Questions tagged [equilibrium]

Equilibrium is the condition of a system in which all competing influences are balanced. These can range from forces (static/dynamic equilibrium), to chemical processes (chemical equilibrium) and temperature gradients (thermal equilibrium).

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Difference between stable manifold and basin of attraction?

In 'Nonlinear Dynamics and Chaos' by S. Strogatz, a distinction is made between a stable manifold and basin of attraction of a fixed point in phase space: Here, the stable manifold of a saddle point ...
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Equilibrium points in lagrangian mechanics with generalized potentials

I understand the way i calculate equilibrium points when i have a lagrangian without mixed terms (with coordinates and velocities multiplied), thinking of the coordinate dependent part of the ...
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Why is bulk modulus positive in equilibrium?

$B=-PV/\Delta V$ The negative sign indicates that when pressure increases, the volume decreases. That is, if $P$ is positive, $\Delta V$ is negative. Thus for a system in equilibrium, the value of ...
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Apparently extracting work from a gas in equilibrium from fluctuations in the entropy [duplicate]

Suppose there are two gases in a recipient with a movable piston in the middle, separating the recipient into two halves. If both halves have different pressure, work can be extracted from the system ...
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A gas immersed in a higher-pressure gas: spherical shape?

I'm considering a bubble of gas of some arbitrary shape immersed in another gas of higher pressure. There is no gravity (and hence no buoyancy), the gases are ideal (so there are no attractive forces ...
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What is temperature: function of energy or the value of this function in thermal equilibrium?

As far as I remember, many textbooks on statistical physics introduce temperature as a condition of equilibrium of a composite thermodynamic system. E.g., if the system consists of two parts with ...
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Points where electric field is zero when charges are present at vertices of a regular polygon

There is a $n$-sided regular polygon with a charge $q$ at each vertex. I know that there are $n$ points, other the center of the polygon, where the electric field is zero. But why is this so? Is there ...
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Lopsided planet

Something that has always puzzled me about Pangaea. If we have a "roughly" spherical mass of solids, aren't two points on opposite sides approximately the same distance from the center of ...
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Would a black teapot midway between the temperatures of the tea and air cool down or heat up? If neither, then how do the 3 reach thermal equilibrium? [closed]

Say you had a matt black teapot with hot tea inside it but cool air around it. Originally, I’m guessing the matt black teapot should absorb more joules of IR energy than it emits per second. This is ...
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Doubts about direction of normal contact force acting on a tilted rod supported by another body

I'm confused about the direction of the normal contact force acting on a body supported by another body. I have read the following : If a body is being supported by a surface, the normal force acting ...
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Mathematical equation of the obliquely balanced system [closed]

why doesn't the system behave like a pendulum? 1. state of equilibrium (the pivot point of the bar is at the center of gravity) How do we write the equilibrium equation of the system in the 1st ...
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Proof that minimum free energy corresponds to equilibrium

I've tried to derive the relation between free energy, $F$, and equilibrium of a closed system. From the derivation i've written below it seems that if $T$ is constant and the system can't exchange ...
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For rotational equilibrium of a rigid object, about which point does the torque of the body have to be zero?

In the definition of rotational equilibrium for a rigid body, the net torque about a point has to be zero. Now, about which point will the torque be calculated? Will it be the centre of mass or centre ...
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Problem with possibly infinite possible solutions [closed]

Problem figure: In the problem, the string is light, inextensible and initially, before the application of the external forces, the string is just taut with no tension and the blocks were at rest. ...
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What is the meaning of a conductor in equilibrium?

Electric field lines are always perpendicular to the surface of a conductor in equilibrium. what is the meaning of a conductor in equilibrium?
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Lever and principle of moments

Consider an ideal lever which consists of a rod pivoted at its fulcrum as shown in the picture. Without any rigorous justification the textbook I am reading mentions that, $$F_{1}d_{1}=F_{2}d_{2}$$ ...
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What the are forces acting on a wheel of a moving bicycle?

