Questions tagged [equilibrium]

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How to calculate equilibria of the sum of “similar” Hamiltonians

Determining equilibria of a Hamiltonian system is equivalent to finding the zeroes of a function, so in general it is a hard task- But what if we have some additional information on the Hamiltonians? ...
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260 views

Direction of frictional force on a particle on a plate in circular motion

If we have a particle on the surface of a round plate ,at a distance $r$ from the center, that is rotating with an angular acceleration $k$ , and this particle is in equilibrium with respect to the ...
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982 views

Why do we consider the tension in a taut cable to be zero Newtons or Pound Force?

I have been browsing for a few hours now and I can't seem to find a reason for why this assumption is made for calculations and such in engineering problems like statics. It's a little embarrassing to ...
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Why are clockwise and anticlockwise moments not balanced in this equilibrium scenario?

If we take moments about the peg, which is directly below centre of mass of the cone (which is $r$ cm from its circular base) we get $3rTcos(90-ø) = Trcos(90-ø)$. $T$ = tension in string. Clearly this ...
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Thermodynamic equilibrium

I am a bit confused with the description of the thermodynamic equilibrium from my course. By definition the system is in equilibrium if all state parameters are constant in time and there are no flows ...
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Can you prove the interesting relation in equilibrium thermodynamics?

Problem and background I noted the following interesting relation in a paper discussing the liquid-vapor phase change, in which it was given directly without any derivation and reference: $$d\ln p^\...
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1answer
137 views

How is this system in equilibrium? [closed]

So, after mathematically calculating the answer I found it to be zero. But my teacher says I don't have to do the calculation as this system is in equilibrium and the initial acceleration is zero. But ...
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2answers
317 views

Thermal Physics “Thermal Equilibrium” Confusion on statement

I am reading a book regarding the work of Anders Celcius that states the following - By definition, any object at 100ºC must be in thermal equilibrium with boiling water. I am confused by this ...
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1answer
353 views

Determining the equilibrium position of a uniform rod pivoting about its center

here is the question: A uniform rod pivots about a frictionless, horizontal axle through its center. It is placed on a stand, held motionless in the position shown below, and then gently released. ...
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1answer
833 views

Thermodynamic stable equilibrium conditions

If I understand correctly (which I clearly don't) the condition of stable equilibrium of a closed system at constant $(P,T)$ is that $G$ is minimum. That implies that $dG=0$ and $d^2G≥0$. Since $dG=...
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Energy Considerations and Equilibrium in a Multipole

Thank you all ahead of time for your guidance, it is much appreciated. Currently I'm solving some problems out of Purcell's Electricity and Magnetism. In problem 1.5, the reader is asked to consider ...
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189 views

Center of mass of motor: rotational equilibrium

Two people place a motor on a $2$m uniform board that weighs $200$ newtons. They lift it, On one side one person lifts with a force of $600$ newtons and on another end the other person lifts it with ...
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How to consider another Cartesian axis?

Well, I solved the problem. The point is that I used a x and y axis with x parallel to the inclination of the box, but I wanted to think differently, if one considers the y axis itself containing the ...
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1answer
406 views

An approach to the Thomson problem for $N$ electrons embedded on the surface of a sphere

I asked this question on the mathematics board but it received no attention and it received no attention so I am lead to believe that I posted on the wrong board. The Thomson problem is concerned ...
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1answer
397 views

Basic Static Equilibrium of a rigid body

I'm trying to understand static equilibrium in 3-dimensions, but I feel like I should understand it in 2-dimensions first let's assume we have a rock with inhomogeneous density (black rectangle) with ...
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2answers
67 views

If a planet is always directed with the same side to the sun, does a the thermal equilibrium develop, and how does it look like?

If a planet with an atmosphere and a flat surface is always directed with the same side to the sun (or star), how does the (nonstatic) thermodynamic equilibrium look like? Has eventually an ...
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1answer
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If the fundamental definition of thermal equilibrium is no net heat transfer, how does one derive that temperatures must be equal?

