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4

I am answering the question formulated after the "edit" in a newer version of the text because that one seems well-defined. Indeed, a situation with a uniform field $\vec E$ may be said to be "uniform" or translationally invariant in space. Noether's theorem says that this "uniformity" (spatial translational invariance) implies the existence of a conserved ...


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In simple terms the internal energy can be thought of as the sum of the kinetic energy and the potential energy of the molecules. The kinetic energy of the molecules depends on the temperature - a higher temperature means that the molecules have more kinetic energy. The potential energy of the molecules depends on the bonds (interactions) between them - ...


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Your intuition that the same amount of fluid goes down and then up by the same amount is incomplete, you are forgetting what happens inside the fluid. It is easier to see using solid blocks as in the figure below: Here you can see that the effect of moving block 1 down is to shift block 2 to the right, and moving block 3 back up the same amount that ...


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Precisely, the point is that the slope is not equal to 1. The ratio $\dfrac{F}{\Delta L}=k$. Therefore, $Z=\dfrac{1}{2}(x)*(\dfrac{x}{k})$ $= \dfrac{1}{2k}x^2$. Which looks wrong but is true because in the notation you are using, $x$ is not the elongation but is rather the force acting. So in a more familiar notation $E=\dfrac{1}{2k}F^2$. If you want to ...


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Work is always force times displacement in the direction of the force. The only place where the gas is doing work is at the bottom surface that is moving downward. The force it is exerting there is $PA$, where $P$ is the gas pressure and $A$ is the cross sectional area of the tube. If the lower surface moves downward a differential distance dx, the work ...


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Suppose we lift a particle by doing mgh work on the particle. How will this energy be stored in the particle? we normally lift a body (designated by a point on paper-called a particle) of mass m and do some work- It means something is operating to prevent this action /or oppose our action of 'lifting' that's why one has to do work- meaning thereby that ...


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Gravitational field is a vector field and is determined by negative gradient of the gravitational potential. $$\vec g=-\vec\nabla \phi$$ Frome equation above, it is obvious that $|\vec g|=|-\vec\nabla \phi|$ (magnitude of $\vec g$ is equal to magnitude of $-\vec \nabla \phi$) and we know that $|-\vec\nabla \phi|$ is a non-negative quantity. You have made a ...


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If you accept that no external work was done, then if there is a change in the state of a system through which the kinetic energy changed, there must be a corresponding change in potential energy. The key to understanding the (rather poorly narrated) video is that the lecturer implies (at T=2:30) that $\Delta E=0$ from which it follows that $\Delta KE= - \...


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A simple pendulum performs simple harmonic motion when it is displaced very slightly. You can say that a simple pendulum performs a periodic motion which can be treated as simple harmonic motion in small oscillation Now lets move forward supposing it to be pure SHM. The time period of a simple pendulum does not depend on how much it is displaced( but it ...


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My explanation is as follows Force on the spring in stretching it to length x can be written as $F=k(x-L_0)$ where x is the displacement, $L_0$ is the initial length of the spring and k is spring constant. energy stored is $dE=F.dx$ upon integration we will get $E=\frac{1}{2}.k.(L-L_0)^2$ where $L$ is the final length of the spring. This is I think ...


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First, let's pick a field to work with, because particles act differently in different vector fields. Let's say we're dealing with a charged particle in an electrostatic field. EM fields can be seen as a deformity in spacetime, the field is warping the space in which it is defined. In fact, for advanced EM we use tensors to describe electromagnetic ...


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First of all, we must be talking about a field that would affect (exert a force on) the object (like a charge in an electric field or an object with mass in a gravitational field). Now, what does potential energy mean? It is a measure of "stored energy" in the system. That means, if you released it, this energy would be released. Put a book on a shelf and ...



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