Toffo Talks about Trains

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Re: Toffo Talks about Trains

Postby elasto » Tue Jul 15, 2014 3:46 pm UTC

Toffo wrote:But we don't have any missing angular momentum problem here.


Oh, forgive me. When you said:

When cannonballs are sitting at the bottom of the barrells, the cannonballs have angular momentum.

When the cannons have been just fired and the cannonballs are at the middle of the barrells, the cannonballs have less angular momentum.

And when cannonballs are out of the barrells, cannonballs have no angular momentum.


I assumed you were asking where the momentum went.

The answer is always the same: Either the momentum hasn't really been lost or it has been gained by another portion of the system.

Both possibilities seem to have been covered now, so it seems you need to state your query rather more precisely.

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Re: Toffo Talks about Trains

Postby Toffo » Wed Jul 16, 2014 2:32 am UTC

Let's say we have tank full of high pressure superfluid liquid.

Immersed in the liquid there's an object whose speed is continuously changing between 0 and 0.86 c, then of cource the volume of said object is changing between V and 0.5 V. (The object might be attached to a vibrating spring)

If we add two valves we have a high pressure pump. Does this pump require input energy?

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Re: Toffo Talks about Trains

Postby ConMan » Wed Jul 16, 2014 4:01 am UTC

Toffo wrote:Let's say we have tank full of high pressure superfluid liquid.

Immersed in the liquid there's an object whose speed is continuously changing between 0 and 0.86 c, then of cource the volume of said object is changing between V and 0.5 V. (The object might be attached to a vibrating spring)

If we add two valves we have a high pressure pump. Does this pump require input energy?

Well how are you going to get an object to accelerate repeatedly between such extreme speeds in a dense medium without inputting energy?
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Re: Toffo Talks about Trains

Postby Toffo » Wed Jul 16, 2014 3:54 pm UTC

Well ok then. A tank is full of static liquid, then a vane spins the liquid around so that the liquid lorentz-contracts, more liquid is added, then the vane stops the spinning of the liquid so that the liquid expands, now we have high pressure liquid.

Why would this process use energy?

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Re: Toffo Talks about Trains

Postby Tyndmyr » Wed Jul 16, 2014 4:10 pm UTC

Well, obviously, the vane will require energy to make the liquid spin, and further energy to make it stop.

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Re: Toffo Talks about Trains

Postby gmalivuk » Wed Jul 16, 2014 10:05 pm UTC

All your relativistic-fluid scenarios involve accelerating matter up to relativistic speeds. Why are you imagining such a process would not use ridiculous amounts of energy?
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Re: Toffo Talks about Trains

Postby Toffo » Thu Jul 17, 2014 2:23 pm UTC

We use energy to accelerate liquid -- liquid accelerates


... and magically liquid is also pressurized.

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Re: Toffo Talks about Trains

Postby p1t1o » Thu Jul 17, 2014 2:44 pm UTC

Is this not the case?:
In the frame of the liquid, the container can be considered as rotating around the liquid - from the liquids point of view, the container contracts around it, the opposite of the liquid contracting inside the container.
The two balance each other out and there is not change in relative volume between the liquid and the container cavity?

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Re: Toffo Talks about Trains

Postby gmalivuk » Thu Jul 17, 2014 6:18 pm UTC

Toffo wrote:We use energy to accelerate liquid -- liquid accelerates

... and magically liquid is also pressurized.
I don't understand why this is more "magical" than cooling down a gas, letting more gas fill the now-lower-pressure tank, and then warming it up again to find the pressure higher than when you started.
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Re: Toffo Talks about Trains

Postby Toffo » Fri Jul 18, 2014 4:47 am UTC

p1t1o wrote:Is this not the case?:
In the frame of the liquid, the container can be considered as rotating around the liquid - from the liquids point of view, the container contracts around it, the opposite of the liquid contracting inside the container.
The two balance each other out and there is not change in relative volume between the liquid and the container cavity?



It's better to ask a neutral third party, like an observer standing next to the tank.

He says: "The tank stays still and is not contracted. The liquid moves and is contracted."

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Re: Toffo Talks about Trains

Postby Toffo » Fri Jul 18, 2014 5:00 am UTC

gmalivuk wrote:
Toffo wrote:We use energy to accelerate liquid -- liquid accelerates

... and magically liquid is also pressurized.
I don't understand why this is more "magical" than cooling down a gas, letting more gas fill the now-lower-pressure tank, and then warming it up again to find the pressure higher than when you started.



It's kind of magical, if you put one energy into an empty box, and then when you look into the box, you find the energy you put there plus another energy.

