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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Finding the potential energy of a geosynchronous satellite above earth [on hold]

I am trying to find the gravitational potential energy of a 1kg geostationary satellite above the earth. So far: $E=mgh$, and $g=GM/r^2$ so substitution of $g$ into the energy equation gives: ...
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Thomson problem vs. maximizing sum of distance

Given $N$ equally charged points lying on the unit sphere ("electrons"), the Thomson problem consists of finding the configuration of these points such that the electrostatic potential energy $$ ...
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Why is the objective function used in Nudged Elastic Band method reasonable?

In Nudged Elastic Band (NEB) method, which is used to find reaction pathways when both initial and final states are know, an objective function is first constructed and then minimized to find reaction ...
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Work in electric potential

I've read that if we want to move a charge in an electric field then we need a work of an external force to move it from a low potential energy to a high one , but then I read on another source that ...
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How would we find what sort of a force this one is? [closed]

The potential energy for a force field is given by $U = -Kxy$, where $K$ is a constant. The body moves in an $x$-$y$ plane. Find the force vector. $i$ is the unit vector along the $x$ axis, $j$ is ...
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Mathematical misunderstanding of Work-Potential Energy Theorem?

This is a relatively basic question, but I don't understand why it is the case. This is from my dynamics book and is mainly a mathematical misunderstanding. $$ \ dU = F\cos\theta ds $$ Which means ...
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Help understanding the solution to a problem regarding kinetic energy of a group of point charges

The problem provided by my professor goes as follows: "Now consider a situation in which all charges are equal to q and they simultaneously become "unglued". What speed will each charge have when a ...
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Why molecules in this potential have a common average distance $r_m$ to their neighbors?

A commonly used potential describing intermolecular interactions in liquids and real gases is the so-called Lennard-Jones potential. In this model the interaction of atoms and molecules with each ...
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What happens to gas molecules after ionization?

I know that gas molecules conduct electricity after they get ionized but what will happen if we keep increasing the voltage even after ionization? Will it explode? If it will then how much energy ...
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267 views

Center of mass error - calculating systematic error in change in PE

Suppose we have to calculate systematic error in change in PE. Let's suppose systematic error due to scale is 1%. I'm confused about the center of mass error. \begin{align} \Delta PE = m*g*h_1 - ...
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Lennard Jones potential is bad in my plot made with python [closed]

Note that this question is about formula, not about code debugging. I made a program which draws LJ potential with parameters gamma and sigma adjusted with sliders in GUI. However regardless what ...
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What is the total energy? [closed]

So, there was this example in my book with a rock being lifted upwards. The person lifting the rock does 20J of work and gravity does 20J of work. I know Wnet = 0, since there isn't a change in ...
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Generalization of Feynman's derivation of the formula for gravitational potential energy in FLP volume I

In the Feynman Lectures on Physics, Feynman derives the formula for gravitational potential energy by applying a line of reasoning he borrowed from Carnot on reversible weight lifting machines (FLP I, ...
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What does it mean to charge a length of wire up to potential v?

I have to study the text "On the Theory of the Electric Telegraph," By William Thomson, 1855. I am having trouble gaining a conceptual understanding of the opening: "Let c be the electro-statical ...
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Why potential energy of a dipole in an electric field has a negative sign?

In the following equation $$V = -\mathbf{P}\cdot \mathbf{E}$$ why I have to take Potential Energy as negative. Is there any simple reason behind this ? I am preparing for my high school ...
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Potential Energy of Springs and Gravity, and Work of a force

I am currently really stuck on this problem and I am not sure how to actually solve it, I think I can reason it out logically but I do not know how to show it. Here it is and under I will show what I ...
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547 views

Mechanical Equivalent of Heat

Recently I have been looking up James Joule's experiment regarding the mechanical equivalent of heat. After viewing some drawings of the apparatus, I assumed that the lines holding the weights would ...
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4answers
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How is potential energy (PE) actually stored in a steel spring at the atomic level?

