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The problem is what Konstantin Tsiolkovsky discovered 100 years ago: as speed increases, the mass required (in fuel) increases exponentially. This relation, specifically, is $$\Delta v=v_e\ln\left(\frac{m_i}{m_f}\right)$$ where $v_e$ is the exhaust velocity, $m_i$ the initial mass and $m_f$ the final mass. The above can be rearranged to get $$... 50 One word: inertia. When you're riding a bike on a level gradient you just need to give it a push to get going, then you can coast for quite a while before friction and air resistance slow you down. The human body doesn't have wheels that can store kinetic energy, so while running you have to give a good kick to get going, and then another kick to keep going ... 33 For the photons that make up light to exist they have to be travelling at the speed of light. This means that to store them you have to put them in a container where they can move around at the speed of light until you want to let them out. You could build the container out of mirrors, but no mirror we can build is 100% reflective, or indeed can be 100% ... 30 At the physics 101 level, you pretty much just have to accept this as an experimental fact. At the upper division or early grad school level, you'll be introduced to Noether's Theorem, and we can talk about the invariance of physical law under displacements in time. Really this just replaces one experimental fact (energy is conserved) with another (the ... 23 Your examples are a bit misleading. For example you say: We can store cold (ice),heat (i.e. hot water bag) But we can only store heat temporarily, just as we can only store light temporarily. Your ice pack will eventually heat up and your hot water bottle will eventually cool down, just as light stored between two mirrors will eventually escape. ... 20 TL;DR: This answer arrives at roughly the same conclusion as Kyle Kanos', i.e. in addition to payload considerations, the difficulty lies in stuffing a small rocket with a mass of fuel exceeding to the mass of the rocket itself. This answer, however, is more rigorous in how the \Delta v budget is treated. Developing a relationship between rocket and ... 19 We treated this a while back at University... First of all, I assume you mean global cancellation, since otherwise the energy that is missing at the cancelled point simply is what is added to points of constructive interference: Conservation of Energy is only global. The thing is, if multiple waves globally cancel out, there are actually only two ... 17 Contrary to what is stated in many textbooks, energy-momentum conservation alone cannot explain the behavior of Newton’s cradle. For N balls we have two equations and N final velocities to calculate. Hence, conservations laws can do the job only for N=2. This means that if we want to give an explanation of the cradle behavior based on conservation laws, we ... 17 The topic of "Energy Conservation" really depends on the particular "theory", paradigm, that you're considering — and it can vary quite a lot. A good hammer to use to hit this nail is Nöther's Theorem: see, e.g., how it's applied in Classical Mechanics. The same principle can be applied to all other theories in Physics, from Thermodynamics and Statistical ... 16 A longer popular text why energy conservation becomes trivial (or violated) in general relativity is e.g. here: http://motls.blogspot.com/2010/08/why-and-how-energy-is-not-conserved-in.html To summarize four of the points: In GR, spacetime is dynamical, so in general, it is not time-translational-invariant. Because it's not, one can't apply Noether's ... 16 Yes, kinetic energy is a relative quantity. As you might guess, this means that when you're using energy conservation, you have to stay within a single frame of reference; all that energy conservation tells you is that the amount of energy as measured in any one frame stays the same over time. You can't meaningfully compare the amount of energy measured in ... 14 Magnetic field in this case (a set of magnets in space, no relativity involved) is conservative, which means it has a potential -- each positional configuration of charges (or dipoles in this case) has its fixed energy which does not depend on history or momenta of charges. So, the work you put or get from displacing them is just exchanged with the potential ... 14 I think that the other two answers miss an interesting point of your question. Lets put a light bulb inside 100% reflecting sphere. All emitted photons will stay inside the sphere and intensity of light will continuously increase to infinity. Real mirrors are never 100% reflective but there are mirrors with 99.98 reflectivity (these are dichroic mirrors ... 14 In non-relativistic and non-gravitational physics (both conditions have to be satisfied simultaneously for the following proposition to hold), energy is only defined up to an arbitrary additive shift. In this restricted context, the choice of the additive shift is an unphysical, unobservable convention. Special relativity However, in special relativity, ... 14 To answer the question simply, E=mc^2. Energy is a manifestation of mass, and mass is a manifestation of energy. In a fusion or fission process, the total "energy" of the system remains constant, it just changes shape. By "energy" I mean the totality of the already present energy, and the bound energy of the mass that takes part in the reaction. 14 Many of us have ridden bicycles at some time in our lives. and in fact this mode of transportation has become markedly more popular recently as a result of the energy shortage. Each morning at my own university, Duke, people can be seen riding machines with masses of 10 to 20 kilograms and struggling to reach one of the ... 14 Repeat lifting books to height h several times per minute for an hour or two, and observe who gets tired. You do work lifting the book, burning up biological energy stored in ATP molecules in your cells, to activate muscles, which apply some force upward on the book (as well as suffer some internal friction). The biological energy used up is converted ... 13 By "light in the room" I assume you mean Energy given off by the light bulb per second, this is commonly know as "Power" (measured in units of watts). You can also define how much power is hitting a certain area, for example the newspaper you may be reading. This new quantity is called Intensity (watts per area). By putting mirrors in the room you never ... 13 Dear QEntanglement, the photons - e.g. cosmic microwave background photons - are increasing their wavelength proportionally to the linear expansion of the Universe, a(t), and their energy correspondingly drops as 1/a(t). Where does the energy go? It just disappears. Energy is not conserved in cosmology. Much more generally, the total energy ... 13 If you write down the formulas for kinetic energy,$$E_k = \frac{1}{2} m v^2$$and momentum$$p = mv$$you see that you can write the energy in terms of momentum via$$E_k = \frac{p^2}{2m} So, if two objects have the same energy $E_k$, they only have the same momentum if they also have the same mass. Since the bull has a much larger mass than the bullet, ...

