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86

The anthropomorphic formulation "tries to" is misleading. Under the effect of ambient noise, matter explores the possible configurations around its current state: e.g., two single hydrogen atoms wiggle around and meet. If they happen to bind, this releases energy which goes away, and we say that the energetic state of this new $H_2$ molecule is lower than ...


70

Now, in my head, if you give the pendulum a little impulse, it will swing up in one direction and get attracted by the magnet just a tiny bit. You've neglected to account for the magnetic attraction as the pendulum bob goes back to its central position. On the outwards leg, you are correct that the magnet's attraction will pull on the bob and give it more ...


37

The waves will not travel forever. Water particles moving against and around each other will have friction, and the friction will cause motion energy to be converted to heat (which will dissipate throughout the water and air). The wave will eventually cease to exist unless energy is added.


30

All fundamental forces are conservatives and I would say that this is a postulate. Fundamental physics is constructed in such way that there is a quantity called energy which can be assigned to every possible state. If any fundamental process seems to violate conservation of energy we nowadays believe that there are some states, processes or even ...


28

The reason it is better to unroll the cable is because it improves its ability to dissipate heat, which could be important for heavy loads, i.e., when the cable could potentially become hot. The role of the inductance here is minimal, since the current in the cable is flowing in both directions and the net current is zero.


26

Your initial circuit is like this: So you get 2A flowing and a power of 20W dissipated in the resistor. Then you double the voltage and the resistance: The two batteries add up to single source of 20V. The two resistors add up to a total resistance of 10$\Omega$. So, as you correctly state, the current is the same as before (2A). Therefore the power is ...


24

What I fail to see is how moving too quickly could also impair cooling performance as stated in a lot of online forums. One argument I clearly remember from reading about this a while back was: and: You shouldn't crank the pump speed too fast or the water won't have time to pick up the heat from the waterblock as well. The latter statement you quoted is ...


24

Yes, this would be horribly inefficient compared to pumped hydro or even a regular flywheel. With a rotating fluid, there's a lot of viscosity. This viscosity generates heat and slows the fluid down. You would be able to offset this somewhat if you kept the container for the fluid moving with the fluid itself; but even then I believe there would still be ...


22

This is a consequence of the second law of thermodynamics, which states that In a closed system with fixed internal energy (i.e. an isolated system), entropy is maximized at equilibrium. It can be shown that this statement is equivalent to the following: In a closed system with fixed entropy, the energy is minimized at equilibrium. Callen in his ...


22

To answer this, I would appeal to the general principle which we call the 2nd law of thermodynamics. One way of expressing it is that the entropy of an isolated system cannot decrease. This means that in order to keep going for ever, a wave motion would have to involve no entropy increase. But almost all processes involve some increase of entropy, and in the ...


21

Physics theory and experimental reality have something like a mathematical epsilon delta relationship, imo. Here is a review of the matter. From the introduction in the PDF of the paper Resistance in Superconductors: The ability of a wire to carry an electrical current with no apparent dissipation is doubtless the most dramatic property of the ...


21

Problem: Given Newton's second law $$\tag{1} m\ddot{q}^j~=~-\beta\dot{q}^j-\frac{\partial V(q,t)}{\partial q^j}, \qquad j~\in~\{1,\ldots, n\}, $$ for a non-relativistic point particle in $n$ dimensions, subjected to a friction force, and also subjected to various forces that have a total potential $V(q,t)$, which may depend explicitly on time. I) ...


20

Batteries do not behave in such an ideal way across all conditions. The simplest model of a battery as a circuit element is the one you describe - a pure voltage source. A slightly-more sophisticated model is as a voltage source connected to a fixed resistor, called the battery's internal resistance. A typical battery has an internal resistance of between 1 ...


20

The real world is full of small effects that only matter when you've eliminated everything else. For example, if the pendulum has a non-zero conductivity its motion through the Earth's magnetic field would cause eddy currents and dissipate energy. This would be a tiny effect, but it would mean the pendulum wouldn't oscillate for ever. I imagine the more ...


20

More generally, Lagrange equations$^1$ read $$ \frac{d}{dt}\frac{\partial (T-U)}{\partial \dot{q}^j}-\frac{\partial (T-U)}{\partial q^j}~=~Q_j-\frac{\partial{\cal F}}{\partial\dot{q}^j}+\sum_{\ell=1}^m\lambda^{\ell} a_{\ell j}, \qquad j~\in \{1,\ldots, n\}, \tag{L}$$ where $q^1,\ldots ,q^n,$ are $n$ generalized position coordinates; $T$ is the kinetic ...


