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61

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 $$ ...


60

Can photons push the source which is emitting them? Yes. If yes, will a more intense flashlight accelerate me more? Yes Does the wavelength of the light matter? No Is this practical for space propulsion? Probably not Doesn't it defy the law of momentum conservation? No In fact that last question is the key one, because photons ...


53

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 ...


37

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 ...


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% ...


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. ...


22

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 ...


21

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 ...


20

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 ...


18

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 ...


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

Can photons push the source which is emitting them? Yes, photons have momentum and momentum must be conserved. The source is pushed in the opposite direction of the photons. If yes, will a more intense flashlight accelerate me more? Yes, more photons means greater momentum. Does the wavelength of the light matter? Yes, shorter wavelength ...


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 ...


15

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, ...


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

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

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

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

You have successfully discovered that the kinetic energy depends on the reference frame. That is actually true. What is amazing, however, is that the fact that kinetic energy is conserved is NOT reference frame-dependent. So, when you balance your conservation of energy equation in the two frames, you'll find different numbers for the total energy, but ...


13

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 ...


13

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) ...


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

Philosophers and engineers have often thought that the notion of a real number is, indeed, unphysical, but this has nothing to do with the Banach-Tarski paradox. One can find seven pieces of a sphere which, when re-assembled, produce a sphere twice as large. That is not strictly speaking a paradox, but it certainly violates one's geometrical intuition and ...


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

Waves always travel. Even standing waves can always be interpreted as two traveling waves that are moving in opposite directions (more on that below). Keeping the idea that waves must travel in mind, here's what happens whenever you figure out a way to build a region in which the energy of such a moving wave cancels out fully: If you look closely, you will ...


13

As you probably know, Newton thought that energy is linearly proportional to motion. The second law's original formulation reads: "Mutationem motus proportionalem esse vi motrici impressae" = "change of motion is proportional to the force impressed" It was Gottfried Leibniz, as early as 1686, who first realized that KE (m = unitary mass) is proportional ...


12

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 ...


12

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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