetic energy as they accelerate down the slides.  The OP does not explain what happens to the kinetic energy of the blocks at the end of the slide... (do they hit a sand pit?)  but is there any doubt that the energy "followed the blocks" and traveled from the top to the bottom of the ramps?

TimFox:
G is the universal gravitational constant, and does not vary with altitude.
g is the acceleration of gravity, and does vary with altitude.

adx:

--- Quote from: SilverSolder on January 18, 2022, 02:19:03 pm ---The gravitational potential energy of the blocks is converted to kinetic energy as they accelerate down the slides.  The OP does not explain what happens to the kinetic energy of the blocks at the end of the slide... (do they hit a sand pit?)  but is there any doubt that the energy "followed the blocks" and traveled from the top to the bottom of the ramps?

--- End quote ---

I took it to be that the kinetic energy was small enough to not be important (there to stick with the analogy of resistance in wire, show that part of the experiment is the same, and block makes its way under its own steam). The difference is that one block dumps 100m of mgh of energy (and arguably had that extra to start), and the other only 1, plus subtle nonlinearities like you mentioned. We can go on about as much "potential" energy as we want, but the question is over whether the slide "carried" more energy. If you don't like the fact it is 100m higher, then allow the block to fall in a 99m hole and rest there until the end of the universe where this potential energy never becomes "real" (no work), and depending on the situation with the big bang, might never have been. This implies a weak form of acausality. Not mathematically because we can tack imaginary quantities in to match experiment, but conceptually, where the whole meaning of an energy flux rests. To add insult to injury, we don't get our blocks back, so we might not even know what happened to them. We don't know how long it took. Confuse-o-land.

Sredni:

--- Quote from: SilverSolder on January 18, 2022, 02:19:03 pm ---
The gravitational potential energy of the blocks is converted to kinetic energy as they accelerate down the slides.  The OP does not explain what happens to the kinetic energy of the blocks at the end of the slide... (do they hit a sand pit?)  but is there any doubt that the energy "followed the blocks" and traveled from the top to the bottom of the ramps?

--- End quote ---

No,  the blocks slide at constant velocity at very low speed (ideally on a frictionless slide there is no need for a slope). They arrive at the machine with the same velocity (ideally near zero).
All the energy when falling is converted by the machine into heat, so the blocks reach the bottom with zero velocity.  Imagine the machine is the perfect brake.

The EM case has the following differences, tho.

1.  The charge carry a field that can significantly alter the overall field of the system (while a rock does not alter in a perceptible way the gravitational field of the earth - it will be essentially constant near the surface).
The electrons that travel along the wire contribute to maintain the dynamical equilibrium where there is an excess on one side of the resistor and a lack of charge on the opposite charge. It is this charge imbalance that creates the 'hole in the ground' - the potential difference that confer the electron the energy that will be lost into heat.

2.   Momentum and energy are not necessarily independent. For electromagnetic waves, it is well known that we have E = c p. What about the EM field of our system? I have read something interesting on Panofsky and Phillips bit I want to merge it with what I've read in Zangwill and right now I have zero time.

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