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7

Mass, or more correctly, rest mass is not conserved in special relativity. Particles are able to be created and annihilated in special relativity, for instance, an electron and a positron can interact to produce two photons: $$e^++e^-\rightarrow 2\gamma $$ Here mass is clearly not conserved, because both the electron and positron are massive but photons are ...


7

The $\nu_e$ is a mixture of three mass eigenstates $\nu_1,\nu_2,\nu_3$, at least two of which are massive. The mixing coefficients form the PMNS matrix. For neutrinos, mass and flavor are not simultaneous observables, so the $\nu_e$ does not have a well-defined mass of its own.


6

When the I nternational prototype kilogram (IPK) was created, copies were made and sent to the most important countries in the world and are kept in a protected environment. Periodically they are returned to France, checked and compared and, surprisingly enough, their masses do not match anymore. Factories that produce these items have access to them or ...


5

The E=mc^2 formula only applies to an object at rest, and light is never at rest. You want to use the more general formula: $E^2={m_0}^2c^4+p^2c^2$ Then you can set the mass to zero. $E=pc$ What this says is that light has momentum, which is related to its energy.


4

The rest mass of the system is conserved, it's just that the rest mass of the system isn't the sum of the masses of the parts. The rest mass of a system is just the length of the total energy-momentum vector. And that vector is conserved, so the length is conserved. The sum of the rest masses of the parts is not conserved. But that simply isn't the rest ...


4

We know that mass can neither be changed nor be destroyed, but I want to know if there is any circumstance under which the mass of a body can be changed? You are clearly not referring to relativistic phenomena or to pair annihilation and Einsteins' formula $E=mc^2$, as the other answers suggest, but to change of mass in massive bodies. In the first ...


3

Here is my comment in more details For any system or single elementary particle mass $M$ is defined as $$ M = \sqrt{E^2 - \textbf{P}^2} $$ where $E$ is total energy and $\textbf{P}$ is total momentum. For an elementary particle (like electron) mass is always conserved. For a system $M$ is conserved as long as $EdE - \textbf{P}d\textbf{P} = 0$, in ...


3

Yes. The so called rest mass $m_0$ is the magnitude of energy-momentum four vector and is always conserved. It is not just conserved but is also invariant since it is the magnitude of a four vector. Perhaps you are confused between rest mass and relativistic mass. The relativistic mass is the total Energy divided by $c^2$. $m\equiv \gamma m_0 $ This ...


3

You have linked a YouTube video that shows the rubber sheet analogy for the curvature of spacetime. The trouble is that while the rubber sheet analogy is not a bad way for beginners to get a rough idea what is going on, it can be very ,misleading if you push it too far. In this case I suspect it has lead you to imagine the sheet wrapping round the surface of ...


3

For the rest mass we have $$m^2=p^2=p^{\mu}p_{\mu}$$ where $p^{\mu}=(E,\vec{p})$. It is Lorentz invariant, which means the rest mass of the particle is always the same no matter in which frame the observer is in. While for relativistic mass, it's simply equivalent to the total relativistic energy, which is always conserved. Note the difference between ...


3

In classical physics mass has two definitions: It measures the amount of inertia that you have. In order to accelerate something you have to apply a force to it. The heavier your thing is, the less it will accelerate, $$ a = \frac{F}{m} \, .$$ If you know the force and can measure the acceleration, you have access to the mass. In the physics of gravity, ...


3

In the US, if you purchase a balance or set of reference weights (masses) or a scale for scientific purposes, you can also purchase with it a certificate of traceability. This is a document that states how your device was compared to a reference, and how that reference was traceably compared to an even better reference, and so on, up to the standard kilogram ...


2

If there is no resistance then there will be no net torque applied about the center of mass. So any initial rotational speed will remain. The rotation center is going to be the center of mass. The effect of gravity will be to accelerate the center of mass, and it will have no effect on the rotational motion of the body. See this accepted answer for a ...


2

The kinetic term of the Lagrangian is proportional to $$g_{ij}v^iv^j$$ where the $v$s are the generalised velocities. Writing them as the time derivative of the generalised coordinates, i.e. $v^i\dot q^i$, taking the square root, and multiplying by a small time lapse $\epsilon$ you get $$\sqrt{g_{ij}\dot q^i\dot q^j}\epsilon,$$ which is a first order ...


2

Yes. A decent approximation of impact was found by Isaac Newton. Simply put, it is $$D=L\frac{A}{B}$$ where $D$ is depth, $L$ is the length of the projectile, $A$ is the density of the projectile and $B$ is the density of the object being impacted. Velocity doesn't play into it. So double the density of the impacted object and the impact depth will be ...