17

To be concrete, let us here assume that the dissipative force $$ {\bf F}~=~-f(v^2)~ {\bf v} \tag{1} $$ has a direction opposite of the velocity ${\bf v}=\dot{\bf r}$ of the point particle. Here $f=f(v^2)$ is a function that may depend on the speed square $v^2\equiv {\bf v}^2$. Drag is of this form (1). Linear friction/drag corresponds to a constant $f$-...


17

This is really a statistical effect, as pretty much all of thermodynamics. You have two free hydrogen atoms. They tend to move around the space they have, and when conditions are favourable (there's enough energy, the atoms come "close enough" together), they might interact - chemically or otherwise. Now, "enough energy" is the important bit here. When a ...


16

As you know, energy is always conserved. When we talk of a force being non-conservative, it means that the force is operating within a system from which energy is allowed to escape. Perhaps the most common example of this is a system where work is being done in the presence of friction. We talk of work being useful or not and that defines a parameter of ...


16

This is an interesting article with some numbers for the energy in waves A wave with a height of 2 m and a wavelength of 14 m breaking along 2 km of coastline (surface area = 32,000 m2) has approximately 45 kWh of energy. How it will be dissipated will depend on the approach to the coast. A wave as seen above will start losing energy by transferring it ...


15

I'm going to take a slightly different approach and say it's because we defined energy to make it so. In other words, systems "try" to find the lowest energy state because energy is a concept humans invented in order to describe what we observe. This is the reason that for any given set of constraints, you might need a different "energy" to describe the ...


15

Your calculation is perfectly correct, under the standard idealizations in mechanics. From a mathematical point of view this isn't that surprising; divergent times are pretty common. For instance, for a generic nonsingular drag force like $F = - bv$, the time it takes anything to stop is infinite. In that particular case, the velocity decays exponentially, ...


14

The answer by niels nielson is much more useful than my answer. But just in case you really do want a rough estimate of how much power is emitted as sound... According to [1] (references are listed at the end), a sound level meter is a hand-held instrument with a microphone that measures the sound pressure level (SPL). I'll assume that this is the kind of ...


13

Of course, no. Tsunamis are a series of pressure waves with a longitudinal mode and have much higher wavelengths, speed, and period than the normal ones. Normal ocean waves only involve motion of the uppermost layer of the water, but Tsunami waves involve the movement of the entire water column from surface to seafloor. However, they are still akin to ...


13

Think of sucking liquid through a straw. It flows at a certain speed. Now squeeze the straw (increase the resistance). The flow (volume per second) slows down. In order to keep the flow-speed high, you must suck harder. That's the voltage (think of it as an electric "pressure"). This dent in the straw is now "using up" all of the pressure, which now is much ...


12

The interplay of Hamiltonian and Lagrangian theory is based on the following general identities, where $L$ is the Lagrangian function of the system, $$\dot{q}^k = \frac{\partial H}{\partial p_k}\:,\qquad(1)$$ $$\frac{\partial L}{\partial q^k} = -\frac{\partial H}{\partial q^k}\:.\qquad(2)$$ Above, the RH sides are functions of $t,q,p$ whereas the LH sides ...


12

One horsepower represents 746 watts. A refrigerator motor develops (typically) 1/4 to 1/3 horsepower of which only a tiny fraction of wattage is dissipated as vibratory noise. The leakage of heat into the refrigerator through its walls is a far more significant loss mechanism than noise generation. By the way, the front-most rubber feet of a refrigerator ...


10

Actually no, because even in a perfect vacuum the object will emit gravitational waves and slowly spiral into the planet. However this is a somewhat pedantic answer since for all but very high masses orbiting very close to each other, the gravity wave radiation is so small that the orbit would be stable on timescales far longer than the age of the universe. ...


10

Because the basic feature of a potential is that it is path-independent. It is a property of a point in phase-space, not of the system's history. Think of it this way: if you take your system to a little trip in phase space, and come back to your starting point, the potential cannot change in the process (as it is a function of your position in phase-space)....


10

To apply Noether's theorem, which is what you are alluding to here, one needs to look at continuous symmetries of a Lagrangian description of a system's dynamics. The damped oscillation equation you have written, although it is invariant with respect to a time translation as you rightly say, is not a Lagrangian description. If you write the Lagrangian for ...


9

Mathematical demonstration It's straightforward to see why this happens if you use a bit of linear response theory. Consider a generic damped harmonic oscillator. There are three forces, the restoring force $F_\text{restoring} = - k x(t)$, the friction force $F_\text{friction} = - \mu \dot{x}(t)$, and the driving force $F_\text{drive}(t)$. Newton's law says ...


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