# Tag Info

5

Car collision "damage" usually goes with the energy in the zero momentum frame. In both cases that is (since in the zero momentum frame, the two cases are equivalent, assuming the masses of the cars are equal): $$E_1 = 2 \times \frac{1}{2} m v_{rel}^2 = m \left( 30 \frac{km}{h} \right)^2$$ Therefore a priori there is no difference between the two situations....

2

It loses organization, e.g. matter changes into pure energy or some such thing. It's not entirely clear what form there is (some suggest there is no form at all, but it's obvious that it doesn't follow Pauli's exclusion principle). This is nothing special, it happens all the time - when you burn carbon, for example, you get a bit of disorganised energy (heat)...

10

In thermodynamics, a closed system is a system which cannot exchange matter with the environment. An isolated system cannot exchange matter nor energy with the environment. So, an isolated system is also closed, but the reverse is not true.

7

To expand on @dmckee's answer, if we have a speacetime that has the matter concentrated in a central area, we can definte an overall conserved energy-momentum vector called the ADM energy. It can be further shown that the ADM energy does not change when the matter falls into the black hole.

20

Energy (in any form) falling into a black hole contributes to the mass of the hole, and mass is one of the many forms that energy can take, using the usual conversion factor: $E = mc^2$.

1

In the book "Plasmonics and Plasmonic Metamaterials: Analysis and Applications" edited by G. Shvets, Igor Tsukerman, we read in section 2.1: In other words - they clearly state that the enhanced reflectivity is a result of the presence of a inverted dye - that is, a dye with a population inversion, meaning that it can be subject to stimulated emission. ...

1

Coriolis force on a moving object originates when you look at its motion from a non-inertial reference frame. Earth is a non-inertial reference frame, but that fact alone is not sufficient to cause Coriolis force on air. Air must also be set into radial motion by some agency, that agency being our Sun, as pointed out by @James Rowland and @CuriousOne.

1

You understand that mechanical devices such as levers, gears, springs and pulleys all conserve energy. Do you think that some elaborate combination of such devices can violate conservation of energy? The same applies if magnets are included - we know that interactions between magnets conserve energy, so any combination of mechanical devices and magnets also ...

4

The Earth+windmill system has conserved angular momentum. When the windmill starts spinning the angular momentum of Earth must change in response. However this change is marginal. Furthermore the windmill system will stop spinning when the wind dies down and this will restore the original angular momentum of Earth (when I say Earth I mean everything inside ...

2

Your question makes sense overall, but for the sake of discussion I need to tidy up the first part your question just a bit: What other forms of energy can gravitational potential energy be converted in to? The short-and-sweet answer is that gravitational potential energy can be converted into any other form of energy. The possibilities are limited ...

0

Way back in time, scientists studied the following equation intensely because it was so new: $$F=m*a$$ By experiment, they discovered that if you apply a force to a mass and it's free to move, then it will accelerate according to that equation. Back then, it was considered a LAW. It was immutable. It was a "law of physics". It wasn't derivable. Never in ...

0

You have only counted the energy stored in one spring. There are two springs in the diagram. The springs have elastic potential energy initially as well as finally. Look at the formula you have used : you have calculated the increase in elastic energy stored in each spring: $\frac12 k (x_2^2-x_1^2)$. There was elastic energy stored in the springs before ...

1

If you think of it in terms of conservation of momentum and collisions, the simplest version works just the same as tossing a handball at a on-coming freight train. The interaction is elastic, and the ball returns with the same speed it had going in in the center of momentum frame, but the center of momentum frame is moving in the ground frame, so the ball ...

0

Clearly the first law, as stated in Ján Lalinský's answer implies the conservation of energy. Let us consider a system $S$ and a surrounding $\Omega$. Since energy is additive one can writhe the first law to the universe $T=S+\Omega$ as $$\Delta U_T=\Delta U_S+\Delta U_\Omega=Q_S-W_S+Q_\Omega-W_\Omega.$$ But The system can only exchange heat with the ...

0

(Subscripts $w,i,m$ correspond to water, insecticide, and mixture respectively.) First, $Q_m=Q_w+Q_i$ only if $\rho_w=\rho_i=\rho_m$. Otherwise you must equate mass flow rates, $\dot{M}_m=\dot{M}_w+\dot{M}_i$, to find $v_m$, assuming that mixture density is uniform over the cross-section at point 3. Second, the form of Bernoulli equation you have written ...

0

In principle you can't apply Bernoulli to what is in effect a (simple) network of pipes but in some cases approximations will do. Let's apply Bernoulli's equation to the left and middle sections of the pipe: $$P_1+\frac12 \rho v_1^2=P_2+\frac12 \rho v_2^2$$ As liquids are incompressible ($A$ is the cross-section of the pipe): $$A_1v_1=A_2v_2$$ So with ...

