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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Two expressions for potential energy in the gravitational field of the earth

Let $M$ be the mass of the earth, considered as a point mass, then the potential energy of a point with distance $r$ away from the center (assume $r > \textrm{radius of earth})$ is $$ U(r) = ...
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Why is all the voltage used up in a circuit?

We always assume that all the voltage, in no matter what type of (basic, I guess) circuit we are dealing with, is used up. I can see why this is true. Imagine a circuit with low resistance - and ...
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31 views

Why potential energy of external force on particle attached to spring is equal to full force multiplied by full displacement?

I am having quite difficult time to understand the meaning of total potential energy on spring. All references I read say that the total potential energy on particle attached to spring is: ...
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Potential energy graphs of chemical systems

I really wish someone could dissect this for me in the language of physics. The system is that of two atoms that approximate each other along 'r' (or distance themselves apart). My concerns are ...
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Action Reaction Pairs and Work

Say that a ball is sitting in front of a compressed spring launcher. The spring is then released. The spring applies a force on the ball for a certain distance. This force is accompanied by an equal ...
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40 views

Work done by Internal Forces

Why is it that internal forces do not change the potential energy of the system? Assume that a man stands on earth with a dumbell. If the dumbell is the system, when it is raised a height h, the work ...
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Is quantum tunneling related to imaginary time?

I was studying for my exam and looking at the chapter which talks about Potential-energy graphs. Let's take this as an example: My book states that: "If the object is in $B$ and has a total energy ...
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47 views

Computing average force exerted by ground when jumping

Problem: A man of mass $m$ jumps vertically into the air from a sitting position in which his center of mass (CoM) is at a height $h_1$. When his feet are just about to leave the ground his CoM is at ...
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30 views

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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40 views

Calculate Potential Gravity Energy converted when star collapses [closed]

We want to calculate how much gravitational potential energy converts to heat, when the star has no nuclear fusion, the gravity will cause the star to shrink in nano seconds. Now assuming the Sun ...
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297 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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80 views

Potential energy & entropy of three particles

Let me first say that I am not a physicist, but I am trying to make a simulation on my computer and I have the following question. Let's consider that we have three free charges that somehow can ...
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194 views

Where do flying gas molecules get their energy from?

If you heat up water in a tank to boiling point, some of the water will turn to steam. Gas bubbles are created in the water. According to Archimedes principle, the gas bubbles will have a force equal ...
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How to restore the potential energy? [duplicate]

How to restore the potential energy, of a particle with variable mass and variable coordinate, by —Āartesian coordinates and mass of the particle? ? Dimension - one dimensional. Data that is to ...
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21 views

How to find the potential energy? [duplicate]

how to find the potential energy of a particle with variable mass and variable coordinate ? Data that is to compute, only the mass and Cartesian coordinate of the particle, like this: x;m ...
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2answers
74 views

Explanation for $M{\ddot{r}}=-\nabla \phi$

Could someone please explain this equation $$M\bf {\ddot{r}}=-\nabla \phi$$ Where $\bf r$ is a position vector and $\phi$ is the potential function. Could someone brief explain the potential function ...
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60 views

How to show that the gravitational potential energy of a two particle system is -2 times the total kinetic energy, without using the virial theorem?

Consider a two-particle system with identical masses, orbiting in circles about their center of mass. I'm supposed to prove that: $$U_p = -2U_k$$ With $U_p$ potential energy of the system, and $U_k$ ...
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58 views

Sea surfer position displacement

Waves are means by which the energy propagates through a medium (e.g., sea water). This is not associated with a net movement of water in the direction of wave propagation. If this is the case, then ...
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Where is the potential energy due to internal interactions in total energy?

In thermodynamics the total energy of a system consists of kinetic energy of motion of the system as a whole, potential energy of the system as a whole due to external force fields, and energy ...
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If batteries are a source of energy, would not lower-valued resistors cause a violation of the conservation of energy?

Here's the conundrum I have been facing. Yesterday I asked the question: how can batteries constantly motivate electrons to complete a circuit? (What maintains constant voltage in a battery?) After ...
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29 views

How do I describe the energy an electron gains (and loses) in a circuit?

I am looking at the simple circumstance of an electron traveling through a long wire by a potential. I see how one would be motivated to use the usual formula, W=F*d, to describe the electron's net ...
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49 views

What maintains constant voltage in a battery?

I know there's lots of questions that address similar situations, (Batteries connected in Parallel, Batteries and fields?, Naive Question About Batteries, and the oft-viewed I don't understand ...
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Writing Schrodinger equation with central potential in Atomic unit

I'm struggling to write Schrodinger equation with a central potential in Atomic unit. $$ ...
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24 views

Calculate amount of energy based on height of object

How can you calculate the amount of energy an object produces that falls from a particular height? Or water. In an eg i would like to know how can you calculate the amount of electricity water can ...
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1answer
91 views

Loss of gravitational potential energy in an infinitely far object

Now consider I went into a rocket which goes an infinite distance far from earth. By infinite I mean very far. The gravitational attraction between me and the earth will significantly decrease and ...
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What is the mathematical definition of work?