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There are a few different ways of answering this one. For brevity, I'm going to be a bit hand-wavey. There is actually still some research going on with this. Certain spacetimes will always have a conserved energy. These are the spacetimes that have what is called a global timelike (or, if you're wanting to be super careful and pedantic, perhaps null) ...

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It conserves both energy and momentum in the collision at the same time. By design, when the balls collide the strings that hold them up are vertical (assuming balls are only swung from one side). This means there are no horizontal forces from the string on the balls so linear momentum in the direction of swing must be conserved in the collision. Energy is ...

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There is a basic misunderstanding of elementary classical physics in your question. We all know (or maybe know) that to move, we need to spend energy The first law of Newtonian mechanics says" The velocity of a body remains constant unless the body is acted upon by an external force. So there is no need to spend energy to keep on moving, unless ...

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The energy conservation becomes vacuous or invalid in the general theory of relativity and especially in cosmology. See http://motls.blogspot.com/2010/08/why-and-how-energy-is-not-conserved-in.html Why and what does it imply? First of all, Noether's theorem makes the energy conservation law equivalent to the time-translational symmetry. In general ...

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Electrical analogies of mechanical elements such as springs, masses, and dash pots provide the answer. The "deep" connection is simply that the differential equations have the same form. In electric circuit theory, the across variable is voltage while the through variable is current. The analogous quantities in mechanics are force and velocity. Note that ...

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In order to build any thermal engine as envisioned by you, you need both a cold and a hot reservoir, such that heat can flow from the hot part to the cold part and the entropy doesn’t decrease while you’re making energy. The efficiency of such a machine has an upper limit of $(T_{\textrm{hot}} - T_{\textrm{cold}})/T_{\textrm{cold}}$ (as given by the perfect ...

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The energy conservation law is compatible with every single observation we have made inside the Milky Way in science, or outside science, so the empirical evidence in favor of it is overwhelming, diverse, and universal. Theoretically, the case is also clear. Emmy Noether demonstrated that conservation laws are linked to symmetries. The validity of the ...

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The depictions you're seeing are correct, the electric and magnetic fields both reach their amplitudes and zeroes in the same locations. Rafael's answer and certain comments on it are completely correct; energy conservation does not require that the energy density be the same at every point on the electromagnetic wave. The points where there is no field do ...

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It is possible to "block" light based on its polarization in a number of ways. In the situation you are describing, where the light hits a polarizing filter, it is simply absorbed by the filter. The filter does indeed heat up, and in fact if you put your hand near the screen you can usually feel that it is quite warm. It is also possible to have a polarized ...

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Note: This question was cross posted by the OP on the Mathematics Stack Exchange. Here is a copy of my answer for it there. This is it.  The perfectly centered billiards break.  Behold. Setup This break was computed in Mathematica using a numerical differential equations model. Here are a few details of the model: All balls are assumed ...

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