Bob182

google on the Dirac equation

I've added you to my msn - it'll be easier to explain that way!

I am referring to the ions yes.

What occurs at the cathode when a positive ion approaches?

Yes they will conduct electricity, but the current would also be due to +ve charges and the questions ask which one will be due only to negative carriers.

The key would be to look at possible charge carriers in each of the substances.

Molten NaCl comprises of Na+ and Cl- ions.

Potassium Nitrate, KNO3, exists as K+ and NO3- ions in solution.

Acidified water contains excess H+ ions.

Aluminium has a large number of mobile electrons available to carry charge.

for c) if the mass of the strut is negligble, then the force exerted on the strut by hinge should be 0?

If you resolve your forces you will find the answer. The key to these kind of questions is that if the system is static, then the net force in any direction is zero - i.e. they cancel each other out.

I suggest looking at the vertical forces and horizontal forces in turn.

It's called invariant because it doesn't depend on the frame of reference, i.e. it's invariant under a Lorentz tranformation.

yes, it is obtained from the energy/momentum invariant equation and has the value:

m0 = sqrt(E^2/c^4 - p^2/c^2)

it is frame independant and has the same value as the rest mass.

I don't know what "invariant mass" is either, hopefully that swansont will explain...

it's just the rest mass, i.e. what you would measure if the object was not moving with respect to you.

 

What I will say is this... If i knew for sure two laser beams attracted one another' date=' i would just ask what the force constant was.

 

If it was G, this would be a closed issue.[/quote']

 

As far as I'm aware, such experiments are performed in plasmas and other non linear mediums, and are well known - e.g. google "self-focusing effect"

 

Lasers do not interact in this way in a vacuum.

 

Assume that the sun is an isotropic radiator.

 

Are you referring to it radiating isotropically over all solid angle' date=' or isotropically throughout the electromagnetic spectra?

The sun's spectra is approximately that of a black body at 5780 K (e.g. see here)

As for the intensity, that of isotropic radiation will drop off as 1/r^2.

PS: Gravity is an electromagnetic wave' date=' better to say, superposition of them. And then you have to link this to the path traced out in the right frame.[/quote']

 

so an object that emits more electromagnetic radiation has a higher gravitational attraction?

 

Let it be stipulated that something emitted by our sun' date=' is what by and large, causes the earth to take its elliptical path around the sun.

 

QUOTE']

 

and that something emitted by the earth causes the moon to take its orbit around the earth

I'm pretty sure that photons mediate the gravitational force now.

So if I were to enclose myself in a sufficient amount of lead, I would become weightless?

The speed of individual photons through a material is still c, however, electrons can absorb a photon and jump to a higher energy quantum state before re-emitting another photon. Thus light appears to travel through a material at a speed less than c, resulting in the optical effect you mentioned.

Such interactions between electrons and photons are described very nicely by QED.

If the "universal velocity" mattered and this shifted the energy' date=' several things would happen. There would be an overal shift in the spectrum because you've changed the energy, and measurements would disagree with the theory. There would also be a splitting of the spectrum depending on the spin orientation of the electrons in the magnetic field you've created. These splittings and the shift would be time dependent, as the earth changed velocity over the course of the year. We don't observe this. This is not surprising, because Maxwell's equations work, and require c to be constant, in all inertial frames.[/quote']

 

Space Time, you haven't addressed Swansonts point.

For G=C=1 google on Natural Units - e.g.

http://quantumrelativity.calsci.com/Relativity/Appendix2.html

It's really just a way of simplifying calculations cause people that work in fields with lots of G's, C's and h bars can't be bothered to write them over and over.

The formula you stated is a consequence of special relativity and gives the total energy for a moving body in a particular frame. The mathematics of special rel uses 4 vectors where the time component features on equal footing as the spacial ones (except it is multiplyed by the speed of light for dimensional consistency). A useful result of using 4 vectors is when you multiply one by itself (using the 4 vector scalar dot product) you get a quantity that is invariant - that is, it has the same value in any frame.

The mass/energy formula that everyone harps on about can be derived from the invariant you get from dotting the momentum 4 vector with itself. There are many more invariants such as dotting the velocity 4 vector with itself etc.

If you haven't covered vectors yet then try this (scroll down about 1/2 way). Or try here for a small rel course covering 4 vectors.

Why so? Can you not just look it up?

Try searching on the net for it, or any maths text book.

If the frictional force causes the smaller ball to roll without slipping, there will also be an equal and opposite force on the larger ball, causing it to rotate also.

indeed

thanks johnny! always make things look so pretty

I think the one your after, for transforming any 4 vector into another frame, is:

g -gb 0 0

-gb g 0 0

0 0 1 0

0 0 0 1

I had to use g = gamma factor and b = beta factor (beta = v/c) because I can't do all the fancy formulas and stuff that other people seem to be able to use.

In your moon/rocket example an observer inside the ship would feel the acceleration due to the engines. It is not an inertial frame, although I realise you are talking about the instantaneous rest frame of the rocket.

The moon would be seen to accelerate away from the bloke in the rocket, but if you were to close the curtains on the ship he would still be aware of an acceleration. The same cannot be said of someone on the moon.

The rest frame of an entire system is also referred to as the "zero momentum" frame just like J.C. said, where the individual momenta involved sum to zero. It is useful when dealing with collisions such as in particle accelerators.

An inertial frame is one that is not accelerating. If you travel in your space ship at constant velocity and then closed the curtains you would have no way of telling how fast you were moving, or indeed if you were moving at all.

If you performed an experiment - say hitting a monkey with a cricket bat - you would observe the same physical laws applying as someone travelling in another space ship travelling twice as fast as your one.

You would be aware if the ship underwent an acceleration. Say it undergoes a uniform acceleration, you would experience a force towards the back end of the ship. The ship is no longer an inertial frame, but by taking the force into account (the same way we take gravity into account in earth bound labs) you can continue to hit your monkey with a bat and deduce that it obeys the same physical laws as someone in a non accelerating frame.