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Re: Toffo Talks about Trains

Postby gmalivuk » Fri Jul 18, 2014 5:16 am UTC

You don't just put the one energy in, though. You also use energy adding more fluid.

Seems to me all that happens is you've arranged to have some of the energy you put in stick around in the form of pressure instead of going wherever the rest of it does when you slow the liquid back down.
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Re: Toffo Talks about Trains

Postby p1t1o » Fri Jul 18, 2014 9:47 am UTC

Toffo wrote:
p1t1o wrote:Is this not the case?:
In the frame of the liquid, the container can be considered as rotating around the liquid - from the liquids point of view, the container contracts around it, the opposite of the liquid contracting inside the container.
The two balance each other out and there is not change in relative volume between the liquid and the container cavity?



It's better to ask a neutral third party, like an observer standing next to the tank.

He says: "The tank stays still and is not contracted. The liquid moves and is contracted."


I've fallen into that probably-common mindspace where I can't wrap my head around the paradox.
A stationary observer sees the liquid contract, an observer suspended in the liquid sees the container contract.
Is there any free space or not? (Assuming the liquid is not compressed classically by the tremendous forces at play.)
I'm guessing the answer is something along the lines of "It depends on the observers situation", but then:

An outside observer sees the liquid contract and adds some more fluid.
The co-rotating observer sees fluid being added but does not see any space for it to fit...where does it go?

I feel like this is a common question, feel free to pawn me off to another thread.

**edit**
Unless the co-rotating observer sees the container contract in such a way as the internal volume increases, the walls of the container contract inwards so that there is space between the walls and the fluid? Then both observers witness some free space available for filling?

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Re: Toffo Talks about Trains

Postby gmalivuk » Fri Jul 18, 2014 11:42 am UTC

I'm not sure what the co-rotating observer says happens to the wall of the tank, but in the rotating frame itself the measurable circumference expands, so all observers agree that there's space for more liquid.

I remain unconvinced that it's any different from a compressed or condensed gas scenario, though.

Or an ice/water one: It's a sub-freezing day and you have some ice completely filling a container. You heat that water to 4C and notice there's now room for about 10% more water in the container. So you add that water, also at 4C. Then you remove the heat source, the water refreezes, and your container bursts.
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Re: Toffo Talks about Trains

Postby p1t1o » Fri Jul 18, 2014 12:55 pm UTC

It takes more energy to accelerate an object to relativistic speed using relativity than it does under classical rules, correct?

Classical description of events:

You have a fluid-filled container and you rotate the liquid at an extreme velocity causing the fluid to be compressed against the walls of the container, opening up a vacuum cavity in the centre of the vessel.
More fluid is introduced into the cavity and as the rotation is halted and the compressed fluid re-expands, oopsy-daisy - pressurised fluid!

Introducing relativity and Lorentz contraction means that in the same scenario there will be some extra space to add more fluid, ergo:the fluid is more highly pressurised, containing more energy.

But then introducing relativity into the scenario means that accelerating the liquid will be subject to those rules meaning that the fluid will require more energy to accelerate it – neatly taking into account the extra energy available from the more highly pressurised fluid.

How's that?

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Re: Toffo Talks about Trains

Postby drachefly » Fri Jul 18, 2014 12:56 pm UTC

In a relativistically rotating reference frame, you can't use special relativity - you need to use general relativity. So it's almost certainly not the case that the rotating observer sees the walls contracted and that's the only change.

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Re: Toffo Talks about Trains

Postby Toffo » Fri Jul 18, 2014 1:55 pm UTC

p1t1o wrote:I've fallen into that probably-common mindspace where I can't wrap my head around the paradox.
A stationary observer sees the liquid contract, an observer suspended in the liquid sees the container contract.
Is there any free space or not? (Assuming the liquid is not compressed classically by the tremendous forces at play.)
I'm guessing the answer is something along the lines of "It depends on the observers situation", but then:

An outside observer sees the liquid contract and adds some more fluid.
The co-rotating observer sees fluid being added but does not see any space for it to fit...where does it go?

I feel like this is a common question, feel free to pawn me off to another thread.

**edit**
Unless the co-rotating observer sees the container contract in such a way as the internal volume increases, the walls of the container contract inwards so that there is space between the walls and the fluid? Then both observers witness some free space available for filling?



Let us consider 10 static railway engines evenly distributed on a very large circular track. The engines accelerate to relativistic speed, simultaneously in track frame.

So we have here Bell's railway engines, that behave about the same way as spaceships in Bell's spaceship paradox.

Each engine says that distance to the nearby engines increased, and more engines could be added to the track. Track says more engines could be added, because the engines contracted.