2

There's no minimum size. There's a minimum density. Stars turn themselves into black holes when they exhaust their fuel and collapse. For that to yield a black hole, they need to start off with around 25 solar masses. If a star starts with enough mass, natural processes cause it to eventually suffer a core collapse which greatly compresses some of its mass. ...


2

In the two-dimensional rubber sheet visualization, it is wrong to think that things fall towards the massive object because they are "rolling down the hill" of the curved spacetime. There is no perpendicular gravity pulling things down into the well. What happens is that you are moving along your world line at a constant velocity, "into the future at one ...


2

Firstly we should note that the universe as a whole is not described by the Schwarzschild metric, so the Schwarzschild radius of the universe is a meaningless concept. However if you take the mass of the observable universe you could ask what the Schwarzschild radius of a black hole of this mass is. For a mass $M$ the Schwarzschild radius is: $$ r_s = ...


2

I don't think creating a vortex effect will increase the velocity of flow, because it would direct movement in a direction other than forward. Smooth bore gunbarrels, for example, have greater muzzle velocity than rifled gunbarrels (assuming all other variables are equal). You might want to maximize laminar flow and to minimize turbulence inside the tube. ...


2

What does conservation of mass mean in classical mechanics? Weight and mass are the same , we know the mass by weighing it, and if we add 1 kilo of sugar to another kilo of sugar, we will have two kilos of sugar. That is what is meant classically that the mass is conserved. Dissolving a kilo of sugar to a kilo of water will give you two kilos of sirop. The ...


2

The mass of a body can be changed in accordance with Einsteins famous E=mc^2. Kinetic Energy for example adds mass to an object. This effect is not noticeable at everyday speeds but velocities approaching the speed of light change the mass of an object significantly. The effect can be named as part of the reason why particle masses are often given in ...


2

Sort of. When you make an object go fast, that is the speed close to the speed of light, requires more and more energy to accelerate. This is attributed to something called relativistic mass, but it isn't mass in the traditional sense, and thinking about it in the same way as mass is detrimental.


2

Actually, mass can be produced and destroyed (particles are produced and destroyed in high-energy collisions). It is popular to say in Chemistry courses that mass cannot be produced or destroyed. This is because the low energies encountered in chemical reactions (per atom chemical energy scales are of order 1 eV) are insufficient to produce anything new and ...


1

Imagine a stone in your hand. Shake it. Its resistance to motion is inertial mass. He calls it answering mas because it is how much the stone answers to your force. Now drop your stone. It is pulled by gravity. The force of pull is due to gravitational mass, what he calls calling mass. He calls it calling mass because that is how much the gravity of a body ...


1

The force between the roller and the road is in the vertical direction so there is no effect of friction. Moreover the speed is constant so there is no acceleration. The only forces acting in the vertical direction are the weight, $W=mg$, and the reaction force between the roller and the road, $F$. As the roller is not accelerating vertically, these must ...


1

Sounds like constant amount of substance (as in the dimension or physical quantity, "mol" being it's unit). Could also mean mass, but mass is often not strictly constant. If you add energy (e.g. heat), the mass of the gas increases slightly via E=m*c2. Could you provide more context?


1

This is because gravity doesn't exert a "force" on objects, gravity works by bending spacetime. Light doesn't tend to accelerate so it will take a geodesic path through spacetime; this means that it takes a "straight" path through curved space, which is what gravity is. The reason we experience gravity is because when not accelerated we will take a geodesic ...


1

The key to flow of macroscopic particles is to make sure they don't "clump" or jam. I don't know what is propelling them down your pipe (gravity? Air flow?) but that will affect the answer. In general, adding some vibration keeps particles flowing freely; a larger pipe diameter with minimal obstructions / bends is the other thing. Making the pipe diameter ...


1

Lightning must have some mass, how else is thunder created. If thunder is the sonic boom created by lightning moving faster than the speed of sound, then lightning must have mass. I don't hear thunder every time I turn a flashlight on.


1

This is because instead of $$\dfrac{1}{2}mv^2$$ or $$E = mc^2$$ the energy of light is given by $$E = hf$$ Where h is a number called Planck's constant and f is frequency (sometimes v is used) Here is an example, as requested: Imagine red light with $620. nm$ wavelength. The frequency of this light is $0.483$ x $10^{15}Hz$ This makes the energy of a ...



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