Potential energy is the energy of a body or a system due to the position of the body or the arrangement of the particles of the system.

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origin of the major symmetry property of the elasticity tensor

In linear elasticity theory the stress tensor $\sigma$ is related to the strain tensor $\epsilon$ via the elastic tensor $C$. Specifically $$ \sigma_{ij} = C_{ijkl} \epsilon_{kl} $$ Because $\sigma$ ...
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Bounce height of ball on Mars vs Earth

I understand that if a ball is dropped on mars and on earth the ball will bounce back to basically the same height on both planets thanks to the law of conservation of energy. But can anyone prove ...
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Why does negative energy imply that a system is bounded? [duplicate]

I wanted to know why "negative energy" of a two particle system implies that it is bounded. That is what happens in the case of a hydrogen atom; my textbooks say so, but they do not give any reason ...
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Pendulum point in polar coordinates for Lagrangian

So I'm really stumped with this. I have a particle in a cone, like pictured. The particle orbits the z axis on the dotted line for $r$. So knowing that $\alpha$ and $r$ remain constant in this ...
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Can we define the zero potential at an imaginary point?

Consider a force field defined as $$\vec{F}(x) = \left(\frac{A}{x^2}-B\right)\hat{i}\space$$ where $A, B$ are positive constants. We want to get the potential energy function for this field. We can ...
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Understanding the relationship between electric energy and force

I'm trying to do the following problem: One of the three types of radioactive decay is "β decay", during which protons decay into neutrons or vice­versa, emitting either electrons (β­) or positrons ...
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Why the gravitation potential in a uniform field has negative values?

As we know the gravitational potential is the work done per unit mass in taking a point mass from zero potential (at infinity distance) to the point in a gravitational field. But why the work is ...
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Velocity increase calculated from kinetic energy in different frames

Say we have an aeroplane cruising along at constant height with velocity $v_0$. It dives by height $h$ and levels out, at a new velocity $v_1$, in a gravitational field of strength $g$. If all the ...
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Potential Energy of Interaction Between a Sphere and a Particle Formula Derivation [closed]

A sphere of radius R has density described by ρ=ρ(r). Derive equation for pontetial energy of interaction between the sphere and some point particle of mass m which is at distance r from the center of ...
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Hooke's Law vs. Elastic Potential Energy

I am currently learning about elastic potential energy and this is a question that was given to us by my teacher: When a 13.2-kg mass is placed on top of a vertical spring, the spring compresses ...
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What's the Relation between Potential of mechanics and electricity?

As we know that for a conservative force field, there is associated a Potential with the force. But we know there is a potential in electricity (That's voltage). My question is that is there any ...
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What is the meaning of the negative sign in $W = -\Delta U$?

What is the meaning of the negative sign in $W = -\Delta U$ ? As far as I understand, $W = -\Delta U = -(U_f - U_i) = U_i - U_f$. While $U_i$ is the initial potential energy (before applying the ...
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Kinetic energy on macro and micro situation

I just have this random question in my mind. If you drop something in deep space, and it falls due to a gravitational pull. As it's falling, its kinetic energy increases. I just wonder, is the average ...
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Determine the value of $g$ with rolling ball

At first, I thought the value of $g$ ($9.8m/s^2$) could be determined simply by placing a ball at the top of a ramp at a known height. The ball was released with no initial velocity, and the final ...
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Can the momentum eigenstates be non-orthogonal?

Consider the Hilbert space of a particle, whose position domain is confined to $q\in[0,1]$ (e.g. a particle in a box with unit width). Using $$ 1=\int_0 ^1 dq |q\rangle\langle q| $$ and the position ...
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Is work needed to bring a test charge from a higher potential to a lower potential?

I don't understand whether work is needed to bring a test charge from a higher potential to a lower potential. It seems that no work is needed because the positive test charge will be under the ...
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Conservation and forces/energy

Are there really non-conservative forces in actuality ? Feynman states in his book that in fact, all forces are conservative ( originating from conservative vector-fields ), provide we look close ...
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Isolation of a Physical System and Energy

I'm trying to grasp basic concepts of energy and i have a little doubt regarding conservation of energy. According to Feynman book and Wikipedia, the Law of Conservation of Energy states that ...
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Energy density in electrostatics

Imagine two hollow spheres with radius $R$ with charges $q$ and $-q$. $L>2R$ is distance between them. Potential energy of the each sphere is \begin{equation*} W_1=\frac 1{8\pi \epsilon_0}\frac ...
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How do I correctly introduce time into this equation?

So, for the past few years it's been my goal to create an equation that would give me the position of an object in a gravitational field at time $t$, given it's initial position and velocity. At first ...
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Using Electric Potential to Float an Object

I've been trying to answer the following question but I'm stuck at one step. The question essentially states that a magician is trying to perform a "floating objects" act, for which she has a thin ...
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How much energy does it take to hold a bag? [duplicate]

I'm holding a bag with some mass $m$. The force required for not letting it fall is equal to its weight $m \cdot g_L$ (where $g_L$ is the local gravity, assuming Earth this is $\approx 9.8 \; \text{m} ...
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What starts the conversion between GPE and KE?

When researching GPE and KE conversion, lots of websites say that as an object with GPE (Gravitational Potential Energy) falls, that GPE is converted into KE (Kinetic Energy), so there is less GPE and ...
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In atoms, what is potential energy?

I was reading about how potential energy in atoms is measured by how far apart they are from one another. From what I have heard of potential energy, it's a way of showing how fast an object could ...
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How can energy be partitioned equally when energy is relative?

According to the Equipartition theorem in a system at equilibrium the energy should be on average be divided equally between the available degrees of freedom. The most common examples are the three ...
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Why is the gravitational potential energy of ideal uniform massive spring $mgx/2$, not $mgx$?