So during the acceleration each engine says: "the engine ahead is moving away from me, and the track under that engine is moving towards me" ... Interesting.

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Re: Toffo Talks about Trains

Postby p1t1o » Fri Jul 18, 2014 1:58 pm UTC

Won't there also be an effect from the inwards acceleration, from the curved path - would the radius of the track appear to shorten? And the engines appear to grow narrower (width-ways)?

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Re: Toffo Talks about Trains

Postby gmalivuk » Fri Jul 18, 2014 2:45 pm UTC

No, there's no radial contraction.

Again, some of the energy you put into the system when you accelerated 20 locomotives to relativistic speeds remains in the system as pressure. What's the confusion?
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Re: Toffo Talks about Trains

Postby p1t1o » Fri Jul 18, 2014 3:00 pm UTC

gmalivuk wrote:No, there's no radial contraction.


Is it just analogous to a straight-line acceleration of an object then? How come?

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Re: Toffo Talks about Trains

Postby Tyndmyr » Fri Jul 18, 2014 3:02 pm UTC

Toffo wrote:We use energy to accelerate liquid -- liquid accelerates


... and magically liquid is also pressurized.


It isn't magic. It's a result of energy input.

Things don't just happen for free. That seems to be a repeated assumption. That effect is still costing energy. You're merely utilizing your torque for pressurization in an interesting way.

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Re: Toffo Talks about Trains

Postby elliptic » Fri Jul 18, 2014 3:55 pm UTC

All these questions are just variants on the barn/pole paradox, shirley.

In motion the pole is shorter then the barn due to length contraction. Shut both doors to trap it and when it comes to rest it still fits, because now it's under compression. And where does the energy to compress it come from? From its KE, of course, not all of which is returned to the environment.

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Re: Toffo Talks about Trains

Postby speising » Fri Jul 18, 2014 4:49 pm UTC

elliptic wrote:All these questions are just variants on the barn/pole paradox, shirley.

In motion the pole is shorter then the barn due to length contraction. Shut both doors to trap it and when it comes to rest it still fits, because now it's under compression. And where does the energy to compress it come from? From its KE, of course, not all of which is returned to the environment.

that works in a SR setup, because of relativity of simultaneity it also works in the ladders frame. in a rotating system, though, things get a little bit more complicated.

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Re: Toffo Talks about Trains

Postby gmalivuk » Fri Jul 18, 2014 6:44 pm UTC

It's still the same underlying thing happening, though: some kinetic energy end up as compression instead of heat or whatever else when the thing stops suddenly.
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Re: Toffo Talks about Trains

Postby Tyndmyr » Fri Jul 18, 2014 8:14 pm UTC

speising wrote:that works in a SR setup, because of relativity of simultaneity it also works in the ladders frame. in a rotating system, though, things get a little bit more complicated.


Not really. You don't even need to bring in relativity to understand it...centrifigual force will apply some pressurization to a rotating frame even at sub-relativistic speeds. And this energy is coming from the rotational energy supplied.

Now, I'll grant that the math gets harder in a relativistic setup, but that's not changing the underlying nature of energy, or where it comes from...it still ain't free. If you think you've gotten free energy, it's time to examine your inputs, because you probably missed something.

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Re: Toffo Talks about Trains

Postby Toffo » Sat Jul 19, 2014 3:48 am UTC

gmalivuk wrote:Seems to me all that happens is you've arranged to have some of the energy you put in stick around in the form of pressure instead of going wherever the rest of it does when you slow the liquid back down.


:o
If we decide that we dont wan't pressure energy after all, then we speed up the liquid again and pressure energy becomes kinetic energy automagically.

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Re: Toffo Talks about Trains

Postby gmalivuk » Sat Jul 19, 2014 1:08 pm UTC

No it doesn't. With more liquid, you have correspondingly more outward (centrifugal) pressure once it's spinning.
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Re: Toffo Talks about Trains

Postby Toffo » Sun Jul 20, 2014 10:32 am UTC

Let's say an astronaut is given the task to keep two Bell's spaceship -type spaceships at constant distance from each other, by every now and then attaching a rope between the spaceships and then shortly pulling on the rope.

Said astronaut is doing work when he's pulling. He could cheat by letting the rope to do the work, by letting the rope stay attached all the time.

Let's say the astronaut is cheating, the rope is doing the work that the astronaut was supposed to do. There is also a backup rope coiled up in the storage room. That rope is contracting too, but not doing any external work.

So is the backup rope heating up, or what?

