Gravity and Magnetism the same?

[ramparts]

Let us continue with this

Air resistance only applies above ground, right? Where there's, like, air. So if we're going to include in our problem a period of falling through the air (say we start at a height above h off the ground), we need to make our differential equation a piecewise one. The first piece applies for R<r<h and would take the Earth to be a point source, but factor in air resistance. The second piece, for 0<r<R, is as I stated in my last post (but with different initial conditions).

Now we need to work out the nature of our travel through the Earth. Have we drilled a shaft through it? I prefer to treat our observer as a small particle that can pass through rock and stuff, but more realistically, let's say we drilled a hole. It's possible air would come through and we would, in fact, have to include air resistance throughout the whole problem. Even if not, the hole would have to be tight enough that we'll certainly have to take friction into account. Can someone please look up the coefficients of dynamic friction for each mineral found in the Earth's surface and for human flesh?

This is a problem I never, ever want to have to solve :lol:

Now, while we're being ridiculous, I'd like to propose that our problem take the density of the Earth not to be constant, but to scale with sin^2(r)

 

[cpumasterwv]

Wait, gimme a minute. I've got Seven of Nine on speed dial. She can figure this one out for us.

 

[Deeyo]

okay guys

so what if the OP was onto something and like, magnetism and gravity are just flips of the same coin

like magnetism is falling away and gravity is falling towards and stuff stays in orbit because they're balancing each other out!

im sorry if I just blew ur minds.

where do I register for the noble prizes?

 

[emperor_of_localgroup]

r(t) = R cos(kt)

I have a problem with this equation/solution. Using this formula I have calculated the time a ball will take to reach the center of earth, say T.
T=250412.54 sec = 69.56 hrs.

But the problem is T depends on only universal constants G and Pi. Which means an object will take the same amount of time to reach center on Mars, moon, Jupiter, or the sun. There is something missing in here. Air resistance doesn't matter. Even in a very ideal case, no resistance, constant density, the time to reach the center is the same!!!!!

I used numbers this way, tell me if there is any mistake.
At center r=0, t=T
0=RCos(kT)
kT=Pi/2. then solve for T.

 

[ramparts]

So you did the calculation exactly right (T = π/2k), but you need to make sure you're calculating k right. Just looking back, I think it would be k^2 = 4πGρ/3. I think that's right, the units work out. If we use ρ=5.5153 g/cm^3 (mean density of the Earth, source Wiki ), then I calculate just under a half hour. That doesn't seem too terrible. I'll go back and check some notes I have lying around, and think about it a bit more (I have to run now), but while it seems counter-intuitive that it wouldn't matter what planet you're in, so did Galileo dropping those balls from the leaning tower Think about it like this: we're assuming the same density regardless, which takes both the masses and radii into account. Of course, if you were on, say, Jupiter, which is much less dense, the travel time would be much longer.

 

[ramparts]

Okay, I think I had the more important points in my last post, they just weren't sufficiently fleshed out.

For anyone who's not familiar enough with cosine plots to visualize them, here's a plot of two cosine functions with the same period, but different amplitudes:

http://www28.wolframalpha.com/input/?i= ... cos%28t%29

This corresponds to objects with the same k (in other words, the same density) but different radii and masses. The bigger curve is the one with larger R, so that's a more massive planet. The graph shows time on the x-axis, and height above/below the center of the planet/star/etc. on the other, so it's pretty simple to interpret. The two start at different heights (obviously the larger planet has a higher surface, so the object on the bigger planet starts higher), and then fall at different rates - the one on the larger planet falling faster than the other - until they meet in the center. So they start at different heights, but the one on the more massive planet clearly accelerates faster, so the two end up taking the same time to the center.