For the wheel of moving bicycle or bike why is net torque $0$ i.e $\tau_{\text{NET}}=0$? If it can be shown that the wheel is in translational equilibrium i.e. $\sum_{}^{}\vec{F}=0$ then it's also in ...
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How to control the balance of a floating object?

I have this 3D printed object which I hope to float water. I added my printed object to a piece of foam (Glued) and then gently put it on the surface of the water. Every time I put it, it flips over ...
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Why is lever in mechanical equilibrium?

Let's consider a lever with a fulcrum (see image below), such that it's load arm and load are $d_1$ and $F_1$, respectively, and it's effort arm and effort are $d_2$ and $F_2$, respectively. Now my ...
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Equilibrium in blackbody radiation

I was reading this post and I think I am still confused. A blackbody $radiator$ is not in equilibrium, by definition, since it is radiating. If so, why does the blackbody spectrum accurately describe ...
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Minimum number of non-coplanar forces required to keep an object in equilibrium

The minimum number of non-coplanar forces that can keep a particle in equilibrium is: (a) 1 (b) 2 (c) 3 (d) 4 Answer given is option $(d)$ , i.e $4$. But can’t it be $(c)$ , i.e $3$ too? Suppose I ...
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Trying to understand the horizon problem

I'm trying to understand the horizon problem better. For the record, I have read this post and this post, which have been tremendously helpful. My understanding of the problem is that even if we ...
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Equation of equilibrium in a case where the partition allows particle exchange

... two physical systems [seperated by wall], A1 and A2. A1 has $\Omega_{1}(N1,V1,E1)$ possible microstates, and the macrostate of A2 is $\Omega_{2}(N2,V2,E2)$ ... at any time $t$, the subsystem $...
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How does a gravity defying stand comes in equilibrium?

The gravity defying wine bottle stand are now becoming very common these days. Can someone explain in detail the physics involved here? Here is a video that gives details about its making.
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Why does a uniform flexible rod sag?

Imagine a long flexible rod with uniform mass. The rod is supported by a pivot at its center and it is at equilibrium. How do we explain why the rod sags at the far ends? If we attempt to draw a free ...
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Conceptual problem understanding chemical equilibrium in the context of cosmology

In the context of describing the departures from equilibrium in the early universe (i.e. Big Bang Nucleosynthesis, recombination), one uses Boltzmann equations. Let's suppose we have a binary ...
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How to find the force needed? [closed]

To keep the system in equilibrium, the Fg should equal FBuoyant + FMagnetic. However, I'm having trouble seeing how the FMagnetic would push the tube upwards. We're using conventional current, and the ...
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How can an object on top of a Norton dome start to move?

The Norton dome is a dome-shaped surface in a gravity field on the top of which a symmetrical object is placed in perfect balance. According to Newtonian determinism, the object will remain in balance ...
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Question regarding the choice of axis to satisfy equilibrium conditions

I have a question regarding the choice of axis needed to satisfy the equilibrium conditions of $F_y=0$ and $F_x=0$ as demonstrated in the picture below. My question is, can we choose any axis ...
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Stress tensor and equality of normal stresses on opposite faces

Consider a body arbitrarily loaded as shown, At a particular point in the body, I take an element and show all the stresses acting on its faces. To specify a plane I will be using the the axis which ...
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Time-Independent Quantum Hamiltonians and Thermodynamic Equilibrium

Suppose we have a time-independent Hamiltonian operator $\hat{H}$ of some system. We know that we can express the canonical partition function of said system as $z = \text{Tr}(e^{\beta\hat{H}})$ for ...
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Question about the modulus of elasticity of a half-string

Question The ends of a light elastic string of natural length 0.8m and modulus of elasticity $\lambda$ N are attached to fixed points A and B which are 1.2m apart at the same horizontal level. A ...
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Confusion regarding effects of changing any mass in Principle of Equilibrium of Mixtures/Principle of Calorimetry

My book says that a calorimeter is made of thin copper sheets, and the thinner the better since less mass means less heat capacity, which means for the same temperature change, less heat is required ...
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Function of equilibrium position in a system with two springs and a mass

Consider a mass $m$ with a spring on either end, each attached to a wall. The mass can freely move horizontally, without friction forces. Let $k_1$ and $k_2$ be the spring constants of the springs ...
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Why everything wants to come into its lowest state of potential energy and why there manybe more than one position of stability?

