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35

Here is a free body diagram of the balls: … and one of the water volume: The four balance equations are $$ \begin{align} B_1 - T_1 - m_1 g & =0 \\ B_2 + T_2 - m_2 g & = 0 \\ F_1 + T_1 - B_1 - M g & = 0 \\ F_2 - B_2 - M g & = 0 \end{align} $$ where $\color{magenta}{B_1}$,$\color{magenta}{B_2}$ are the buoyancy forces, ...


20

The weight on the left bowl would be the weight of the water plus vase plus ping-pong ball (plus thread, ignored). The weight on the right bowl would be the weight of the water plus vase plus the buoyancy of the steel ball (plus the buoyancy of the submerged thread, ignored). That buoyancy is the weight of an equivalent volume of water. Since the ping-pong ...


18

A Thought Experiment We can arrive at an intuitive explanation without any special knowledge of physics. The strategy is to re-create the setup as closely as possible while keeping the two sides in balance. Imagine that you start with two identical beakers, filled with the same amount of water, no balls. Placed on the scale, they balance. On the left, ...


8

From the Wikipedia article for Reynolds number: In fluid mechanics, the Reynolds number (Re) is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions. In addition to measuring the ratio of inertial to ...


7

Instead of assuming the earth is made of metallic hydrogen, let's just compare Earth's density of $5.52 \times 10^3 kg/m^3$ to that of neutrons' $2.3 \times 10^{17} kg/m^3$ because degenerate matter consisting of neutrons is what you get when electrons are forced into nuclei. That's a density increase of about $4.17 \times 10^{13}$ (at least 3 orders of ...


6

When you look at crystalline substances, there is really not that much space between the atoms. What people mean when they say that an atom is mostly empty space, is that the INSIDE of the atom is very sparsely populated with stuff. This is because the stuff in question, the nucleus and the electrons, are tiny in comparison to the actual size of the atom. ...


5

Molecules vibrate with frequencies in the range 10$^{12}$ to 10$^{14}$Hz. Although I don't know of any strict definition, I would take the view that a molecule must hold together for a few vibrations otherwise what you have is a collision not a molecule. That means the lifetime must be greater than 10$^{-14}$ to 10$^{-12}$ seconds, depending on the molecule. ...


5

In real life, the current can't jump instantaneously because there is always some finite inductance in a circuit. However, this is just a typical idealized textbook problem where the inductance is assumed identically zero, so the current can jump instantaneously according to the assumptions of the problem. Note the current also jumps in their solution for ...


5

There is a phenomenon called decoherence in quantum mechanics which is largely responsible for this. Basically (the following is a simplification), all the strange behavior that occurs in QM tends to happen when the wavefunctions of different particles are in phase. Decoherence occurs when the phases are randomized, so there's no special correlation between ...


4

There are many physical intuitions often presented in various texts on fluid dynamics. I won't mention those here. I will, however, mention that mathematically the passage from a particle point of view to a continuum point of view is still a largely un-resolved problem. (With suitable interpretation, this problem was already posed by Hilbert as his 6th of 23 ...


4

You can't do it for real in quantum field theory, there are always adjustible parameters. The reason is that quantum field theory doesn't have a fundamental length, it is defined on the continuum, so it can always be rescaled. But if you have a quantum gravity theory that reduces to quantum field theory at energies less than some large energy, you can get ...


4

It's the same problem because the low scale matches in both definitions; and the high scale matches in both definitions, too. Both problems are the puzzle why the two scales are so much different. First, the low scale. In the Higgs fine-tuning, you define the low scale as the Higgs mass. But the Higgs mass can't be parameterically greater than the Z-boson ...


4

All we can do precisely is give a probability for some physical quantity to have its observed value. For example (subject to various assumptions!) the probability of the cosmological constant having it's observed value is around 1 in $10^{120}$. Since this is absurdly low we say it's fine tuned. But where you draw the line between fine tuned and not fined ...


4

Reynold's number is defined to be: $$ \text{Re} = \frac{ v D }{ \nu } $$ where $v$ is the characteristic velocity for the flow, $D$ is a characteristic size and $\nu$ is the kinematic viscosity. Now, why should we care? Why is Reynold's number important? Well, the first thing to realize is that the Reynolds number is a dimensionless number. This means ...


3

Actually, the Higgs scale is not the TeV scale. The Higgs scale is the scale of electroweak symmetry breaking, i.e. $\mathcal O(100 \mathrm{GeV})$. The Terascale comes into play along with the Higgs, as supersymetry - the most popular extensions of the Standard Model - would actually like a small Higgs mass, much smaller than its measured value ($< M_Z$ ...