Does that work? If not, let's look at it more closely. They have the same density, so the mass each object feels is proportional to the interior radius cubed. Each one falls a little bit in some amount of time (say, a second), but the object in the larger planet is further from the center of its planet than is the object in the smaller planet, so it feels proportionally more gravity since there's so much more interior mass pulling in on it. So the object in the larger planet will accelerate faster, and it only makes sense that if this trend continues they'll "meet" at some point. This is the special case where that meeting point happens to be the center of each planet

 

[Skibo1219]

So air density is the same at an altitude of 20k feet as it is at sea level? Would it not be prudent to use separate weather calculations, in your sub-surface calcs? I assume (i hate this word sometimes) that with higher air pressure comes increased air density, how does altitude factor in all this? I theorize that underground air density is constant and not affected by surface weather changes. Furthermore, at 20k feet below ground heat needs to factor in lieu of the cold at 20k feet above.
Normal air pressure is roughly 14.7 PSI at sea level, what altitude does it reach 0, I never seem remember this, /facepalm

 

[emperor_of_localgroup]

So you did the calculation exactly right (T = π/2k), but you need to make sure you're calculating k right. Just looking back, I think it would be k^2 = 4πGρ/3. I think that's right, the units work out. If we use ρ=5.5153 g/cm^3 (mean density of the Earth, source Wiki ), That doesn't seem too terrible. I'll go back and check some notes I have lying around, and think about it a bit more (I have to run now), but while it seems counter-intuitive that it wouldn't matter what planet you're in, so did Galileo dropping those balls from the leaning tower Think about it like this: we're assuming the same density regardless, which takes both the masses and radii into account. Of course, if you were on, say, Jupiter, which is much less dense, the travel time would be much longer.

Yes , I forgot you kept density in the constant k also. With density time to reach the center will be lower. But that was not my problem.

Say, we build a sphere of earth-radius with a material of density 1 Kg/m^3. Then we build a sphere of 1 light year radius and with the same material. A ball will take the same amount of time to reach the center of each sphere, because time depends on only constants. Something is missing here, I'm not sure.

If we dig tunnels through the centers of these spheres, will the ball really go through the centers? Because on the other side of the ball, there's not any mass to attract the ball. My guess is, the ball will get stuck on the wall of the tunnel, because center of mass of a sphere will be shifted due to the tunnel.

Just some food for thought.

 

[ramparts]

So air density is the same at an altitude of 20k feet as it is at sea level? Would it not be prudent to use separate weather calculations, in your sub-surface calcs? I assume (i hate this word sometimes) that with higher air pressure comes increased air density, how does altitude factor in all this? I theorize that underground air density is constant and not affected by surface weather changes. Furthermore, at 20k feet below ground heat needs to factor in lieu of the cold at 20k feet above.
Normal air pressure is roughly 14.7 PSI at sea level, what altitude does it reach 0, I never seem remember this, /facepalm

Absolutely not - as you'd expect, air gets less dense as you go above the surface, until there's no air at all Altitude doesn't factor in at all, as we're assuming the object starts from the surface of the Earth, and similarly we're not taking air friction into account as a) it's hard, b) it's not interesting (IMHO), and c) there's not much air underground!

Yes, there are many, many things one would need to take into account for this to be at all a realistic calculation, the first of which being that the Earth is certainly not of constant density. But this highly idealized calculation was designed more to show a poster above that there is no mathematical error (or singularity) when considering such a problem.

 

[dangineer]

If anyone is interested in discussing high altitude aerodynamics, like reentry, weather balloons, etc., I have some experience in that category. Maybe we can start another post.

As for the other problem, to clarify things for people that havn't dealt too much with harmonic oscillators (pendulums, etc.), a key point to remember is that at the point of highest velocity, the acceleration is zero. This usually occurs at the center of the object's motion (in this case, the center of the Earth).

So, for just about any harmonic oscillator(I can't think of any exceptions), the object starts from rest while acceleration is at a max, acceleration reduces while speed increases, speed reaches a max while acceleration is zero, speed reduces while acceleration increases (in the opposite direction, and finally speed reaches zero while acceleration is max again, and the process can start all over again.

