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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" ...


21

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: $E = mc^2$.


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 ...


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.


9

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.


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....


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 ...


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 ...


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 ...


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 ...


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)...


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 ...


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 ...


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 ...


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 ...


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 ...


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

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, $mgh$....



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