# Tag Info

42

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 ...

27

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% ...

19

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. ...

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.

13

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 ...

12

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 ...

10

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 ...

9

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 ...

9

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 ...

9

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 ...

8

No. The universe is dominated by dark energy, which is consistent with a cosmological constant $\Lambda$. In other words, as the universe expands, the energy density stays roughly the same. So the (energy density)*volume is growing exponentially at late times. Although the total energy is not well defined (as the volume of the universe may be infinite), the ...

7

The tangy taste of sodas comes from an acid in them. In most sodas, it's carbonic acid: ${\rm H}_2{\rm CO}_3$. Under pressure, like in a sealed can of soda at room temperature and usual pressure, the equilibrium reached keeps this molecule together. Once you open the can of soda, the lowered pressure inside the can "allows" this molecule to break apart ...

6

Yes. The Seebeck effect, for example, is the direct conversion of thermal gradient to electric voltage. It is used in the small scale in thermocouples to measure temperatures electronically, or in the larger scales in thermoelectric generators for power generation. In fact, many of the long-range space probes launched by NASA get power this way. ...

6

The answer crucially depends on what is meant by nothing. From the philosopher's nothing, nothing comes. But the physicist's nothing is something, i.e., there is at least physical law and whatever obeys it. For example, matter and anti-matter can materialize from the "vacuum" and, in some sense, this is something (matter) from nothing (no matter). But ...

6

Conservation of energy follows from invariance under translation in time, not inversion. This symmetry states that no matter when you do your experiment, it will give the same results. All isolated systems obey this symmetry (and therefore conserve energy) and no violation of it has ever been detected. (Needless to say, it would be a huge event if it were.) ...

6

If I'm reading rightly, I think your main question is: Why does only a small percentage of rest mass turn into energy [even for fusion]? It's because the universe is very strict about a certain small set of conservation rules, and certain combinations of these rules make ordinary matter extremely stable. Exactly why these rules are so strictly observed ...

6

Bicycles make better use of inertia/momentum. As Nathaniel said, one push and you can coast for quite a while. That's just not possible while running. Running wastes energy moving up and down. In addition to moving forward, running requires a substantial upward push to get your body airborne, giving you time to bring your other foot forward. You then ...

5

The total energy in the space does increase, precisely because of the reason you mention. Energy is not expected to be conserved, because the metric is not invariant under time translations. What does hold is the first law of thermodynamics, $dU = -P dV + \cdots$. Since the pressure in this system is negative, this is one way of seeing the origin of the ...

5

If the neutron decayed to a two body state (any two body state) the energy spectrum of the products in the neutrons rest frame would be single valued (this is required by the conservation of energy and momentum). It is not. Instead the electron energy spectrum is a continuum that runs from that roughly the two-body limit down to as near zero as our ...

5

While writing out my progress on the problem, I managed to give myself the answer. So, I thought that I may as well share the solution as I have seen many people in my class get stuck here. If I have a kinetic energy equal to $K = (1/2)mv^2$ And I later have a velocity equal to half the original $v$ What happens to $K$? Shouldn't it be 1/4th the original? ...

5

This question is quite a common one for those first learning about capacitors. First, let's remember that an electric field caused by stationary charges is conservative--this can easily be explained since a single charge creates a conservative field, and superposition of two conservative fields creates another conservative field. So, the field generated by ...

5

I was so surprised by the types of graphs I saw for this that I felt compelled to add an answer. As mentioned in the Wikipedia article I linked to, there are two radii that are of interest in addition to the Schwarzschild radius $r_s$. Those radii are the "Innermost Stable Circular Orbit" (ISCO) $r_{outer} \approx2a^{2}/r_{s}$ and the "Innermost ...

5

The MET (Metabolic Equivalent Task) readout on your gym equipment is your body doing 1Kcal/kg/h = 4184 J/kg/h and can be reasonably accurately measured by how much oxygen a test victim uses. Sitting still is roughly 1 met and cycling at 100 Watts is around 5.5 Mets. So taking a man of 75kg, cycling at 100Watts (100J/s) he is having to do 5.5 * 4184 * 75 / ...

5

Yes - light waves can destructively interfere. This is the principle behind interferometers. There is no violation of energy conservation because the energy of two waves doesn't add. The energy is proportional to the square of the amplitude, and the amplitudes add. So $E\sim\left(A_1+A_2\right)^2\sim A^2_1+A^2_2+2A_1\cdot A_2$. The third term is an ...

4

The wavefunction of two particles is not the sum of the wavefunction for the individual particles. The total wavefunction is the product of the two wavefunctions for finding particle 1 at $x_1$ at time t and finding particle 2 at $x_2$ at time t: $$\psi(x_1,x_2,t) = e^{i(kx_1 + k x_2 - 2\omega t)}$$ The energy is $2\omega$. The fallacy of adding ...

4

There is no need for any empirical evidence. This is pure mathematics. Step 1: Assume a force is conservative. This means that ${\vec \nabla} \times {\vec F} =0$ Step 2: Then, via Green's theorem, you know that the quantity $\int_{a}^{b}{\vec F}\cdot d{\vec s}$ does not depend on the path you take from a to b. (equivalently, this integral is zero if ...

4

What does this mean? It means that there won't be any (periodic) orbit anymore; the answer to your title question is therefore that it will cease to exist. The value of $r$ will just monotonically decrease. Obviously, when it falls below the event horizon, there's no way for the particle to return outside the black hole i.e. to values of $r$ greater ...

4

The formula you quote does not contain the potential energy, it is valid for a free particle (i.e. a particle which is not affected by external potential). You can link it to classical mechanics by evaluating it for small values of $p$ (more precisely: $p \ll c$): $$E = \sqrt{\left(mc^2\right)^2 + p^2 c^2} = c \sqrt{m^2c^2 + p^2} = \cdots$$  \cdots = ...

4

That's actually a tricky question. The short answer to the title question is yes, it does. But the answer to the follow up question about conservation is, it is still conserved. In a much simpler universe, what hwlau said would be true - as the gravitational potential energy increases, the kinetic energy decreases. But we do know through the Hubble ...

4

In the ideal case where the collision is instantaneous and there is only a single point of contact, the forces experienced by each object can only be along the line that connects the centers and passes through the contact point. Actually, the "force" will be infinite, but it will impart a finite impulse (i.e. change in momentum) during the infinitesimal ...

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