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43

This is a great question. An influential early discussion of it was given in a 1959 talk by Richard Feynman, There's Plenty of Room at the Bottom. Basically the answer is no, machines are not linearly scalable. For example, lubrication doesn't work for very small machines. A general way of looking at this is that we have various physical quantities, and they ...


38

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, ...


22

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 ...


20

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, ...


9

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 ...


5

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 ...


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

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

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 ...


4

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

There is a popular physics book (similar to The Elegant Universe, but different) (EDIT: a comment suggested this is The Black Hole War, and that sounds right, although I can't reference the exact figure) that I remember addressing the significance of the Planck Mass relative to the idea of elementary particles versus black holes. For now, Wikipedia will ...


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

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, ...


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

Well I got this badly wrong, and grovellingly apologise to those I traduced. It seemed easy: the water in both is the same weight, so I thought that removing it would make no difference to the balance. This was wrong: removing the water from the right hand beaker does have an effect, the presence of the suspended ball does add extra weight to it, so the ...


3

I'm assuming you haven't taken any physics courses, so let's start by explaining the concept of a force. Forces are the central focus of classical mechanics. Basically, a force is a push or pull on an object as a result of its interaction with another object. When applied to an object with mass, a force causes the object's velocity to change in some way. ...


3

Exponentials come as solutions of this differential equation: dx/dt=c*x where c is a constant and x and t variables. The solution is of the form: x(t)=e^(c*t) A great number of measurements and observations we make can be approximated by this equation. Once the solution is exponential it is logical to take the log since the numbers become large fast ...


2

If you want the new physics to solve the hierarchy problem, it's best if it is close to the weak scale, or else you will be left with a residual little hierarchy. You are describing the "big desert" between the weak and GUT scales. I think it was motivated by the idea that SUSY lived at the weak scale, solving the hierarchy problem and insuring gauge ...



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