# 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 ...
1 vote
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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 ...
1 vote
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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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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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### 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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### 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 ...
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 ...