Elasticity is one the most intriguing phenomena, wiki gives a summary explanation of what happens in a steel spring: the atomic lattice changes size and shape when forces are applied (energy is ...
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Does the mass of an object change as it moves away from the earth?

The mass of a helium nucleus is less than the mass of two isolated protons and two isolated neutrons. When the component hadrons are assembled, this mass is lost as energy ($E=mc^2$). This makes it ...
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Ballistic Pendulum question?

I am answering a question regarding the ballistic pendulum, and the teacher gave this worksheet. I have figured out both t (time) and the change in y. Where I am getting confused is where he wrote out ...
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Violation of conservation of energy… or not?

The work done by surface tension is double the increase in potential energy. This is a clear violation of conservation of energy. What is the flaw here? Work done by surface tension is \begin{align} ...
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Modelling gravitational potential of a galaxy

I am interested in modelling the gravitational potential of a disc-shaped galaxy with radius $R$, i.e. solving the 2D Poisson equation numerically by Gauss-Seidel relaxation: $$\nabla^2 \phi = 4\pi G ...
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Is there anything interesting about an n-body system whose potential energy is constant?

I am curious about a system of gravitating bodies with particular characteristics. Before describing the characteristics of the system, let me say what I want to know about it: Can this be a ...
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Can energy be created and destroyed?

The indroduction of the principle of conservation of mechanical energy has been tremendously useful from the practical point of view. But .. Consider the case in which we shoot an electron up in the ...
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Electric potential energy and signs

I know that electric potential is negative near a negative charge and positive near a positive charge. But does this mean a small positive 'test' charge has a negative electric potential energy near a ...
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How to find height, when given the velocity at that location, starting height, and mass of object? [closed]

The question: A roller coaster is 100m above the ground, and weighs 1000kg. At one point of the roller-coaster-ride, the velocity is 28 m/s. What is the height of the roller-coaster at that ...
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Electrostatic Potential Energy Integral

I'm trying to calculate the total energy of a simple two charge system through the integral for electrostatic energy of a system given in Griffiths' book: $$U = \frac{\epsilon_0}{2}\int_V E^2 dV .$$ ...
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How is energy converted when massless spring is attached to a rigid support

Say a massless spring of length l is attached to a rigid support. It is extended to length l + x. Now at this position, the ...
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Conceptual Question on Work and Potential Energy

I'm confused by classic description of work and negative work. If someone pulls (slowly) on a rope to lift a bucket in a well, I understand that the person is doing work on the bucket and gravity is ...
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62 views

Finding potential energy of a solid hemisphere on top of another solid hemisphere [closed]

A solid hemisphere with radius $b$ has its flat surface glued to a horizontal table. Another solid hemisphere with radius $a$ rests on top of the hemisphere of radius $b$ so that the curved ...
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54 views

Confused about gravitational potential energy [duplicate]

So learning the concept of gravitational potential energy, my professor says that when lifting an object without any acceleration, the force we exert on the object to lift it is the same as the force ...
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Separating the potential energy of a system of particles.

Assuming all forces derive form a conservative source and that all forces observe the strong form of the third law, how do we arrive at the following equation? \begin{equation} V=\sum _i V_i+\frac ...
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47 views

Hooks Law and acceleration [closed]

A 435 gram sharpened piece of iron rebar into a spring loaded device. It takes a force of 355 Newtons to compress the spring by 27.5 cm. With what speed does the rebar shoot out of the device? ...
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Which inertial observer should I choose when using $\Delta U = -\Delta K$?

