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Thermal energy is exactly the average (with respect to the time interval of your measure) of the overall translational kinetic energy of all the particles of your system. This, in turn, can be related to the temperature of your system in case the Hamiltonian is separable into the coordinates of each one of your particles (the equipartition theorem). In ...


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I do not understand what the accuracy of $1$ part in $10^{14}$ means. [...] reviewed the definitions of accuracy and error [...] In definitions of "accuracy" or "error" you should have noticed mentioning of the true value of some particular quantity, referring to the trial(s) under consideration, and the corresponding, commensurate value(s), ...


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Hold your left arm out to the horizon. Hold your right arm vertically upwards. That's 90 degrees. Now bring your left arm up to halfway between the horizon and your right arm. Your arms are now 45 degrees apart. Now bring your right arm halfway towards your left arm. Your arms are now 22.5 degrees apart. Compare the angle between where your fingers are ...


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There is nothing you can do! Since $B=0$ when $x=x_0$, the relative uncertainty (as you've calculated) diverges when $x\to x_0$ and is therefore undefined at that point. This is always the case for measuring a quantity that is zero. As a consequence, if you make measurements of the magnetic field near $x=x_0$, the relative error is going to be very large.


4

Laser pointer, wire, screen at known distance. You will see the following diffraction pattern: (not trying to make the best image... exposure could have been better, and I could have put a beam stop in in order to avoid the overexposure of the central beam.) The point is that I can see a series of "blobs" that correspond to diffraction peaks from light ...


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copper wires can be measured by using screw gauge. read your text for how to use screw gauge. and use moving microscope to measure the same by optically


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Using optics, you say? Well, you make a Michelson interferometer, with the movable mirror referenced to a mechanical stop. You move the mirror away from the stop, insert the wire and close the gap until the wire is held lightly between the base of the mirror and the stop. Now pull out the wire and slowly close the gap until the mirror makes contact with the ...


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You can also measure the electric resistance of a long piece of the wire and the calculate the cross section of the wire using the fact that the specific resistivity of copper (at 20 C) is $1.68\times 10^{-8}$ Ohm m.


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You can first measure the length of the wire, then put the wire into the water, and see the volume change of the water. Then use $\pi r^2 = V/L$ to get the diameter. edit If you need more accuracy, maybe you can either coil the wire on a pencil or some other object many times, then you can measure the the length of many diameters, like in this graph. ...


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A micrometer would be the preferred method. A caliper would not be appropriate because it would not give you enough precision.


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Technically Micrometers or more commonly called as Screw Gauge are used to calculate diameter or radius of thin wires in physics labs you can refer to this article: https://en.wikipedia.org/?title=Micrometer


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I don't know what accuracy you need, but you can wind (densely), say, 100 turns of wire on a cylinder and measure the length of the coil. EDIT: another approach (which can be more accurate, if you know what material you have): take a long piece of wire and weigh it. There are some ways to measure density as well.


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This is the main point which disallows information exchange. No one had yet discovered the way to set a state on one side and to get a correlated information on the other side. If it was possible, many protocols would allow communication. edit bis : If you cannot set the information to send, even if the two sides are correlated, it's not sending ...


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$\newcommand{\ket}[1]{\left| #1 \right>}$ Assuming that the lenses are some sort of a beam combiner and the vertical direction is $z$ (for convenience) and the I did the following: After the second SG device the upper beam is in the state $\ket {x+}$ and the lower beam is in the $\ket{x-}$. Combining these two with the beam splitter we have the final ...


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We should expect an output in both A and B. This is because (if I understand correctly what your "lenses" do) the first apparatus prepares a pure state spin-y-up, then the second SG produces output in both the positive and negative value for the spin along the x axis (because the two observables do not commute) and the lenses, bringing together the two ...


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The following is a bit oversimplified but I think it conveys the basic idea of what's going on. Let's say the state of the system and the measuring apparatus before the measurement is $$ (|a\rangle_e+|b\rangle_e)|0\rangle_M, $$ where the $e$ subscript refers to the state space of the electron, and $M$ is the apparatus state space. (Strictly it's not the ...


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If the scale is using decimal system, the marks on the vernier scale will be 9/10 the length of each spacing of the main scale. So, say you had a .01cm precision scale and were measuring something exactly 6.00cm, this means the vernier 0 line would match up with the 0 on the "rough" scale. If you now measured something 6.01cm, this is just enough for the ...



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