A hypothetical physics conundrum (You are required to think to enter this thread)
79 replies, posted
DanTehMan, your teacher is incorrect, what DChapsfield said is exactly what would happen.
Take a stick, with another coming out the middle perpendicularly. If you spin the perpendicular part, the other part will resist your movement. Once it is spinning, the outer atoms are not spinning, but have a velocity perpendicular to the stick, but their electromagnetic attraction to the other atoms keeps it connected and oriented to the rest of the stick, which gives the semi-illusion of rotation of the stick. When you try to stop it, the opposing acceleration is not instantaneous, but travels along the stick in a wave.
Uncertainty principle.
[editline]4th April 2011[/editline]
resistance
The edges of the bar are bound to a velocity below the speed of light, you can't push them to go faster than that, and the force required to accelerate an object increases steeply the closer you get to the speed of light even if there is no friction.
With this nugget of info, no matter how much force the motor at the centre exerts on the bar (it could be infinite in which case the edge velocity would be the speed of light), the edges will not exceed the speed of light. The longer the bar is, the lower its rotational velocity will be because the edges cannot go faster than the speed of light.
This holds for a theoretical rigid body which is completely undeformable. In real life the bar would probably have twisted itself into a spiral or broken or something because chucktanium doesn't exist.
Mystery solved everyone can go home now
[QUOTE=gman003-main;28979440]The problem is the energy needed. If a 1-kilogram mass was attached to the end of a 1-meter bar, it would take about 10 joules to accelerate it. However, at the end of a 10-meter bar, the same mass would take 100 joules. This means, effectively, that levers do not change the amount of energy necessary to achieve a given velocity.
That linear scale only holds at low speeds. Once you start getting into relativistic speeds (about .1 c), it becomes increasingly difficult to accelerate any mass, eventually reaching a point where it takes infinite energy to accelerate further (this point is the speed of light in a vacuum). The Large Hadron Collider can accelerate objects to 0.999999991c, but that takes over 200 megawatts of power, and only accelerates tiny nanoscopic particles.[/QUOTE]
In case people miss it, gman003 has provided the correct answer.
The physical impossibility of travelling faster than the speed of light extends from the fact that acceleration requires the input of energy and the energy required to reach and/or exceed the speed of light approaches infinity.
[QUOTE=ChristopherB;28981395]In case people miss it, gman003 has provided the correct answer.
The physical impossibility of travelling faster than the speed of light extends from the fact that acceleration requires the input of energy and the energy required to reach and/or exceed the speed of light approaches infinity.[/QUOTE]
To extrapolate:
As an object approaches the speed of light it's mass approaches infinity.
The formula for acceleration is F=MA
Or force = mass * acceleration
Therefore as the speed approaches infinity, the mass approaches infinity, therefore the force required to accelerate ALSO approaches infinity until you reach a point where even if you had every bit of energy in the entire frackin universe attempting to accelerate the projectile, you wouldn't ever reach the speed of light.
I've always wondered about the "mass approaches infinity" thing. Is this a reasonable explanation?
Kinetic energy is equal to mass x velocity.
So if energy = mass x speed of light^2 then as velocity increases mass must increase to keep the equation balanced.
This theory is similar to "shining a torch accross the surface of the moon". My old physics teacher explained that if you shined a torch at the moon from the earth and moved it around, the beam would appear to be moving faster than light but it would be unable to carry information or be modulated in a useful way. For this reason, it is actually NOT travelling faster than the speed of light.
As longer the bar is, as bigger the momentum of inertia will be and as more energy you will need to make it spin. That is one point.
But if you assume you have a nearly infinite amount of energy left for this, you get another problem:
Since you want to reach relativistic speeds, you have to do your calculations with the relativistic angular momentum. And from that you will just derive that no matter how much energy you put into the rod to make it spin, the angular momentum will increase to infinity but the outer velocity will only go close to the speed of light.
and it's called football since you play with your foot...
[QUOTE=ChristopherB;28981646]I've always wondered about the "mass approaches infinity" thing. Is this a reasonable explanation?
Kinetic energy is equal to mass x velocity.
So if energy = mass x speed of light^2 then as velocity increases mass must increase to keep the equation balanced.[/QUOTE]
It increases in mass because it increases in mass.
It's one of those weird things that just does.
Hypothetically I could rate the OP dumb, but aren't all dumbs just relatively agrees in some other world?
what if you had gokus extendo pole
[QUOTE=Jo The Shmo;28977735]"What if the laws of physics didn't apply, then there would be some CRAZY shit man!"[/QUOTE]
Nothing in that broke the laws of physics, except the unbendable material that I realize doesn't exist. The immovable-ness of the device was just so we wouldn't have two objects of unbelievable mass/size in the equation. Everything else obeys the laws of physics.
[QUOTE=BackOnCrack;28977877]if you are so smart op why didn't you paragraph it, hard to read half a page of a block of words[/QUOTE]
Never claimed to be smart, in fact it is because I am not that I am asking this. But I'm sorry about the horrible formatting of the paragraph.
