Yes – which means that this re-arrangement is not much use for calculation purposes, but I thought it bore an interesting resemblance to x=\frac{1}{2}a_{co-ord}\ t^2. I'm thinking of t^2 - \left(\frac{x}{c} \right)^2 as the space-time interval between (0. 0) and (ct, x).
I do agree.
Just a foonote… I find that the equation for x under constant proper acceleration, a, can be cast into the form x=\frac{1}{2} a \left(t^2 - \left(\frac{x}{c}\right) ^2 \right).
Quite pretty, I thought.
Yes, I've just derived "pervect's equation" for x from constancy of proper acceleration.
Yes indeed – if constant co-ordinate acceleration could be maintained – but it can't.
But I'm being a bit of a devil's advocate; although I still believe that x=\frac{1}{2}at^2 isn't actually wrong for...
PeterDonis. Thank you. I thought that x=\frac{1}{2}a t^2 was an inescapable mathematical consequence, for constant a, of a= \frac{d}{dt} \left(\frac{dx}{dt} \right), but I shall suppress incredulity and start with pervect's equation as you suggest. Thanks again.
pervect: Thank you. My first thoughts are that the a in the equations you quote must be the proper acceleration, \frac {d}{dt} \left( \frac{dx}{d \tau} \right) . My a is \frac {d}{dt} \left( \frac{dx}{dt} \right) .
Thank you. And I approve of your caveat! Perhaps one might say that the innocent-looking kinematics equations I quoted have unexpected consequences in SR ?
Thank you. So a gap between the broken back-end of the rod and the back spaceship will open up and widen? I just want to make sure that this is a valid deduction. [Incidentally, I'm taking the spacecraft as of negligible linear dimensions compared with the distance between them.]
When Bell says that the thread in put under "intolerable stress" and breaks, what happens then? Suppose that instead of the thread there is a light rod, which breaks at the point of attachment to the back spacecraft , so it is left sticking out backwards from the front spacecraft ..
In the...
If, in an inertial frame of reference, a body experiences a force, then that force must be exerted on it by another thing. Your Fpres on the piston is a good example – the force on the piston is exerted by the gas molecules. But what external thing, are you supposing, exerts –Fpg ? I'm afraid...
Didn't you take on board the first sentence of my original post (number 4)? Looking on the diagram at the row of four arrows at the piston-gas interface, -Fpg is the same thing as Fpress; you're showing the same force twice! Similarly with the downward arrows; there's only one force: you're...
I don't want to seem patronising, but I'd like to congratulate you on the precision with which you are phrasing your questions.
A quasi-static change is one that is so slow that the system is always infinitesimally near a state of thermodynamic equilibrium. [I took this from M W Zemansky: Heat...
It depends how your teacher has approached the subject. If you've been taught about Carnot Cycles and suchlike, then I'd back my answer (reply 11). If you've been introduced to entropy without first studying Carnot cycles, then the equation at the beginning of the second paragraph of post 13 can...
That the integral of electric flux through a closed surface surrounding charges, including charges moving in our frame of reference, depends only on the sum of the charges is what this makes this Maxwell equation more universal than Coulomb's law (as the E field of a moving charge is not...