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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 ...


0

We know that mass can neither be changed nor be destroyed It's energy that can be neither created nor destroyed. I want to know if there is any circumstance under which the mass of a body can be changed? Yes, heat it up and you increase the mass. Or lift it up, and you increase the mass. Then when you drop it, some of its mass-energy is converted into ...


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 ...


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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 ...


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 ...


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.


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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 ...


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.


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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 ...


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. ...


0

In General Relativity, Einstein established that gravity is due to the curvature produced by objects in space. That's not quite right I'm afraid. The YouTube video shows the rubber-sheet analogy, which isn't ideal, but it will do. Because the force of gravity depends on the slope, not the curvature. The steeper the slope the stronger the force of gravity. ...


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Your mistake is assuming that the curvature is due to size. The curvature is due to mass. So if an object were taken off of the earth, the earth's curvature would decrease and there would be some curvature away from the wart, due to the mass of the object.


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Using a rubber sheet to visualize gravity may be confusing in some cases, as the deformation of the sheet is affected by the size of an object, while gravity is not. The rubber sheet analogy is only a visual representation of gravitation outside a massive body. As gravity is proportional to mass, not size, the analogy becomes awkward if applied to a large ...


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 ...


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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.


1

To understand how light is affected by gravity, it helps to think of light as energy. So let's ask a basic question: when it come to light, what is energy? By the Planck-Einstein relation, we know $$E = h \nu$$ where $\nu$ is the frequency of the light and $h$ is Planck's constant. So when we talk about the energy of light, keep that in mind. Also note ...


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The answer is no. Dark energy does not exert a force between objects, but causes space to expand. Objects floating in space are carried along, but remain still in space. That means that if you place two objects in a universe with dark energy, sufficiently far apart that their mutual graviational attraction can be neglected, the speed with which they recede ...


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 ...


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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 ...


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As you said $y_{cm}=x_{cm}=0$ by symmetry, now $$z_{cm}=\frac{\int \rho z dV}{\int \rho dV}=\frac{\int_{0}^{2\pi} \int_{0}^{\pi/2} \int_{r_1}^{r_2} \rho z r^2 \sin\theta dr d\theta d\phi }{\int_{0}^{2\pi} \int_{0}^{\pi/2} \int_{r_1}^{r_2} \rho r^2 \sin\theta dr d\theta d\phi}. $$ Next recall in the spherical ccordinates $z=r\cos\theta$, integrate to get ...


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 ...


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 ...


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 ...


1

Dark energy is a concept devised to help explain the expansion of the universe. It is presumed to comprise about 68% of the universe (on a mass-equivalence basis), but it is spread so uniformly throughout the universe that its density is on the order of only 10 to the minus 27 kilogram per cubic meter. Dark energy is not presumed to clump in matter, but ...


0

As a commenter noted, dark energy, whatever it turns out to be, is not thought of as a property of any known object. From the Wikipedia article "Dark energy": In physical cosmology and astronomy, dark energy is an unknown form of energy which is thought by some physicists to permeate all of space, tending to accelerate the expansion of the universe. ...


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 ...


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 ...


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 ...


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

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 ...


1

Does Sphere C have any effect of on the gravitational force between A and B? Nope. C does not make any difference to the force between A and B, but its introduction has the effect that the net force on A has contributions from both B and C. (Likewise for the other spheres too.) This is because gravitation obeys the principle of superposition. Is ...


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The sphere will stay in-between because net force is zero. However, the spheres will all lump together on sphere C because while C will not move, A and B will.


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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.


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 ...


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 = ...


0

The simplified answer for this is that gravity basically means that you are in elevator which is accelerating: even if you are standing on the ground. So if you take that constant gravity field is pretty much the same as a constant acceleration, then if a beam of light bends downward in an accelerating elevator, it must bend downward if it is in an constant ...


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 ...


0

Yes, photons are affected by those curves. They also curve space-time due to something called a stress-energy tensor. Remember that the energy of a photon is given by $$E = hf$$, so photons do have energy. This energy lets them be affected by gravity.


1

It's more sensible to talk about spacetime curvature than spatial curvature as the latter depends on how you foliate spacetime. For example de Sitter spacetime is not flat, but it can be foliated in ways that gives you flat spatial slices and in ways that give you curved spatial slices. One way of seeing that gravity can never be described as purely spatial ...


1

Yes. Space and time are both technically a single entity. The curvature of space-time is actually pretty famous.


0

What exactly is mass? My answer will encompass four very different regimes each separated by a factor of 1027. I'll first look at things on the order of 10-27 kg, then 100 kg (1 kg), then 1027 kg, and finally 1054 kg. Mass at the scale of 10-27 kg This is the domain of atoms and elementary particles. A proton has a mass of 1.672621777×10-27 kg, to ...


1

What is physics? Physics is the modeling with mathematics of observations in the world around us. It is a way of creating a logical sequence that can be predictive and not only explanatory. It reduces the innumerable constants one would need to describe, for example , the trajectory of a ball with just space coordinates, to a simple parabolic function that ...


0

Since your tags are "newtonian-gravity" and "mass" I will attempt to answer this question in a classical framework. In classical mechanics, mass is essentially defined as a measure of an object's inertia. Let me explain further. We have Newton's second law $$F_\text{net}=ma$$ which is assumed to hold for all objects in classical mechanics. Suppose we ...


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, ...


1

The problem with this is that $$E = mc^2$$. Density, however, is given by $$density = \dfrac{mass}{volume}$$ Thus, if volume = 0, then density is infinite. Black holes have a finite mass. It is there density which is finite because all the mass is at a single point (singularity, volume = 0).


1

After some searching, I found a very simple way to do so. The blue disks shows show light traversing up a rod. If the rod were stationary then the light would reach the top in ct where t starts at t' = 0. However, with the horizontal motion of the rods, the light takes a diagonal path, indicated by the red line. By the Pythagorean Theorem, we get $$d^2 = ...


1

No, the energy of a black hole is not infinite. It depends on its mass, angular momentum and charge. Infinite density at a point does not translate to infinite energy in the $E=mc^2$ sense. It is in fact possible to extract energy from black holes by exploiting certain properties of accretion disks or ergospheres, but this is a finite process.


0

After further research and thought, I think I can now offer an answer to my own question. I first restate the key question, then state the conclusions and finally comment on them in the context of clarifications of the original “Background and Commentary” arising from the responses of Timaeus and JerrySchirmer, who I thank for their input. The answer I am ...


1

You have to distinguish between stellar mass and gravitating mass. The quoted Milky Way mass includes dark matter. Despite searching in the literature, I have yet to find reliable apparent magnitudes and good distance estimates for NGC 1097. The total Blue luminosity of this galaxy is near to Minus B-band absolute magnitude -21, but only ballpark ...


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 ...



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