3

I'm amazed that this is so confounding to some. This is too long to be a comment, so I'm making it an answer. The TL;DR version: The answers that say the scale will tilt down to the right are correct. The beaker full of water with the steel ball suspended from above is heavier than is the beaker that contains the ping pong ball anchored from below. ...


3

The classical electron radius is a length scale at which the classical self-energy of the electron completely accounts for the mass. It tells you where the classical theory of a pointlike electron breaks down. The compton wavelength tells you where quantum mechanics takes over. The ratio of the compton wavelength to the classical electron radius is the ...


3

In physics we distinguish between the physics of "atoms and molecules" and nuclei. Atoms and molecules are described by the same theory, thus I will ignore those molecules here completely and only consider the difference between nuclei and atoms. I suppose you recognize that an atom is a bound system, so is a nucleus a bound system. Maybe you have seen how ...


3

According to the same Wikipedia article you cite, ...the zero point is determined by placing the thermometer in brine: he used a mixture of ice, water, and ammonium chloride, a salt, at a 1:1:1 ratio. This is a frigorific mixture which stabilizes its temperature automatically: that stable temperature was defined as 0 °F (−17.78 °C). The second point, at ...


3

The reason the Planck mass is big is the same reason that the Planck length is small--- we are living on a scale which is enormous in Planck units. So everything around us is made from enormous atoms which have tiny, tiny masses, and you need a large number of atoms to make 1 Planck mass, just as you need a large number of Planck lengths to make 1 meter. The ...


3

The hierarchy problem is not only about big numbers, such as $M_{pl}/M_{EW}$, per se'. In fact in QCD there is no hierarchy problem associated to the ratio $M_{pl}/\Lambda_{QCD}$. The problem is actually about the quantum numbers of certain operators in a Wilsonian EFT. The point is that we understand the SM as an effective low-energy description of the ...


3

The theory of fluids introduces material parameters in the stress tensor, which help model the substance. "The viscosity coefficient is the proportionality constant relating a velocity gradient in a fluid to the force required to maintain that gradient. The thermal conductivity is the proportionality constant relating the temperature gradient across a fluid ...


3

This is a very good question. I think there is no quantum field theory which predicts all particle masses. Masses (measured in Planck unit) are real numbers. The real numbers are NOT predictable, just like the radius of the orbit of Earth moving around Sun (measured in Planck unit) is not predictable. So the real fundamental constants are NOT predictable, ...


2

Theories don't predict units unless you put units in. A theory which predicts the masses of the fundamental particles would actually only predict the mass ratios $a_\phi$. Presumably they would emerge as eigenvalues of some operator, or perhaps as the zeros of some complicated function.


2

This is an extremely comprehensive review of electronic properties in two-dimensional electron systems (2DESs): http://rmp.aps.org/abstract/RMP/v54/i2/p437_1 but, as you can imagine, it covers almost everything there is to cover in 2DESs. For areas (in transport) you're focusing on you will find only sections IV C and D useful; it involves computation of ...


2

Even a physical quantity which changes by discrete amounts can often be well approximated by a continuous function of time. The derivative is a property of a mathematical function. Any differentiable function must necessarily be continuous, and a continuous function will change by arbitrarily small values for an arbitrarily small change in inputs. The ...


2

Your "sizes" sequence as one goes to smaller and smaller particles stops at the elementary particle table of the Standard Model. The Standard Model of elementary particles, with the three generations of matter, gauge bosons in the fourth column and the Higgs boson in the fifth. Here is a plot that gives sizes of particles which are composed out of ...


2

For EM, macroscopic bodies are generally electrically neutral so there is no net electric force between them. For gravity, macroscopic bodies are gravitationally "charged"; I can't think of any that are gravitationally neutral.


2

Of the four forces in the quantum field theory framework: the strong is mediated by the gluon and the effective potential this creates is of the order of the size of nuclei, because it is very short range at the current size of the universe . Very short range. The Z and W bosons are mediators of the weak interaction, and are much heavier than protons or ...


2

The story is this, as much as I remember. Fahrenheit chose the zero point on his scale as the temperature of a bath of ice melting in a solution of common table salt (a routine 18th century way of getting a low temperature). He set $32^{\circ}$ as the temperature of ice melting in water. For a reproducible high point on the scale he chose the temperature of ...



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