# Tag Info

2

This is really a footnote to Carl's answer: As Carl explains, in Mathematics we approach the zero volume/infinite density as a limit and this is a perfectly well defined process. However in Physics we generally don't believe that infinite quantities exist and the occurrence of an infinity is usually a sign that our theory needs modification. In the case of ...

0

You need to read up a bit about calculus. This is a case not only of using an idealized situation (cf. the ancient jokes about assuming a spherical cow with a uniform distribution of milk), but, as with delta functions, understanding how a function behaves in the limit, rather than its actual value at that limit. I still recall my first introduction: take ...

1

On your first question: absolutely, energy gravitates (or induces curvature in spacetime) the same way that mass gravitates. If you read general relativity, you will learn that it is in fact the Stress-Energy Tensor that is the source of gravitational interaction (or equivalently spacetime curvature). Energy can be localized very easily; a parallel-plate ...

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You should be able to do it by jumping off a table onto a spring scale. Simply film the jump with a high speed camera and look for the shockwave that moves through your body as you are landing and note when it reaches your neck. At the same time note the distance the spring has moved (call it point x). Then note how much further the spring moved afterwards ...

1

Apart from the fact that the concept of relativistic mass is best avoided, as John Rennie mentioned, it is also a concept of special relativity: it can only be defined in an inertial frame (a Minkowski spacetime) where special relativity is valid. However, the expansion of space is a consequence of general relativity. There is no global inertial frame ...

3

You say: A distant quasar would be less massive in its frame of reference than our observations would suggest and this refers to the notorious expression for the relativistic mass: $$m = \gamma m_0$$ The trouble is that relativistic mass is a troublesome concept that causes more problems than it solves. For example, the gravitational field of a ...

3

Your teacher is correct that the mass of an object if it is moving with very high energies appears to increase according to the formula , it is called the "relativistic mass" . Where E is the energy of the particle and c the velocity of light. But each elementary particle ( these are concepts that apply to elementary particles to start with) is ...

1

Well, the particles won't always follow circular paths (for instance, the particles in this video). But, if you apply a constant magnetic field across the chamber, charged particles moving in the field will be deflected according to the Lorentz Force Law. The centripetal acceleration for a particle moving in a circle is $a=\frac{v^2}{r}$, where $v$ is the ...

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It boils down to balancing the centripetal force, $$\vec{F}=\frac{mv^2}{r}\hat{r}$$ with the magnetic force $$\vec{F}=q\vec{v}\times\vec{B}$$ Equating these and considering the perpendicular velocity, we get $$\frac{mv_\perp^2}{r}=qv_\perp B$$ Which can easily be solved for $q/m$: $$\frac{q}{m}=\frac{v_\perp}{rB}$$ Thus, if you know the strength of the ...

1

If the two objects are equal in mass (or close to it), both orbit their barycenter, which would be a point outside either body. If one object suddenly loses half its mass, the COM of the binary system moves with respect to the current locations of both objects, resulting in changes to acceleration for both ($a=\frac{GM}{ r^2}$, where r is distance to ). i.e, ...

1

The apparent weight is indeed larger when the hourglass is running than at rest. See here for a detailed write-up. This effect has even been verified experimentally. In a nutshell: the net effect of the flow is to move sand from the top surface (where it has a downwards velocity $v$) to the bottom pile, at rest. Thus, the sand is decelerating and the force ...

1

There are quite a few things to consider here. First, The "hourglass" if this vessel is filled with air the results will be much more complex to determine. Second, the diameter of the grains and their uniformity will influence the measurements. Third, The size of the opening will also impact grainflow. Fourth, The sensitivity of the scale in relation to ...

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Analyzing the acceleration of the center of mass of the system might be the easiest way to go since we could avoid worrying about internal interactions. Let's use Newton's second law: $\sum F=N-Mg=Ma_\text{cm}$, where $M$ is the total mass of the hourglass enclosure and sand, $N$ is what you read on the scale (normal force), and $a_\text{cm}$ is the center ...

4

Imagine an hourglass with just one stone inside. When the stone start to falling a scale would stop to measure it's weight, but it will measure a spike corresponding to the moment when it hits the bottom. The bigger the airtime, the bigger the spike. It is like concentrating the weight of the stone in a very specific time interval: when it hits. However the ...

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Suppose you are standing on a tower which is on a scale. Jump off. While you're in the air, what does the scale read? (Assume here that you will land on the scale, so the analogy to sand grains holds.)

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Answer: slightly less mass. In general relativity, mass/energy of any system is conserved from the point of view of a distant observer (I forget the name of this theorem). We use this mass when we talk about how heavy a black hole is because we are (very) far away. If you start with particles that are stationary, the total mass of the system is slightly ...

