I "A system tries to minimize total potential energy"

AI Thread Summary
The discussion centers on the principle of minimizing potential energy in systems, particularly in the context of an object launched from Earth at escape velocity. It questions whether this principle applies to unbound systems, suggesting that it may only be relevant to bound systems that can exchange energy irreversibly. The conversation includes a mathematical example of a harmonic oscillator, illustrating how kinetic and potential energies fluctuate while maintaining constant total energy. It emphasizes that systems do not "choose" to minimize energy, as this anthropomorphism misrepresents their behavior. The conclusion highlights that energy transfer is a fundamental aspect of systems with multiple energy reservoirs.
Swamp Thing
Insights Author
Messages
1,032
Reaction score
770
While reading this thread on Stack Exchange... https://physics.stackexchange.com/q...oes-a-system-try-to-minimize-potential-energy ... a question came to mind : -

Say an object is launched away from Earth at a velocity greater than the escape velocity. This system will not end up with its potential energy less than the initial value. Apparently, therefore, we need to qualify the principle of "tendency towards minimum potential energy" so as to exclude such cases? If so, how would we do that rigorously?
 
Last edited:
Physics news on Phys.org
As far as I know it only applies to bound systems that can irreversibly exchange energy with another system
 
  • Like
Likes vanhees71 and Swamp Thing
There's energy conservation for a closed system. Usually the kinetic and potential energy both change with time but such that the total energy stays constant. Take the harmonic oscillator as an example:
$$m \ddot{x}=-D x.$$
The general solution is
$$x(t)=x_0 \cos(\omega t -\varphi_0),$$
where the amplitude, ##x_0##, and "phase", ##\varphi_0## are integration constants, and ##\omega=\sqrt{D/m}##.

The kinetic and potential energies are
$$T=\frac{m}{2} \dot{x}^2, \quad V=\frac{D}{2} x^2.$$
As a function of time you get
$$T=\frac{m \omega^2}{2} \sin^2(\omega t -\varphi_0), \quad V=\frac{D}{2} x_0^2 \cos^2(\omega t-\varphi_0).$$
Now ##m \omega^2=D## and thus the total energy
$$E=T+V=\frac{D}{2} x_0^2 [\sin^2(\omega t-\varphi_0) + \cos^2(\omega t-\varphi_0)]=\frac{D}{2} x_0^2=\text{const}.$$
 
You're anthropomorphizing inanimate systems. They hate it when you do that.

If you have a system with two energy reservoirs, of any kind (potential and kinetic is but one example), and all the energy is in one, the only thing the system can do with the energy is move it to the other. There is nothing more to this than "if you're all the way to the left, the only direction you can move is to the right".

Swamp Thing said:
While reading this thread on Stack Exchange..
Is that's confusing you, maybe you should go elsewhere.
 
Last edited:
  • Like
  • Haha
Likes jbriggs444, berkeman, Dale and 1 other person
Consider an extremely long and perfectly calibrated scale. A car with a mass of 1000 kg is placed on it, and the scale registers this weight accurately. Now, suppose the car begins to move, reaching very high speeds. Neglecting air resistance and rolling friction, if the car attains, for example, a velocity of 500 km/h, will the scale still indicate a weight corresponding to 1000 kg, or will the measured value decrease as a result of the motion? In a second scenario, imagine a person with a...
Dear all, in an encounter of an infamous claim by Gerlich and Tscheuschner that the Greenhouse effect is inconsistent with the 2nd law of thermodynamics I came to a simple thought experiment which I wanted to share with you to check my understanding and brush up my knowledge. The thought experiment I tried to calculate through is as follows. I have a sphere (1) with radius ##r##, acting like a black body at a temperature of exactly ##T_1 = 500 K##. With Stefan-Boltzmann you can calculate...
Thread 'Gauss' law seems to imply instantaneous electric field propagation'
Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
Back
Top