[QUOTE=JohnnyMo1;28977924]The movement of the bar propagates as a phonon. It can't travel at or faster than the speed of light. Once the center of the bar starts moving, it still takes time for this movement to spread out to the edges, and no place along the bar will be traveling at or above the speed of light.[/QUOTE]
Yeah, I was thinking about that, but I thought that if the speed was great enough and there was absolutely no resistance (which could happen in space) it may bend, but not so much that it would keep all parts under the speed of light. But I can understand how this would happen.
[QUOTE=DChapsfield;28978279]If it were unbendable, the motor in the center would need to accelerate the outer edges first, in layman's terms. So the edges of the bar would reach max. tangential velocity of [i]c[/i] and not be able to accelerate any more, limiting the tangential velocity of the inner portions of the bar. All sections would have the same angular velocity, but tangential velocity would decrease as you got closer to the center.
All force travels through objects in waves; force does not instantaneously act on all particles of an object. This holds true for a motor which rotates a bar from the center; if it were unbendable, the inner sections of the bar would have to "wait" for the outer edges to "receive" the force from the motor and begin to rotate. Unfortunately, nothing of significant mass can be completely unbendable. So the inner portions would begin to accelerate as the outer edges "waited" to begin to rotate, causing a bend. The physics hold firm though; the inner portion's tangential velocity will be stuck at a much lower value than the edges, which will reach the speed of light.[/QUOTE]
Yeah, I was imagining this in my head, but if there was no resistance on the particles I thought maybe they'd have no reason to move out of alignment, but I guess they would.
[QUOTE=Greenen72;28978509]This is basically like saying "I can make a cup of water turn into a cup of boiling water with ice cubes in it, given that the applicable laws of physics don't apply"
There's a bunch of situations similar to this, like the laser on a ship moving just under the speed of light[/QUOTE]
Again, not really breaking the laws of physics, except for that unbendable bar, which I had simply hoped would stop people from saying "it would bend" without any supporting information.
[QUOTE=gman003-main;28979440]The problem is the energy needed. If a 1-kilogram mass was attached to the end of a 1-meter bar, it would take about 10 joules to accelerate it. However, at the end of a 10-meter bar, the same mass would take 100 joules. This means, effectively, that levers do not change the amount of energy necessary to achieve a given velocity.
That linear scale only holds at low speeds. Once you start getting into relativistic speeds (about .1 c), it becomes increasingly difficult to accelerate any mass, eventually reaching a point where it takes infinite energy to accelerate further (this point is the speed of light in a vacuum). The Large Hadron Collider can accelerate objects to 0.999999991c, but that takes over 200 megawatts of power, and only accelerates tiny nanoscopic particles.[/QUOTE]
I tried to word everything so that mass wouldn't be a problem; in the vacuum of space, with no particles or forces to act upon an object, mass would be irrelevant. I would hope. And then again there's the bar's own gravity, which I can't account for.
[QUOTE=Luxo;28979901]You're taking a situation that is physically impossible and trying to apply physics to it. It's really a quiet useless thought.[/QUOTE]
I'm fully aware, thank you.
[QUOTE=MerzBro;28980824]A not-so-hypothetical posting conundrum, starring: the op.
(you are required to indent in order to create this thread)[/QUOTE]
Oh please you're the third person, get over it. I'm sorry it wasn't indented but at least I used proper grammar (not saying you didn't).
And sorry for that brief, horrible edit of the OP earlier today (I live on Eastern Standard Time), I was in Comp Sci and we had a shortened period so I rushed it and didn't check what it looked like after editing it.
Would totally depend on the properties of the material being used (hypothetical or not).
[QUOTE=Empty_Shadow;28982524]It increases in mass because it increases in mass.
It's one of those weird things that just does.[/QUOTE]
It increases in energy. A "mass increase" is just bullshit if you do real physics and sadly often taught in school :/.
[editline]4th April 2011[/editline]
[QUOTE=ZeroMinus;28985625]Would totally depend on the properties of the material being used (hypothetical or not).[/QUOTE]
Even for a perfect rigid rod the limitations concerning the angular momentum stays so outer velocity will never reach the speed of light.
[QUOTE=Empty_Shadow;28982524]It increases in mass because it increases in mass.
It's one of those weird things that just does.[/QUOTE]
As was gone over in the other relativity topic: you gain no mass close to the speed of light, what does happen though is your length decreases, so you get DENSER (you effectively get 'compressed' at higher speeds).
Here's where shit gets confusing, though, because, to the observer (the person travelling close to the speed of light) everything ELSE in the universe seems to get more compressed, while they, to themselves, seem normal.
I find the thought of having a ladder that is perfectly straight and won't bend under stress to be placed flat on the ground, obviously you would start walking along the ladder since it is flat on the ground, but eventually it will get steeper and steeper until you have to climb it. (note, the ladder length is far greater than the diameter of the earth.)
OP, you don't even know what the theory of relativity means... you use Einstein's equation vaguely as if its meaning is to set the universal speed limit.
I also think the OP needs to learn the difference between mass and weight. Just because there's no gravity doesn't mean there's no mass. Mass is an intrinsic property of an object and is completely independent of gravity sources while weight is the force created by gravity acting on a mass. So the object being in a vacuum doesn't really have anything to do with its mass.