 

[Skibo1219]

If anyone is interested in discussing high altitude aerodynamics, like reentry, weather balloons, etc., I have some experience in that category. Maybe we can start another post.

Yes please do start another post, I am fascinated with the subject but know very little about hi-altitude "stuff".

As for the other problem, to clarify things for people that havn't dealt too much with harmonic oscillators (pendulums, etc.), a key point to remember is that at the point of highest velocity, the acceleration is zero. This usually occurs at the center of the object's motion (in this case, the center of the Earth).
So, for just about any harmonic oscillator(I can't think of any exceptions), the object starts from rest while acceleration is at a max, acceleration reduces while speed increases, speed reaches a max while acceleration is zero, speed reduces while acceleration increases (in the opposite direction, and finally speed reaches zero while acceleration is max again, and the process can start all over again.

Aside from the reference to the harmonic oscillator, and while i don't know who's law this is, that statement is more or less a common sense statement, but from a mechanical point of view, an object starting from rest is not immediately at max acceleration. It is practically impossible a plane can't jump to Mach 2 from a dead stop with our current technology.

 

[Mars_Unit]

I first began experimenting with Paramagnetism and Diamagnetism back in 1973. I learned much since then.

I built a Master Magnet to pick up Non Ferrous metals. It repulsed Aluminum!

I even attempted to build an Electro-Gravitational-Magnet or "Gravnet" using insulated copper wire and I had to wind the wire around a torus.

Image a coiled telephone wire in a circle. Dr RL Forward said he needed White Dwarf Matter to make it work.

In theory, when the electrons are accelerated to 20% of Celeritas, it just might start emitting Gravity control.

It did not work because I did not use Superconducting Wire. I couldnt afford it.

http://www.rexresearch.com/mrmagnet/mrmagnet.htm

 

[ramparts]

White dwarf matter?

 

[ramparts]

Yes , I forgot you kept density in the constant k also. With density time to reach the center will be lower. But that was not my problem.

Say, we build a sphere of earth-radius with a material of density 1 Kg/m^3. Then we build a sphere of 1 light year radius and with the same material. A ball will take the same amount of time to reach the center of each sphere, because time depends on only constants. Something is missing here, I'm not sure.

Sorry emperor! I missed this post the first time around.

Yes, it's counter-intuitive, but that's how it works. The ball with the one light year radius will have more distance to travel, but it will have far more mass pulling in on it, too. So it will accelerate much more quickly than the particle in the Earth-sized sphere, and in this particular problem, the point where they meet happens to be the center.

If we dig tunnels through the centers of these spheres, will the ball really go through the centers? Because on the other side of the ball, there's not any mass to attract the ball. My guess is, the ball will get stuck on the wall of the tunnel, because center of mass of a sphere will be shifted due to the tunnel.

Just some food for thought.

Oh, the ball will certainly go through the centers. What's the alternative - it would hit the center and stop? That wouldn't make sense, because of conservation of energy, inertia, and all sorts of other things. Though at the center it would feel no gravity, it would continue moving at some velocity, and immediately (once it left the center) feel an attraction in the other direction. That attraction would grow as the object continued moving away from the center, and finally become strong enough to turn the object around by the surface (on the other side from the starting point!).

 

[dangineer]

Aside from the reference to the harmonic oscillator, and while i don't know who's law this is, that statement is more or less a common sense statement, but from a mechanical point of view, an object starting from rest is not immediately at max acceleration. It is practically impossible a plane can't jump to Mach 2 from a dead stop with our current technology.

If an object were suddenly subjected to a force, it would suddenly have an acceleration; in fact, most forces aren't applied gradually.

