143

Make it simple. If a mass of your weight fell down the height of three flights of stairs through the air, when it landed where would the kinetic energy accumulated by falling go? moving the earth for conservation of momentum dissipated in heat on the ground deformation of the matter of the weight sound That is why humans invented the stairs, to ...


88

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 ...


52

The heat is predominantly generated in your muscles. More direct conversion of potential energy to heat is when a person is sliding down a pole to get to a lower floor quickly. With sufficient friction, the descent is at a constant velocity instead of accelerating. In muscle, some structures slide along each other. Muscle contraction is those structures ...


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.


33

Problem: Given Newton's second law $$\begin{align} m\ddot{q}^j~=~&-\beta\dot{q}^j-\frac{\partial V(q,t)}{\partial q^j}, \cr j~\in~&\{1,\ldots, n\}, \end{align}\tag{1} $$ 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 ...


31

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.


28

This behavior is basically described by Newton cooling with heat generation, using the equation: $$MC\frac{dT}{dt}=G-k(T-T_{\infty})$$where T is the temperature, t is time, M is the mass, C is the heat capacity, G is the heating rate, k is the Newton cooling coefficient (convective heat transfer coefficient times surface area), and $T_{\infty}$ is the ...


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 ...


25

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 ...


25

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 ...


24

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 ...


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

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

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 $f$-...


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

when rotating at constant speed, the fan disc is continuously performing work on the air drawn through it by imparting momentum to it. To perform that work requires a constant input of energy from the motor, and therefore the motor is continually absorbing electrical power while the fan is running. Some of that work is wasted in overcoming drag, but most ...


18

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

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, ...


15

Yes, once you are standing still at the bottom of the stairs then all of the potential energy you had at the top of the stairs has been transformed into heat (due to friction and heat produced by your body) and sound waves. And even the energy in the sound waves ends up as heat once it has been absorbed by the walls, floor, ceiling etc.


14

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 ...


14

At the moment the circuit is completed, the capacitor has zero voltage, while the supply has $V$. This voltage difference creates an electric field that accelerates charges. This acceleration sets up a current. As the current flows, the capacitor charges until the voltage reaches $V$ as well. At this point there is no voltage difference. But the ...


14

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 ...


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 ...


14

Your analogy is faulty. Think instead of the falling ball as having already reached a constant terminal velocity because of air drag when its gravitational potential energy is 10 J. Then since it’s velocity is constant on the way down there is no change in its kinetic energy. Its loss of gravitational potential energy equals the heat dissipated in the air ...


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 ...


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