In this Wikipedia page, $$L= T-V = \frac{1}{2}\frac{m}{3}\dot{x}^2 + \frac{1}{2}M \dot{x}^2 - \frac{1}{2} k x^2 - \frac{m g x}{2} - M g x$$ where $mgx/2$ refers to gravitational potential energy of ...
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How does gravitational potential energy increase, if field decreases as $h$ increases?

(In the following constants are ommitted) Let $ M = 50, m = 5, h = 5$. Then $$ \text{Potential Energy} = \frac{50\cdot5}{5} = 50.$$ While after increasing the height $h$: $ M = 50 , m =5, h =10 ...
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What happens to KE when lowering a raised book?

I understand the conservation of energy theorem and mechanical energy, but there is this question that confused me a bit, so I hope someone explains it. If you had a book and you raised it, you gave ...
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Kinetic energy of the object, but Potential energy of the system: Why is it so?

Examples from Principles of Physics (by Walker,Resnick,Halliday) will say it better: Let us throw a tomato upward. . .as the tomato rises, the work $\mathbf{W_g}$ done on the tomato by the ...
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Paradox of nesting black holes and release of energy

By dumping a gas cloud into a small black hole, I can produce radiation energy, this is how quasars produce energy. By dumping the previous black hole, with the gas cloud inside, into a black hole, ...
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Lagrange’s equation: from energies to Lagrangian form

I don't understand how we step from $$\frac{d}{dt}\frac{\partial T}{\partial \dot q_j} - \frac{\partial T}{\partial q_j} = -\frac{\partial V}{\partial q_j}$$ to $$\frac{d}{dt}\frac{\partial ...
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Has $E=mc^2$ been experimentally verified for macroscopic objects with potential energy?

In relation to this question: What is potential energy truly?, I'm wondering if $E=mc^2$ has been experimentally verified to hold true for macroscopic objects with increased potential energy? I'm ...
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Obtaining angular velocity of a general orbit

Provided you are given a effective potential function i.e. $$ V_{eff}=\dfrac{J^2}{2ml^2sin^2(\theta)} + mgl(1-cos(\theta))$$ how do you obtain the angular velocity for different types of orbits; i.e. ...
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Where is the mass energy of potential energy (such as for the universe?)

As you know, energy has mass via $E=mc^2$. If I understand right, mass must be inside of a particle, and can not just be "free floating." Gravitational potential energy (or what ever its equivalent ...
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What happens for a spoon if you carry it to the top of Mount Everest? [duplicate]

$$U=mgh$$ $$h \to \infty$$ $$U \to ?$$ The potential of a 100 gram-spoon is approximately 1 j when it's 1 meter away from the Earth's surface. It's still a spoon if you carry it to the top of ...
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Where is the potential energy saved? [duplicate]

If you increase the h (=height), potential energy will be increased given by U=mgh. Where does the energy go, into atoms?
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What will be the amount of potential energy?

Suppose, I have an object of mass $m$. By applying a force of $F=mg$, if I withdraw this object with constant velocity and place it at a height $h$ from ground level, then potential energy stored in ...
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Gravity and its energy

Where does gravity get its energy from? So, I'm taking a high school environmental science class and we just started a unit on energy. We were talking about different types of energy and one was ...
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Gravitational potential energy of a system [closed]

I don't know how the gravitational potential energy of a system of particles is defined. For example, how would one calculate the potential energy of a system of two stars, one mass $M$, the other ...
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Potential energy $= mgh$, what is $h$?

NOTE: when I say potential energy I mean gravitational PE The formula for potential energy is P.E = mgh. What is h referring to? Height, obviously. Consider the example: What is the potential ...
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I can make the mechanical energy 0 or in fact anything. Is this normal?

We let the rope fall with $\alpha = \pi/2$ (no initial velocity). if I choose the original of potential energy as the picture indicates there, this means that: $$E_m = E_{pe} + E_c = \frac12mv^2 ...
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Is electric potential a form of potential energy?

As I understand it, the concept of potential energy arises from analytical mechanics. Yet I often see the concept of electric potential $\phi$ introduced without mention of analytical mechanics. For ...
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The work-energy theorem

Well here's the question. From some previous excercises we know that from \begin{align} A&=\int F\;ds,\\ &=\int ma\;ds, &&(F=ma)\\ &=\int m \frac{dv}{dt}\;ds, ...
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How to reconstruct the dependence of the potential from a coordinate?

What is known is that an ion sent along the X-axis of a black box with a speed $V$ returns in a time: $$T=a V^b$$ $a$ and $b$ are some known constants. Having this, can we reproduce the dependence of ...
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Why is the potential energy for a body raised up by a height negative?

I tried deriving the potential energy of a body when raised at a height $h$ above the earths surface, using the formula: $$PE = -W_\text{conservative}$$ where $W_\text{conservative}$ is the work ...
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Relationship between momentum and energy for rocket-powered aircraft

I'm trying to write a problem for my students in an algebra-based physics class. We have a flight simulator and I've got a glider in the simulator that has a couple rocket boosters attached. Students ...
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My total potential energy?

The potential energy in a uniformed gravitational field is $mg \cdot \Delta h$. This assumes of course that $g$ doesn't change and only gives the difference in potential energy for $\Delta h$. How ...
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What is the intuition behind “Net Work is Zero”?

I tried searching the answer to this all over the internet, but still cannot grasp this concept. So, when a book is being lifted, let's say $25 meters$ with a mass of $4kg$, with constant speed. I ...
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Classical Mechanics - Potential Energy Function [closed]

Question The potential energy function of a particle of mass $m$ is: $$V(x) = \frac{cx}{x^2+a^2}$$ where c and a are positive constants. Qualitatively sketch $V$ as a function of $x$. Find two ...