The following thought experiment will help understand my confusion. Note that I'm only considering thermal equilibrium in the context of radiation heat transfer. Let's consider an oven which is an ...
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4answers
498 views

What's the size to talk about thermal equilibrium?

I am confused about what's the time we can talk about the thermal equilibrium? I mean how many particles the system will contain? This link is a lecture note to teach thermal physics following ...
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2answers
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What is a “thermal” particle?

I have seen various uses of the word "thermal" recently (e.g. in black hole physics) that make me wonder what is the exact meaning of "thermal" in particle physics. There are also "thermal neutrons", ...
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321 views

On the stability of black holes

Vera Rubin just passed (RIP) and recent News reviving the theory that the dark matter might be due to (small?) black holes; the idea that smaller black holes may be more prevalent than thought (then ...
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1answer
252 views

the equilibrium concentration of vacancies

In the derivation of the equilibrium concentration of vacancies by statistical mechanics method, I was stumped by this procedure (marked by "?"). $\textbf{Physical Model}:$ 1.Solid viewed as a ...
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3answers
428 views

Under what condition would I fall off a cantilever chair? [closed]

So this question is nagging at me and after many rounds of searching I still can't figure it out. I want to know is how load is distributed through a cantilever chair. Under what circumstances would a ...
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1answer
666 views

How make the perfect Hot Chocolate? Mixing liquids and temperature

I sometimes like to make hot chocolate, though when I do usually use powdered hot chocolate that you mix with hot water. However I think it taste better with some actual milk added in from the fridge. ...
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1answer
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Local thermal vs local thermodynamic equilbrium?

I know that their is a difference between thermal equilibrium and thermodynamic equilibrium. The former only requires no heat transfer whilst the latter also requires mechanical equilibrium, dynamical ...
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Definition of equilibrium in statistical mechanics

Equilibrium statistical mechanics is (amongst other things) about deriving the equations of state of thermodynamic systems (in equilibrium) from a microscopic basis (i.e. starting with a microscopic ...
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644 views

Charge distribution: electrostatic equilibrium in conducting sphere

Consider an uncharged sphere, made of electrically conducting material. We then charge the sphere with excess charges. I understand that these excess charges repel each other till the electric field ...
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1answer
67 views

Can a line of finite point charge configuration be in equilibrium?

Can we arrange a finite number of point charges in a line so that they are all in equilibrium? Earnshaw's theorem proves that there cannot be a stable equilibrium point in an electric field, but what ...
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Is stationary state possible to be achieved for some arbitrary heat radiating objects in an adiabatic room while they have different temperatures?

Assume an adiabatic room and some objects in it. Heat is only able to exchange via radiation. All of the objects and the internal walls have arbitrary $\alpha$'s. After a long time, take a "shot" of ...
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2answers
907 views

Can a system in thermodynamic equilibrium perform work?

For concreteness, consider a hydrostatic system in mechanical equilibrium. For example, a gas in a cylinder with a piston of weight $mg$ in equilibrium. In the situation of equilibrium, $$mg=PA\tag{1}$...
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Why will a non-black body of a temperature the same as that of the internal walls of a cavity be in thermal equilibrium, if brought into the cavity?

The book of Zemansky and Dittman claims that: I am confused with the first line of the second picture. What is written, actually means that if the temperature of the body is the same as that ...
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99 views

Confused by the definition about the inertial frame of reference

In Wikipedia, you can find the definition of the inertial frame of reference, which states: In classical physics and special relativity, an inertial frame of reference (also inertial reference ...
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1answer
426 views

Equilibrium and centripetal acceleration

Why is there still a non zero centripetal acceleration for a particle at equilibrium in uniform circular motion if equilibrium implies total Force = 0?
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1answer
92 views

What is the definition of equilibrium?

Assume that two bodies are rotating about their center of mass because of their mutual gravitational attraction between them. Can they be said to be in equilibrium? I believe that the answer is no, ...
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Understanding thermodynamic equilibrium for a relativistic system

The conventional books on thermodynamics that I know, do not talk about the thermodynamics of relativistic systems. But in Cosmology, the thermodynamic concepts are often applied to the whole universe....
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How to identify the equilibrium state and the steady state?