1

What I think you're trying to get at is the vaccum energy. Weight is always associated with a force, so on earth we feel the force of gravity on our body and we call that our weight. Now Einstein showed us that there is an equivalence between mass and energy. What we know from Quantum Field Theory is that there is some underlying amount of energy just ...

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OK, I watched the video. It consists of two parts. The first part talks about General relativity and the introduction of a cosmological constant, which from the argument should not exist in completely empty space. He then goes to the Quantum Field Theory vacuum which has the continuous creation and annihilation of all possible fields of virtual particles ...

3

I agree with the answer of Quantum physicist , that zero mass for neutrinos was an input to the standard model , not a prediction, because measurements showed a mass compatible with zero. But I will add that the discovery that neutrinos must have mass does not destroy the Standard Model, just different Lagrangian for the neutrinos has to be included. ...

3

Standard model doesn't predict that neutrinos are massless. It's a "Model", where initially neutrinos are considered massless, because no mass was observed. The way we know, now, that neutrinos have masses, is through the mixing between the different neutrino types, through a matrix called the PMNS matrix (similar to the CKM matrix for quarks). This mixing ...

1

First of all, it is the NATURAL behavior of ALL particles (with our without mass), to move along time-like geodesics (if they're massive) or null geodesics (if they are mass-less). So they could accelerate relative to each other (without any external or external forces). Moving along geodesics could pull the particles together or even scatter them to the ...

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Until recently, quark masses were thought to be one-third of a protons' (612 "electrons"). Now, experimentalists state "bare quark mass" to be about one percent of this at any given moment (based upon their observations). But a difference exists between how positive and negative charges carry mass because the more massive quarks (e.g. "top") are positive ...

0

The mass would scale in the other direction: as you increase the diameter of the plate, you would have to decrease the mass. This is due to the loss of stiffness as your plate gets larger. To give exact detail may require a little more information about the physical setup, but here are some basics. Frequency is related to $\sqrt{k/m}$. Given the perceived ...

0

The equation E = mc^2 is the conversion, not declaration, it told you that if you convert mass to energy, you will get energy, and if you convert energy to mass, you get mass Photon is pure energy (it is particle) it can be converted to mass and it will be gone while itself have no mass

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To be simplified. Mass can be converted from energy. Photon is just the thing that is a pure energy without any mass at all. You can convert photon to mass. But while it is a photon, run in speed of light, it has no mass The equation E = mc^2 is the conversion, not declaration, it told you that if you convert mass to energy, you will get energy, and if you ...

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With the first question you are correct. Any "thing" with nonzero mass cannot achieve light speed. From this equation you can see why $$m=\frac{m_{0}}{\sqrt{1-\frac{v^2}{c^2}}}$$ where $m_{0}$ is the rest mass of the body (i.e. the mass it has when its speed is zero). As you can see from the equation, when $v=c$, the right hand side will blow up to ...

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We know that we can describe a spin $1/2$ massless particle using only a single Weyl field (lets say left-handed $\psi_{L}$). To introduce a mass term we have to use two spinor fields (one left-handed and one right-handed) and this gives the Dirac mass term. The question is now that if we can describe a massive particle with a single Weyl field. Well yes, ...

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I just want to point out that it seems some people may be conflating 'dark matter' with 'dark energy.' Regular "normal" matter like electrons, neutrons, and the like, are estimated to make up about 5% of the matter/energy density of our universe. Dark matter, estimated to make up about 25% of the matter/energy density of the universe, is matter that has ...

3

The answer has to do with the form of static friction. There are two types of friction, static and kinetic. Static friction is the type of friction that occurs when the bit of object that's touching the ground doesn't move (relative to the ground). Kinetic is the type that occurs when there is relative motion. Let's focus on static friction. Consider a ...

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So, your question is how one can move something sideways without complete elimination of friction by lifting it into air. On a molecular level objects do not really "touch" each other but keep a minimal distance due to the repulsive interaction of electromagnetic forces. So when somebody stands on the ground she is actually "hovering" a little above the ...

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how can he even judge the relationship between two forces without knowing the quantitative defination of force ?? One can't. The concept "Force" is an abstraction from observation and must be well defined before quantitative relationships (once, twice, thrice, etc.) can be established. But this was Newton's accomplishment, correctly recognizing and ...

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If I take a heavy lead object of arbitrary shape and mount it in a cardboard sphere such that the center of mass of the object coincides with the center of the sphere, you would never determine the lead object's shape nor mass density to be anything other than that of a point source using Newtonian mechanics or external field measurements. Referencing your ...

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