Suppose we have a solid hemisphere , one can observe that from both curve and flat surface is kept on ground it acquires a stable position on its own , why its does so ? And if its true then why not ...
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Why are total kinetic energy and interaction energy roughly the same for a liquid?

Let's say one has a collection of point particles, each with a kinetic energy and (e.g. Coulomb) repulsion between all of them. Under certain conditions, the system will evolve to the stable state ...
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2 votes
2 answers
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Will static friction be zero unless it's necessary for maintaining equilibrium? [closed]

While solving a problem related to equilibrium, I assumed that friction would be zero (I wasn't sure if it was correct) unless friction was required to maintain the system in equilibrium. This got me ...
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2D statics problem with 5 unknowns? [closed]

In this problem there are 2 hinges (each one with 2 reaction) one at point C [$C_x$,$C_y$] and the other at point G [$G_x$,$G_y$] , Also there is a cable that Dc that has tension $T_{DC}$. Then how ...
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What is "equilibrium position" in simple harmonic motion?

In simple harmonic motion (SHM) is equilibrium position equal to the extreme position (i.e. where the external force and restoring force are equal), or where all kinetic energy of the body is ...
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Static equilibrium of a small spring network [closed]

Three springs $AB$, $OB$ and $CB$ with equal spring constants are fixed at the nodes $A$, $O$ and $C$ respectively and attached to a common node $B$, as shown below. The springs are at rest in this ...
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Why do these 2 different methods of finding tension in a string give 2 different answers?

A uniform rod BC of length $L$ and weight $W_1$ is hinged to a fixed point at $B$. A particle of weight $W_2$ is attached to the rod at $C$. The system is in equilibrium by a light elastic string in ...
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How to solve for the torque when there is more than one lever arm?

I have encountered this problem in my Giancoli physics textbook and I would like to seek your kind guidance regarding a simple point of confusion of mine. In this problem, we are asked to find the ...
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A question on static physics (equilibirium) [closed]

I have a question about static physics which includes multiple pullies and parts. I have tried to solve it but I have a problem which prevents me from solving the whole question. so I started from ...
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Proof that the second condition of equilibrium is equivalent to no rotation

I'm currently working my way through an introductory mechanics course, using University Physics with Modern Physics by Young and Freedman. I understand that the first condition for equilibrium, i.e. $\...
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What do we mean by "fixed pressure Ensemble" compared to a "fluctuating pressure" ensemble?

I know that there exists a pressure ensemble (NpT): given inverse temperature $\beta$ and pressure $p$, this ensemble has an equilibrium probability distribution \begin{align} \rho(\Gamma) = e^{\beta(...
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Cylinder on double edge with different angles - normal force

I'm looking for normal forces for this case: So, let's say it's a case with cylinder of weight G in wedge with two different angles. What are the values of normal forces? It's confusing for me, ...
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Equilibrium positions of a tilted rod rotating around vertical axis

First of all, this is my first ever question on any forum so forgive me if it's not so well written. Second, I'm not a native English speaker so if there is any writing error, I'm sorry. The problem ...
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3 votes
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Liouville's theorem and uniform probability density

In Kardar's book on statistical physics it is claimed that Liouville's theorem gives support for the common assumption that the points in phase space compatible with the hamiltonian are all equally ...
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Calculating the bending moment in 3D [closed]

I'm studying for exam week, and I met this problem in my text book. I thought it was quite cool, however, I couldn't arrive at the correct result according to my text book. Hence, I want to present my ...
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Does heat balances out or Temperature balances out?

Let's say we have $2$ elements Tin: Thermal Capacity $226\ \text {J/kg°C}$ Magnesium: Thermal Capacity $1024\ \text {J/kg°C}$ Let's say I have a $1\ \text{kg}$ block of each element at $40°C$, and I ...
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