1.Is there any difference between the equilibrium state and steady state? 2.Can I just understand thermal equilibrium and nonequilibrium state just from whether the Hamiltonian of the system is ...
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431 views

Simple harmonic motion about an unstable equilibrium position?

In the typical scenario for simple harmonic motion, we have a spring providing a restoring force back to the equilibrium position. This gives rise to the equation (for undamped SHM) $$\ddot x +\frac {...
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2answers
611 views

Conditions for Equilibrium in 3 dimension and 2 dimension

The book describes that there are two conditions for equilibrium of rigid body, $$\sum \vec{F} = 0, \quad \sum \vec{M}_{o} = 0 $$ where $\sum \vec{F} $ is the vector sum of all the external forces ...
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1answer
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$N$-body system subject to charge and gravity: explicit formulas for equilibrium?

Consider a system of $N$ classical particles $x_1, \ldots, x_N$ in $\mathbb{R}^2$ of the same mass exerting a repulsive "charge" force against one another (where all particles have the same charge ...
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1answer
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What can it be an interpretation of the change of entropy in an equlibrium process?

I've been having some issues with this subject, and I'm pretty confused about the definition of entropy and specially concerning what could it mean when you consider the change on entropy from a ...
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1answer
196 views

Thermal equilibrium thermodynamics

If two bodies are in thermal equilibrium with each other does it mean that there is no heat transition between them or is it that there is no NET heat transit between them ? I think that the heat ...
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3answers
66 views

thermodynamic equilibrium under self-gravitation [closed]

Suppose you have a point mass M in space that is surrounded by a gas of particles mass m at temperature T. Let the gas distribution be spherically symmetric about M. What is the radial dependence of ...
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1answer
465 views

Why the convexity of $E(S,V,N)$ implies that at thermodynamic equilibrium the energy is minimal?

I do understand that in the case of mechanics for example, if there is a soccer ball inside a "well", at mechanical equilibrium, the ball will be at the bottom of the well. ball http://electron6.phys....
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3answers
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How $4$ forces achieve equilibrium? [closed]

Two identical uniform rods, each of weight $W$, are hinged together to form a structure which is resting on a rough floor as shown. If the reaction forces acting on the structure by the floor are $...
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2answers
762 views

Is a pendulum in dynamic equilibrium?

When obtaining the equation of a pendulum following classical mechanics (Virtual Work) we state that: The work is in equilibrium, therefore $\textbf{F} = 0$ and the Virtual Work is $$\textbf{F} · \...
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1answer
233 views

Torque of the contact forces about the centre of mass

A person leans in the opposite direction when he or she lifts a heavy load in one hand. I read a reason for the same in a book. According to the book, if a body is placed on a horizontal surface, ...
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4answers
533 views

Could a gas be in thermodynamical equilibrium even with a gravitational field?

Let us consider a cylinder filled with ideal gas, and let us assume that the gravitational field is parallel to one of its sides, well in this case, how would the system be in equilibrium? Suppose ...
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2answers
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Is it true that an object, in course of its motion, always seeks the position of minimum potential energy?

I have heard the statement, in a Classical mechanics course, that the motion of an object is always toward the position of minimum potential energy. I don't think that this statement correct because I ...
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1answer
218 views

Reaction forces in pyramid stacking of steel coils

I was tasked with solving this problem at work as we are out of coil holders and we bought 140 coils and need to stack them asap. Companies that make the storage holders are on back order for several ...
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Mechanics question [closed]

I came across a question which I have been struggling to get the same answer as provided in the textbook: A parent holds a small child in a swing so that the angle of the swing support is at 20 ...
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1answer
242 views

Microcanonical ensemble energy relation to kT

So today I derived the Boltzmann distribution and I stumbled across a particular assertion whose correctness I am wondering about: In the limit of the microcanonical ensemble (where the energy range ...