2

The answer is simply that not every space-time has a corresponding effective potential in the sense that we have a coordinate $x$ such that $\dot{x}=\sqrt{2(E-V_{eff})}$. But this is true even in Newtonian mechanics, consider a problem with a Lagrangian $$L = \frac{m}{2}(\dot{r}^2 + r^2 \dot{\varphi}^2) - V(\varphi)$$ Obviously, $p_r\equiv m \dot{r}$ is ...

1

The reason that energy is usually conserved in most contexts is that Noether's theorem guarantees that energy is conserved in systems with time translational invariance. But the metric of the universe as a whole is (approximately) the Friedmann–Lemaître–Robertson–Walker metric, which does not have time translational invariance (more precisely, there does ...

-1

The temperature in space is not as easy thing, because it is not clear, what is actually whose temperature we want to know. On the Earth, the temperature in the meteorology means the temperature of the air in shadow. But there is no air in the space. The cosmical microwave background has a temperature of around 2.7K, but it is -270C and not -246C. But in ...

3

These schemes have been proposed and studied. A spacecraft with a magnetic field could steer charged particles away from it. The magnetic field would have to be much stronger than the Earth's magnetic field. The reason is pretty easy to see. The Lorentz for $\vec F~=~q\vec v\times\vec B$ for the charged particle velocity perpendicular to the magnetic field ...

0

As the question already beyond exact science, I will take a stab at it. There are three components here - Kinetic Energy (KE), Energy of gravitational waves (GW), and lost mass in merger. KE and GW - As the GW are ripples in space (time), they have to be generated by motion and/or its disruption (i.e stoppage at moment of merger). Therefore, the energy ...

0

In Elastic collisions the interaction forces are conservative. We can represent the total Energy of the System as : E = U + K When the particles are far away from each other (separation > 2R) their potential energies remain constant which I choose to be U. This is true except when the particles are in contact which other. After collision the colliding ...

2

Let me try to explain this by making an analogy with a simpler system i.e. a hydrogen atom. If you measure the mass of a hydrogen atom you find it is less than the mass of an electron plus the mass of a proton. In fact it is 13.6eV less. This happens because if you let a separated electron and proton fall together under their mutual electrostatic attraction ...

3

You've forgotten an important player in the system: the gravitational field. Here's a pretty argument that gravitational fields are physically meaningful objects that carry energy: imagine two masses accelerating towards each other from rest, from a great distance away. The rest energy of the system is $E_\text{rest} = (m_1+m_2)c^2$; the kinetic energy is ...

0

Feynman is using definite small quantities (inches) in place of infinitessimals $\delta x$ etc. Probably he wanted to avoid non-essential mathematical formality, in line with his casual, hand-waving persona. The Principle of Virtual Work requires the structure to undergo infinitessimal displacements (hence "virtual"). He could instead have used units of ...

1

Suppose you move the body down at constant speed, as small as you like, then the net force on the weight will be zero, that is, the force upwards you make will be exactly the same as the weight, $mg$. This upwards force makes negative work, as the displacement is opposite to its direction, and this work is exactly equal to the loss of potential energy, $mgh$....

-1

If the process is quasistatic, no energy is lost as heat, which is obviously impossible in the real case.

4

When exploring deep questions in physics, like you are, it is important to remember that nature appears to obey the laws of physics. Empirical studies such as science cannot prove ontologically that nature does obey the laws of physics, or obey laws at all. For an extreme test case, consider the concept of idealism. In idealism, one claims that there is ...

4

We know or reasonably assume that momentum and energy are conserved because of two reasons mainly: Mathematical plausibility: If we assume that nature follows mathematical descriptions, then e.g. Noether's theorem makes it a necessity that momentum is conserved. Otherwise, something with the mathematical description would be wrong. And so far, in the vast ...

12

The answer by WetSavanna... is complete but I want to particularly address the part I hope it is clear that I'm not trying to suggest that I don't trust these laws to be true but rather that I'd like to know how we know they are true. Physics theories are mathematical models that fit current observations/data and are predictive of new ones. Prediction ...

32

We know through experimental observation. That is the beginning and end of the subject of physics, at least the part of it the tells it apart from, say mathematics. Conservation of momentum is simply an inductively reasoned hypothesis to summarize certain patterns in experimental data. You are alluding to the conservation of momentum's being "explained" ...

2

Any quantised system has a ground state and excited states, and in any quantised system relaxing into the ground state requires energy to be shed in some fashion. In an isolated system like a hydrogen atom the energy is normally emitted as photons. However add other hydrogen atoms and this opens new routes for energy to be lost. For example an excited ...

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