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Re: Toffo Talks about Trains

Postby gmalivuk » Sun Jul 20, 2014 12:46 pm UTC

In the ropes' own frame, neither is contracting. The rope between the ships doesn't do any work by itself, it just exerts a constant tension to keep the ships from drifting apart. But a constant tension that doesn't actually move anything is not doing work.

Answer: Neither rope is doing any work.
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Re: Toffo Talks about Trains

Postby Tyndmyr » Mon Jul 21, 2014 5:04 pm UTC

Toffo wrote:Let's say an astronaut is given the task to keep two Bell's spaceship -type spaceships at constant distance from each other, by every now and then attaching a rope between the spaceships and then shortly pulling on the rope.

Said astronaut is doing work when he's pulling. He could cheat by letting the rope to do the work, by letting the rope stay attached all the time.

Let's say the astronaut is cheating, the rope is doing the work that the astronaut was supposed to do. There is also a backup rope coiled up in the storage room. That rope is contracting too, but not doing any external work.

So is the backup rope heating up, or what?


Not sure how you get the backup rope into this. A backup rope sitting in a storage room would not be contracting or...doing much of anything but sitting there. It's not really interesting from an energy perspective.

The currently used work may stretch somewhat while in use. Any work from this is obviously coming from the spaceships, not the rope. Additionally, if you want a constant distance, you'll want to rotate the spaceships around their mutual center of gravity(which can be utilized to provide centrifigal force for a gravity-like sensation). Otherwise, they'll tend to drift together.

Yes, using an astronaut instead of a rope is a much less efficient means. There are often varying ways to accomplish human goals, some of which are, from our perspective, less efficient. Consider, if your goal is to walk one mile east...you could walk directly there, or you could take some sort of little billy-esque path. The latter is much less efficient from a human perspective, but neither violates conservation of energy. Nor does the existance of another possible solution affect how much energy you are putting out.

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Re: Toffo Talks about Trains

Postby gmalivuk » Mon Jul 21, 2014 6:24 pm UTC

Tyndmyr wrote:There are often varying ways to accomplish human goals, some of which are, from our perspective, less efficient.
Particularly when you consider how human bodies do things like exert force. Holding a weight steadily in front of your face for an hour does no work on the weight itself, but requires a great deal of energy and endurance from you, to the point where most people couldn't do it at all.

Holding a rope taut between accelerating spaceships is the same. The rope doesn't do any work just maintaining a certain tension, but you would have to expend energy if you were trying to maintain that same tension with your own body.
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A new relativity paradox

Postby Toffo » Fri Feb 05, 2016 10:59 am UTC

Let's say a train powered by an overhead electric wire moves frictionlessly along an infinitely long linear track, and some light is shining out of the train's side windows. That's what the train needs the electricity for, for lights.

The aforementioned light carries linear momentum in track frame, like light emitted from moving things tends to do. During a very long time a very large amount of momentum would be carried away by the light.

Where does all that momentum come from?

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Re: A new relativity paradox

Postby SDK » Fri Feb 05, 2016 1:25 pm UTC

... The electricity?
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Re: A new relativity paradox

Postby sevenperforce » Fri Feb 05, 2016 2:22 pm UTC

SDK wrote:... The electricity?

What he said.

Energy is mass, so if energy is moving from the overhead electric wire to the train, mass is moving from the overhead electric wire to the train. Not a lot, mind you (mass flux is equal to the power consumption divided by c2), but some.

However, the train is moving and the overhead electric wire is not. Thus, in order to move from one inertial reference frame to another, this mass flux must be accelerated. The transfer of energy from the overhead electric wire to the train thus represents a change in momentum. If, every second, 1 microgram of mass-energy is transferred (let's say these are REALLY bright lights), then the change in momentum each second is equal to the 1 microgram * the speed of the train. Using the mass flux value from above, we derive a required constant force on the electrical energy, given by F = Pv/c2.

Where does this force come from? Well, Newton's laws of motion require forces to be equal and opposite. If the force is being applied to the electrical energy by the electric wire, then an equal and opposite force is applied to the (fixed) electric wire by the electrical energy, and so the speed of the train remains constant. If, in the alternative, the force is applied to the electrical energy by the train, then an equal and opposite force is applied to the train by the electrical energy, and the train will slow down over time.

In the second case, the loss of momentum of the train as a function of time will be equal to the momentum carried away by the emitted light, because that was the momentum it took to get the electrical energy up to the train's speed.

Where is the paradox?