In the case of our example with the Earth, the assumption is made that the object is held above, or at the surface of the Earth, at rest relative to the Earth, until the experiment begins. While it's being held, the object is actually experiencing the force of gravity the whole time. The hand or whatever that is holding the object is just providing a force that is counteracting gravity and causing the net acceleration to be zero. Once the object is released, the counteracting force dissappears and the force of gravity instantly takes over, giving the object an instant non-zero acceleration. Since it's starting from rest, the velocity will be zero and will grow, but the acceleration is not zero.

 

[ramparts]

Skibo, you also seem to be confusing acceleration and velocity. A plane can't suddenly go to max velocity - say, rest to Mach 2 - but Mach 2 isn't an acceleration, it's a velocity. Acceleration is how fast speed changes, and as dangineer says, that can certainly be applied instantaneously.

 

[dangineer]

Sorry to be nitpicky, but Mach numbers aren't actually velocities, although they are used to convey a sense of velocity. The Mach number is actually a dimensionless parameter used to define certain flow conditions in a medium, sort of like Reynold's number, Prandtl number, or various other numbers named after famous fluid dynamicists.

The Mach number relates velocity to a fluid's temperature and compressibility properties (specific heats). I just want to make sure this more accurate definition is out there, since this is a common misconception, not that it has any bearing on the argument at hand.

If anyone is curious, Mach number is equal to V/sqrt(gamma*R*T)

V=velocity
gamma=ratio of specific heat of a gas at a constant pressure to heat at a constant volume
R=specific gas constant
T=absolute temperature

 

[Skibo1219]

Skibo, you also seem to be confusing acceleration and velocity. A plane can't suddenly go to max velocity - say, rest to Mach 2 - but Mach 2 isn't an acceleration, it's a velocity. Acceleration is how fast speed changes, and as dangineer says, that can certainly be applied instantaneously.

You are correct, however my mind types faster then my fingers do. I am slowly learning that unless one types the exact and perfect wording the first time here @SDC, ones then has intentions mis-quoted and twisted.

an object starting from rest is not immediately at max acceleration. It is practically impossible a plane can't jump to Mach 2 from a dead stop with our current technology.

"jump to Mach 2" meaning accelerate to a velocity of Mach 2. I was taught that Mach speed was a multiple of the speed of sound (768mph in air), Mach 1 being 2x, Mach 3 is 3x, etc. Acceleration can go from 0 to max instantly? That's a bit hard to chew.

Mach number per wiki M= v(s) / u
M is the Mach number
v_s is the speed of the source (the object relative to the medium) and
u is the speed of sound in the medium

 

[dangineer]

"I was taught (wrongly obviously now ) that Mach speed was a multiple of the speed of sound (768mph in air), Mach 1 being 2x, Mach 3 is 3x, etc."

Well, given a fixed speed of sound, Mach number can be used like a velocity. Unfortunately, the speed of sound isn't constant. The number above is the average speed of sound at sea level. The speed of sound is different on different days due to temperature variations, and changes significantly (>15%) with altitude.

"Acceleration can go from 0 to max instantly? That's a bit hard to chew."

If a force is applied instantly, which isn't impossible, then the acceleration will change instantly. When brakes are applied on a car, the change in acceleration is instantaneous, for example.

*edit*
The term sqrt(gamma*R*T) represents the speed of sound, by the way.

 

[ramparts]

Sorry to be nitpicky, but Mach numbers aren't actually velocities, although they are used to convey a sense of velocity. The Mach number is actually a dimensionless parameter used to define certain flow conditions in a medium, sort of like Reynold's number, Prandtl number, or various other numbers named after famous fluid dynamicists.

The Mach number relates velocity to a fluid's temperature and compressibility properties (specific heats). I just want to make sure this more accurate definition is out there, since this is a common misconception, not that it has any bearing on the argument at hand.

If anyone is curious, Mach number is equal to V/sqrt(gamma*R*T)

V=velocity
gamma=ratio of specific heat of a gas at a constant pressure to heat at a constant volume
R=specific gas constant
T=absolute temperature

I bow to your knowledge, dangineer! *looks for a bowing emoticon* I'm no engineer. Like skibo, I always assumed Mach 1 was just sound speed, Mach 2 twice that or something, and so on.