I'm looking for the pure mathematical definition of work, but I haven't yet learned line integrals. My book says that the work due to a force ${\bf F}$ from point $A$ to point $B$ is $$ W= |AB|\cdot ...
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Potential energy of a rotating bar

I have a bar of length $L$, mass $m$, and negligible width. The bar can rotate along an axis through its center of mass (the rotation is in the $x$-$y$ plane), and also can move up and down (in the ...
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Is gravitational potential energy proportional or inversely proportional to distance?

We know that if an object has been lifted a distance $h$ from the ground then it has a potential energy change: $$\Delta U = mgh $$ so $h$ is proportional to $\Delta U$. However, we have also the ...
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299 views

Why can't the work done by a non-conservative force be zero?

Why can't the work done by a non-conservative force be zero? The displacement along a closed path is always zero. So, whatever be the type of force, variable or constant, the work has to be zero. Why ...
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28 views

Variation of Electrostatic Potential with Distance in a Uniform Field

I came across this question in a problem book: If a proton is released from rest in a uniform electric field, does the electric potential at those points where the electron moves increase or decrease. ...
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239 views

About mass defect

Here's how my book explains mass defect: Particles inside the nucleus interact with each other - they feel attraction. The potential energy $U$ of such attraction is negative, because in absence ...
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1answer
44 views

Sign of gravitational force

I'm reading Lanczos's The variational principles of mechanics, and on pp. 80-81 there is an example involving a system made up of $n$ rigid bars, freely jointed at their end points, and the two free ...
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Why don't we consider electrostatic energy of the pair in the case of pair production?

I have seen this Wikipedia article and many others, but in none of them I find any mention of the electro-static energy of the generated pair. Why? I mean, the energy conservation should be written ...
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Work done by magnetic field on magnetic dipole

In the above slide, it reads that $W=\int\mu B sin(\theta)d\theta=\mu B cos(\theta)$. But, I thought that $\int\mu B sin(\theta)d\theta=-\mu B cos(\theta)$ by some calculus calculation. Can ...
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Who of these cyclist travel takes less time? [closed]

There are two cyclist. They start off with equal velocity $v_0$. The first one bikes a straight path, while the other bikes through a valley, something like this: We assume friction doesn't affect ...
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Conservation of energy and the 'crazy ball' product

Well I'm not sure how many people remember the crazy ball - a small ball made of rubber which bounced like crazy. What I noticed is that the ball seemed to bounce higher than the point from which it ...
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1answer
74 views

Finding the Shape of a Hanging Massive Wire

This came from a physics wave book. I have a static, massive wire on the x-axis, with a y-displacement due to a force per unit length $F_y$. I start with the equation $F_y = ...
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Finding the components of the tensor for potential and kinetic energy

I have a rather poor understanding of what a tensor is, but enough to apply it to the biggest part of the classical mechanics I'm studying. However, I've run into a small problem while studying "Free ...
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Double pendulum find first integral [closed]

Consider the following situation of a double pendulum in 2D. We found the moving equations as $$ \ddot{\theta_1}=-L_1\sin\theta_1 + \frac{m_2}{m_1}\cos\theta_2\sin(\theta_2-\theta_1),\\ ...
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Potential at Center of Earth

If using the surface of the earth as a reference point how much work is needed for gravity to pull me to the center. Is it negative infinity or am I wrong? Also is a single value of potential ...
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Questions regarding rubbing catfur on glass

I have certain questions regarding the electrostatic charge developed by this rubbing effects: 1-what is the threshold for electrostatic charges by this process? 2-can we define potential energy ...
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114 views

Gravitational potential energy negative?

Can the gravitational potential energy be negative? $PE=mgh$, we kind of have the same fig as this (minus the car)! and we choose the arbitrary point to be the G of the pendulum (point of ...
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Infinite chain of alternating charge

The problem There is an infinite chain (1d) of alternating charges that are in a distance a from each other. That is there is one charge +q and next to it -q and so on. Now calculate how much work it ...
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93 views

Rotational Potential Energy of a Hamster Wheel

Background (unimportant back story)A colleague of mine showed me what i considered flawed statistics, that Internet Explorer had faster Index and array functions than Chrome(we are software ...
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Why does a system try to minimize potential energy?

In mechanics problems, especially one-dimensional ones, we talk about how a particle goes in a direction to minimize potential energy. This is easy to see when we use cartesian coordinates: For ...
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Statements about gravitational potential energy contradicting intuition?

So in my textbook I am told: two masses have gravitational potential energy because work had to be done in order to move one the masses form a position very far away (lets say infinity) to the ...
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104 views

For an object at rest is the potential energy completely zero?

It is said every object in this universe tends to be at their lowest state of potential energy. What can be the lowest state of potential energy? And can the potential energy of an object be 0?
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Bending of a spline

The introduction section on this page states: "the spline will take a shape that minimizes the bending", while showing the formula for curvature of a real curve. Question is, what is the formula for ...
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Where does the potential energy associated with the field go if it is removed? [closed]

I have an electric field and a certain charged particle in it that has a certain potential energy associated with it. Where does the energy go if I remove the field?
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How do you know which way to choose the limits of an integral?

I am reading http://www.feynmanlectures.caltech.edu/I_13.html#Ch13-S4 In the beginning of equation 13.18, in which Mr. Feynman calculates the potential energy of an object outside a spherical shell, ...