You can't apply physics to this situation. Because what you described is impossible. I guess if anybody here knows a theoretical physicist, he/she could provide a proper answer.
I don't think I'll ever understand physics :/
[QUOTE=ElChrisman99;28991659]You can't apply physics to this situation. Because what you described is impossible. I guess if anybody here knows a theoretical physicist, he/she could provide a proper answer.[/QUOTE]
Yes you can, we already have. And this doesn't require a theoretical physicist. It just requires a surface knowledge of relativity. Two physics students at least have already responded.
Man i'm too drunk to think this shit yknow
[highlight](User was banned for this post ("Posting under the influence" - JohnnyMo1))[/highlight]
Newton's second law: Force = mass * acceleration. As the bar speeds up and approaches the speed of light, its relativistic mass increases towards infinity. The force required to accelerate the bar any more will therefore also approach infinity, so the machine that applies the torque will fail.
(I know newton's second law doesn't really hold true for relativistic physics, but I think you get the same result with[B][/B] F = dp / dt ...)
[QUOTE=sltungle;28986038]As was gone over in the other relativity topic: you gain no mass close to the speed of light, what does happen though is your length decreases, so you get DENSER (you effectively get 'compressed' at higher speeds).
Here's where shit gets confusing, though, because, to the observer (the person travelling close to the speed of light) everything ELSE in the universe seems to get more compressed, while they, to themselves, seem normal.[/QUOTE]
We once had a home-exercise in an experimental physics course where we had to discuss about "Does a too big car a at speed x fit into a smaller garage?".
The outcome was that the train really appears smaller than the garage itself when it is close to the speed of light and observed from a static observer, but in fact the driver of the car sees something totally different: The garage is smaller than his car, so the opposite case.
A better explanation is given here with the [url=http://en.wikipedia.org/wiki/Ladder_paradox]Ladder Paradoxon[/url]
[editline]5th April 2011[/editline]
[QUOTE=Krepps;28992186]Newton's second law: Force = mass * acceleration. As the bar speeds up and approaches the speed of light, its [u]relativistic mass[/u] increases towards infinity. The force required to accelerate the bar any more will therefore also approach infinity, so the machine that applies the torque will fail.
(I know newton's second law doesn't really hold true for relativistic physics, but I think you get the same result with[B][/B] F = dp / dt ...)[/QUOTE]
[b]Energy[/b]!!! (Relativistic Mass = Bullshit)
Anyway, Newtons laws HOLD true for relativistic speeds. All you need to do is using the relativistic momentum (Force is the derivative of momentum concerning time).
Also you can increase that ladders rotational energy and therefore relativistic angular momentum up to infinity, still the outer part will never go (just close to) the speed of light.
Also2: I find it curious how people first reply with "the machine to accelerate will fail" when you assume perfect conditions without technical limitations. Because only then, we can talk about physical limits (the technical one still exist, but are irrelevant in this case. We want the ultimate physical limit)
[QUOTE=aVoN;28992456]Length contraction is not making you "denser", it makes you appear thinner from an observer who is stationary. If someone moves with you at the same speed, he keeps his length. You [b]always[/b] have to speak about someone [b]relative[/b] to someone else or it makes no sense at all.
But yes, mass does not increase. Energy does. Something like a relativistic mass is bullshit.
Also another note: We once had a home-exercise in an experimental physics course where we had to discuss about "Does a too big car a at speed x fit into a smaller garage?".
The outcome was that the train really appears smaller than the garage itself when it is close to the speed of light and observed from a static observer, but in fact the driver of the car sees something totally different: The garage is smaller than his car, so the opposite case.
A better explanation is given here with the [url=http://en.wikipedia.org/wiki/Ladder_paradox]Ladder Paradoxon[/url]
[/QUOTE]
I swear I read something somewhere about how ion collisions at relativistic speeds could only be explained when an increased nucleon density was taken into account due to a Lorentz contraction. I'm probably mistaken though and muddled it up with something else.
[QUOTE=laharlsblade;28977668]When turned on, this device will spin the bar, completing one rotation in ~1 minute.[/QUOTE]
This is where you deviate completely from believeable hypothetical scenarios and go into fantasy. This is physically impossible, hence your conundrum isn't one at all.
"What if physics died? That'd be fucking crazy!"
[QUOTE=sltungle;28992510]I swear I read something somewhere about how ion collisions at relativistic speeds could only be explained when an increased nucleon density was taken into account due to a Lorentz contraction. I'm probably mistaken though and muddled it up with something else.[/QUOTE]
You have to take lorentz contraction into account for both packets so the density has to change. I was wrong (it was too early in the morning and I hadn't breakfast at this point).
Density changes by [img]http://math.daggeringcats.com/?\rho = \rho_0 \gamma^2[/img]
Imagen this, you are in a very large ship that is traveling at 99% the speed of light, on this ship you have a suit that enables you to run 2% of the speed of light, you have now broken the light speed barrier, go fuyck yourself physics!
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