 

[ramparts]

Skibo - if I go to max acceleration instantaneously, it still will take some length of time to reach, e.g. Mach 2. But it looks like you've got that.

To be nitpicky, I was also under the impression that strictly speaking, instantaneous force is impossible. Force that looks instantaneous, sure, but if you measure x(t) for something you apply a force on, and graph out the second time derivative, I'd imagine if you looked at a short enough time interval you'd see the acceleration climb up. But I could be wrong - and for all practical purposes, we can certainly talk about "instantaneous" acceleration (just try pushing something!).

<3 thread drift

 

[Mars_Unit]

White dwarf matter?

LOL Yes! He said only it was dense enough to generate a Non-intrinsic artificial Gravity Field and even AntiGravity!

Originally, I wanted to use a hollow Torus filled with Liquid Superfluid Helium magnetically pumped around.

He said there wasnt enough energy. I even tried thinking that an Accelerator Synchrotron could generate Gravity.

Since then they have generated Singularities that can suck in matter in a trillionth of a second.

Nowadays, I am convinced it can be achieved by a specially designed magnet that I call a Gravity Magnet.

I am still trying to figure out E. Plodkletnov's device.

I hope I'm not boring you Guys!

http://en.wikipedia.org/wiki/Eugene_Podkletnov

http://en.wikipedia.org/wiki/Electrogravitics

http://en.wikipedia.org/wiki/Gravitomagnetism

http://en.wikipedia.org/wiki/Robert_L._Forward

http://en.wikipedia.org/wiki/Gravity_shielding

http://en.wikipedia.org/wiki/United_Sta ... %931974%29

 

[Skibo1219]

Skibo - if I go to max acceleration instantaneously, it still will take some length of time to reach, e.g. Mach 2. But it looks like you've got that.

To be nitpicky, I was also under the impression that strictly speaking, instantaneous force is impossible. Force that looks instantaneous, sure, but if you measure x(t) for something you apply a force on, and graph out the second time derivative, I'd imagine if you looked at a short enough time interval you'd see the acceleration climb up. But I could be wrong - and for all practical purposes, we can certainly talk about "instantaneous" acceleration (just try pushing something!).

<3 thread drift

The larger (or longer) the object being propelled the less force is required to keep from damaging the object being propelled during instantaneous 0 to max acceleration, we talking practical application. So why is it that we need such huge rockets with such huge initial thrust? Clearly instant max acceleration is not applied here, the short interval is tho. {{Thought, the greater the mass the greater the magnetic signature (??) the greater vertical force is needed? }}
If you split this into 2 applications "on paper" and "real" then yes its possible to do instant max force but only on paper
If scientists had more practical real working knowledge maybe our planet more be more technology advanced then where it is. We might find that magnetism can be controlled and directed, henceforth we would be manipulating gravity to our desire.

Ok now im rambling...

 

[Skibo1219]

White dwarf matter?

LOL Yes! He said only it was dense enough to generate a Non-intrinsic artificial Gravity Field and even AntiGravity!

Originally, I wanted to use a hollow Torus filled with Liquid Superfluid Helium magnetically pumped around.

He said there wasnt enough energy. I even tried thinking that an Accelerator Synchrotron could generate Gravity.

Wouldn't flow in the Torus have to equal Earth's speed of rotation?

 

[ramparts]

White dwarf matter?

LOL Yes! He said only it was dense enough to generate a Non-intrinsic artificial Gravity Field and even AntiGravity!

Your friend sounds like a crank Or a SciFi writer (the latter being far better than the former). Sufficiently dense matter will not create "anti-gravity"... and good luck getting the stuff that's in white dwarfs to the Earth! Ooh, that would cause issues...