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Re: Toffo Talks about Trains

Postby gmalivuk » Fri Feb 05, 2016 5:47 pm UTC

This is not new and it's not a paradox and it's not actually much about relativity, but it is from Toffo and it is about a train, so I merged it with the more appropriately titled "Toffo Talks About Trains" thread.
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Re: A new relativity paradox

Postby Toffo » Fri Feb 05, 2016 6:53 pm UTC

sevenperforce wrote:
SDK wrote:... The electricity?

What he said.

Energy is mass, so if energy is moving from the overhead electric wire to the train, mass is moving from the overhead electric wire to the train. Not a lot, mind you (mass flux is equal to the power consumption divided by c2), but some.

However, the train is moving and the overhead electric wire is not. Thus, in order to move from one inertial reference frame to another, this mass flux must be accelerated. The transfer of energy from the overhead electric wire to the train thus represents a change in momentum. If, every second, 1 microgram of mass-energy is transferred (let's say these are REALLY bright lights), then the change in momentum each second is equal to the 1 microgram * the speed of the train. Using the mass flux value from above, we derive a required constant force on the electrical energy, given by F = Pv/c2.

Where does this force come from? Well, Newton's laws of motion require forces to be equal and opposite. If the force is being applied to the electrical energy by the electric wire, then an equal and opposite force is applied to the (fixed) electric wire by the electrical energy, and so the speed of the train remains constant. If, in the alternative, the force is applied to the electrical energy by the train, then an equal and opposite force is applied to the train by the electrical energy, and the train will slow down over time.

In the second case, the loss of momentum of the train as a function of time will be equal to the momentum carried away by the emitted light, because that was the momentum it took to get the electrical energy up to the train's speed.

Where is the paradox?



I see. Now let's say a train is moving on two rails frictionlessly, then the train arrives to a segment of tracks where the rails are hot. The train happens to be a good heat conductor, and it happens to have a large heat capacity, that's why the train sucks energy from the hot rails, which causes the train to lose velocity, as so well explained by you. Where does the kinetic energy of the train go ?

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Re: A new relativity paradox

Postby p1t1o » Fri Feb 05, 2016 7:10 pm UTC

Toffo wrote:Let's say a train powered by an overhead electric wire moves frictionlessly along an infinitely long linear track, and some light is shining out of the train's side windows. That's what the train needs the electricity for, for lights.

The aforementioned light carries linear momentum in track frame, like light emitted from moving things tends to do. During a very long time a very large amount of momentum would be carried away by the light.

Where does all that momentum come from?


SDK wrote:... The electricity?


Where else? It is a closed system with a conspicuous energy input, and a stated lack of energy outputs, except for the one in question. In fact, why is it even a train? It boils down to representing an electric light! No infinite frictionless track required.

Its impressive to know all the tons of complicated maths and right-hand rules and mass-energy equivalency and reference frames etc etc but even if all you knew of was the conservation of energy, you'd get the answer.

The momentum must be coming from the electricity, the question is set up so that there is no other plausible answer.

Toffo wrote:I see. Now let's say a train is moving on two rails frictionlessly, then the train arrives to a segment of tracks where the rails are hot. The train happens to be a good heat conductor, and it happens to have a large heat capacity, that's why the train sucks energy from the hot rails, which causes the train to lose velocity, as so well explained by you. Where does the kinetic energy of the train go ?


More complicated, yes.
I'll eat my hat if that kinetic energy doesn't become heat.
The only question is, is the [extra] heat [from that kinetic energy] now in the rails or in the train?

The train definitely slows down? I'm not clear on that :(

If it definitely slows down, then the train is going to experience drag over the hot part of the track. Drag force is going to have to go through the wheels, since we are ignoring all other sources of friction/drag.

I'd wager (with my no-maths approach) that its in the wheels (or related track-contacting gear) now as heat.

This is at odds with a "frictionless" track however, it may not be compatible with the question?
Can you have a frictionless track that conducts heat? Seems incompatible.

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Re: Toffo Talks about Trains

Postby SDK » Fri Feb 05, 2016 7:43 pm UTC

Uh, isn't that one really easy too? The thing slowing the train down is this energy (mass) having to be brought up to speed. The kinetic energy from the train is being transferred to the energy (mass) it's picking up. It's a simple trade-off, same as if a stray hobo hopped on board instead.
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Re: Toffo Talks about Trains

Postby doogly » Fri Feb 05, 2016 8:37 pm UTC

A really hot hobo.
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Re: A new relativity paradox

Postby Toffo » Fri Feb 05, 2016 9:00 pm UTC

SDK wrote:... The electricity?


That does not make any sense. I suggest you study carefully Sevenperforce's answer.

Let me summarize:

"From the train" was one answer to question "were does all the momentum come" ... other answer was "from wires".


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