I just read and undertood that For any conservative force $F$ (which is not necessarily constant), we can define a potential energy change $\Delta U$ of an object on which the force exerts as ...
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Physics of every-day life: rotating bag of tea

Whilst studying for my physics courses, I like to drink tea. Today, I noticed that if you pull a bag of tea out of a hot cup of water, it gradually starts to rotate, picking up speed as time ...
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Show the equivalence of two electrostatic energy

$$U = \frac{1}{2}\iint_{all space}^{ } \frac{\rho(1)\rho(2)}{4\pi\epsilon_{0}r_{12}}dV_{1}dV_{2} $$ and $$U = \frac{\epsilon_{0}}{2}\int_{allspace}^{ } \vec{E} \cdot \vec{E} dV.$$ In the left ...
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Why is Energy = Voltage x Charge, and how to prove that?

As you know the equation $\mathbf{E=V\times Q}$. Where: $\mathbf E$ is the energy measured in joules, $\mathbf V$ is potential difference (Voltage), $\mathbf Q$ is the charge. So my qustion is: ...
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Conservative force as a potencial energy gradient

A conservative force $\vec{F}$ is apparently defined as the gradient of a potential energy $U$: $$\vec{F} = -\nabla\ U$$ I am curious if this definition was originally used to describe a ...
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345 views

Potential Energy Concept

Imagine a book that we lift it with a force that is exactly equal to the force of gravity so the forces cancel out and the book moves with a constant velocity. Consider the situation after the book ...
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The Delta-Function Potential

I'm reading through Griffiths Intro to QM 2nd Ed. and when it comes to bound/scattering states (2.5) they say: $E<0 \implies$ bound state $E>0 \implies$ scattering state Why doesn't this ...
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Can anyone give me a simple proof for the sign change of electronic wavefunction when taken around a loop containing a conical intersection?

How and why does the sign of the electronic wavefunction changes when it is taken around a contour? For example, suppose the initial wavefunction is $f(s;S_0)$ at nuclear configuration $S_0$ and now ...
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Food calories vs gravitational potential energy [closed]

Imagine you could use all of the energy you have ever extracted from your food as a source of propulsion. Is the energy contained in the food you’ve eaten over the course of your lifetime enough to ...
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Confusion with Grounded Conductor: bringing in a point from infinity

Suppose, for sake of argument, we have a spherical grounded conductor at the origin. Additionally, let our reference voltage be at infinity. Now, I view the potential of a point in space as being the ...
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trying to understand the electricl potential and potential energy

I am trying to understand some facts on electrical potential and potential energy. It is quite confusing in the text to say that the zero potential could be freely chosen for convenience. In that ...
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1answer
72 views

Integrals and Legendre Polynomials

I was told by a professor that this equality: $$\frac{1}{2\pi}\int_0^{2\pi}\frac{1}{|r-r(\varphi)|}d\varphi = \frac{1}{r}\sum_0^{\infty} \bigl(\frac{a}{r}\bigr)^n{|P_n(0)|}^2$$ ( where: $a$ is the ...
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685 views

Why doesn't the potential energy of any object equal 0

Consider a particle on the ground. This particle is raised by a force of magnitude $mg$ to a height $h$ above the ground. At this point, the work done on the particle by the force is $mgh$, which is ...
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Particle in a Box: Energy Less than the Potential Energy

I am reading quantum mechanics from Shankar's Principles of Quantum Mechanics. On page 157 he defines the box potential $V(x)$ as $$ V(x) = \left\{ \begin{array}{rl} 0 &\mbox{ if $|x|< L/2$} ...
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Using gravitational potential energy and elastic potential energy in a problem?

This is a problem my professor worked on in class: The first thing he said was that we would use position 2 as the "reference height" and I'm not sure what that means exactly. He goes on to say ...
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How to understand whether potential energy increases or decreases?

I am confused by how to deal with the negative sign in the equation $U=-GMm/r^2$ in the following problem: If the distance between two masses is tripled, then the magnitude of the gravitational ...
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Confusion with Newton's Second Law : Position & Time Dependence of Force

For a conservative force $\vec{F}(x,y)$ we have $$\vec{F}(x,y) = - \vec{\nabla}\phi(x,y)$$ where $\phi(x,y)$ is a potential function for $\vec{F}(x,y)$. Again, Newton's second law states that $$ ...