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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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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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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43 views

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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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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Why is gravitational potential energy negative, and what does that mean?

I usually think of gravitational potential energy as representing just what it sounds like: the energy that we could potentially gain, using gravity. However, the equation for it (derived by ...
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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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Signs in proof of gravitation potential energy (GPE)

Proof of gravitational potential energy. Work done by gravity in bringing mass from infinity to a distance of $r$ between masses. When we use the integration formula and arrive at the answer we ...
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38 views

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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51 views

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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237 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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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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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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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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1answer
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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90 views

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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68 views

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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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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1answer
50 views

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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What is the most efficient machine for translating gravitational potential energy of one mass into kinetic energy of a different mass?

As the question states, what is our current best machine for translating falling gravitational potential energy, such as a large weight, into launching a smaller projectile vertically? A lever? A ...
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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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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 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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69 views

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 restore the potential energy? [duplicate]

How to restore the potential energy, of a particle with variable mass and variable coordinate, by сartesian coordinates and mass of the particle? ? Dimension - one dimensional. Data that is to ...
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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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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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3answers
112 views

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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44 views

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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1answer
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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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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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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190 views

In continuum mechanics, what is work potential in the context of total potential energy?

I'm reading a book on the finite element method. Specifically I'm looking at the background material where they are discussing potential energy, equilibrium, and the Rayleigh–Ritz method. The book ...
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129 views

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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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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42 views

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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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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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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1answer
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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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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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56 views

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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Shape of a string/chain/cable/rope/wire?

The height of a string in a gravitational field in 2-dimensions is bounded by $h(x_0)=h(x_l)=0$ (nails in the wall) and also $\int_0^l ds= l$. ($h(0)=h(l)=0$, if you take $h$ as a function of arc ...
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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 ...