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-1

It constantly gets away from equilibrium, it just has a very low probability of getting away far enough to be measurable. In my mind, equilibrium is maximal entropy, so I'm having difficulty understanding the question. To correct an error: the energy U does not change in an isolated system.


1

First of all, as this is a homework question, I can't tell you the complete solution. Choose P as the origin of coordinate system and resolve the forces into x and y component. And as the body is in equilibrium, the net force is zero. So you get these two relations (when the net force on x and y component equated to zero.) $$G\cos\theta=H\cos\phi\\ ...


2

Ok, I do not know the Sage algorithm but I am going to offer a conjecture of what is happening. You have to verify the conjecture by further numerical investigations. I assume that the Sage algorithm works optimally for bifurcations of a single equilibrium and can run into problems such as we see here when dealing with equilibria (AKA fixed points) ...


1

The centre of mass exactly below the point of suspension is the equilibrium position. For a small displacement from the equilibrium position you need to have a restoring torque back toward the equilibrium position. Put another way you want the potential energy vs displacement graph around the equilibrium position to exhibit a minimum. Nice description ...


1

At every joint you need the center of mass of the suspended material to be below the support. For mobiles, that is fairly natural.


3

The difference between an office chair's 5 wheels/supports and a regular chair's 4 legs is that the latter has all of its load going straight down. The legs only need to be strong enough not to shatter. In fact, a chair could easily get away with 3 legs but for the stability. In contrast the office chairs legs support load perpendicular to their ...


26

Consolidating some of the points made in the answers to the question you linked, and comments: When constructing a chair, 4 legs is easy when you use traditional (wooden) construction - 90 degree angles, and easy to make stackable. A little bit harder than three legs because you have to make sure they are all the same length (or the chair will wobble). ...


0

Whenever i say that the pressure of a gas is 2 atm then it is known that at the time i say this, the gas is in equilibrium. Well what i want to say that we define a state of any system when it is in equilibrium and by equilibrium i mean thermal equilibrium which means every knid of equilibrium like mechanical, chemical, etc. Now to define a state we use ...


1

No - in the video, the instructor calculates $A$ and $B$ which are the total tension in the cables. Taking a screen shot at 6:16 shows this: The horizontal components are $A \cos 60$ and $B\cos 40$ respectively - and these cancel exactly. $A$ and $B$ are indeed the total tension. You could get that by summing the $x$ and $y$ components according to ...


1

Because the barbell is symmetrical, its weight $m_bg$ cannot exert a moment about the point $A$. Standing on its own the barbell would be meta-stable but in combination with the frame and its weight $m_fg$ this is a stable arrangement.


4

The center of mass stays inside the supports because the bar itself is heavy. To tip over, the center of mass would have to move outside the supports. Here is how you can calculate it: The picture shows a simplified "asymmetrical barbell". The weight of the bar is $W_1$, the weight of the disk added is $W_2$. Now the bar creates a counter-clockwise ...


2

Two bodies in thermal equilibrium are at the same temperature. See the Zeroth law of thermodynamics. Temperature is a direct function of average molecular Kinetic energy - by definition. There is no dependence on anything else like degrees of freedom etc. There are other forms of molecular thermal energy storage - rotation and vibration about molecular ...



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