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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Total Energy of Inverted Pendulum

I have to find the total energy $V$ of an inverted pendulum (rod). The following parameters and their values are given: Mass $m$ and length $l$ of the pendulum $\theta$ as the angle of the ...
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Derivation of Interaction energy of Dipole - Induced Dipole Interaction

I see that the formula giving the potential (interaction) energy of a dipole and an induced dipole is $$V=-\frac{C}{r^6}$$ where $$C=\frac{\mu_1^2 \alpha'_2}{4 \pi \epsilon_0}$$ and that the formula ...
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What is the difference between the potential $V$ and the effective potential $V_{eff}$?

What is the difference between the potential $V$ and the effective potential $V_{eff}$? Some times when solving problems, an effective potential $V_{eff}$ is defined and its usually equal to the ...
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143 views

How did Feynman prove that energy cannot be extracted from electric field?

In the Feynman Lectures, vol. II, chapter 4, Feynman discusses electric potential and says: If we carry a charge from point $a \to b$, $$W = -\int_{a}^{b} \mathbf{F} \cdot ds.$$ Now, in general, ...
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60 views

Is potential energy an energy exists or potentiality of energy? [closed]

I want to ask whether Potential Energy is truly existing Energy - though i know the energy concept is abstract and we do not know what is energy truly as Feynman said - or it is the potentiality that ...
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Susceptibilities and response functions

It is often confusing whether a susceptibility is the same as a response function, specially that often they are used interchangeably, in the context of statistical mechanics and thermodynamics. Very ...
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67 views

Are black holes an infinite source of energy? [duplicate]

Black holes are considered particularities because in a determined point in time they are pointless, as consequence there are some mass in a null space so the density become infinite. Finally if ...
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Why should Conservative forces have their curl equal to zero?(intuition)

There are several conditions that must be met in order for a force to be conservative. One of them is that the curl of that force must be equal to zero? What is the physical intuition behind this? If ...
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42 views

Metric in Lagrangian and the minimum total potential energy principle

I was wondering why physical systems "like" to go to the minimum of potential energy and I found this question, that tries to justify the minumum total potential energy principle. I was also reading ...
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54 views

Potential Energy in modified Atwood Machine

The initial length of the spring is $l_0$. I need help understanding how the potential energy of this system comes to be. I know the answer: $$ U = ...
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Why is the total energy of an orbiting system negative?

Assume it's an circular orbit. Object A orbits around object B. Take object B as frame of reference. .$E=KE_a + GPE$ .$E=\frac 12m_av_a^2 +(-\frac {GM_bm_A}r)$ .$E=\frac 12m_a(GM_br)+(-\frac ...
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Lagrange equation and a force derivable from a generalized potential

I was reading the solution of this exercise and I have a doubt: A point particle moves in space under the influence of a force derivable from a generalized potential of the form $$U(r,v) = ...
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How does potential energy work out for floating things?

Seeing a ship canal lift in TV spawned the following thought: "Oh my, this sure is a heavy ship and it can be lifted by simply adding water. What a marvellous machinery. After all, I could lift that ...
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58 views

What is this equation $f^e = f^a - \nabla U$?

Recently in a mechanics class my prof scribbled down something looked like $$f^e = f^a - \nabla U.$$ Where he claimed $f^e$ is the external force on an object, $f^a$ is the applied force on the ...
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Is negative energy a consequence of gravitational energy? [closed]

Assumption Treat all objects as a point. Gravitational constant = 6.67384 × 10^-11 m^3 kg^-1 s^-2 Acceleration of the object is 1 ms^-2 The setup Imagine there are 2 identical objects with mass of ...
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55 views

How this formula for work follows from the definition?

If a particle moves along a path $\gamma : I\subset \mathbb{R}\to \mathbb{R}^3$ then the work done by a force $\mathbf{F}$ is defined by $$W = \int_{\gamma} \mathbf{F} = ...
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30 views

Water in a U-tube [closed]

I'm currently working on a problem that states: a U-tube has vertical arms of radii $r$ and $2r$.... The U-tube contains liquid up to a height $h$ in each arm. The liquid is set oscillating and at ...
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What was the amount of energy released in the 9/11 terrorist attacks?

I read somewhere on the internet that the amount of energy released by the terrorist attacks on the twin towers on 9/11 should have been of the order of 100 tons of TNT. This number surprised me, ...
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23 views

Buckling of a slender column - total energy

I'm following Goldbart's Mathematics for Physics book, and I ran into a problem with exercise 1.4 (page 43). We have a formula for the energy stored in a slightly bent rod aligned on the $z$ axis: $ ...
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What kind of potential profile that an electron live in provides bound state energy levels?

Given the electron Hamiltonian $$H=T+V(r)$$ where $T$ is the kinetic energy, $V$ is the potential energy and it is not necessarily isotropic. If $$V \sim -\frac1{|r|},$$ we have hydrogen-like bound ...
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40 views

Which is the right sign convention for the potential difference?

The circulation of the electric field gives the potential difference, but is it : $$V_B-V_A = \int_A^B\vec{E}.\vec{dOM} \hspace{1.5cm} (1)$$ or $$V_B-V_A = - \int_A^B\vec{E}.\vec{dOM} \hspace{1cm} ...
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Rest masses, binding energy - mechanism for negative mass

Let us have an two objects (in a box) both of mass $m_0$ far from each other. They attract each other and at some moment their distance is close and they have substantial kinetic energy. Something ...
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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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34 views

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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63 views

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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38 views

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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86 views

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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52 views

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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90 views

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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56 views

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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193 views

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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61 views

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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72 views

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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56 views

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 ...