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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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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41 views

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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362 views

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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31 views

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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65 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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2answers
54 views

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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330 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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78 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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116 views

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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69 views

Food calories vs gravitational potential energy [on hold]

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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28 views

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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1answer
24 views

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
63 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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565 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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105 views

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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1answer
47 views

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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79 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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44 views

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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1answer
79 views

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 $$ ...
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504 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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65 views

Simple harmonic oscillator, calculate the trajectory in real space

Potential of a simple harmonic oscillator: $$U=\frac{1}{2}k x^2$$ I'm asked to calculate the trajectory of a particle moving in this potential, with initial conditions $x(t=0) = 0$ and $v(t=0)=v_0$. ...
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How come we talk about gravitational potential energy and not gravitational potential?

With regards to gravity the equation learned is $$U=-\frac{GMm}{r}$$ And the relationship to force is $$F=-\frac{dU}{dr}$$ In electrostatics we instead talk about electric field and electric ...
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37 views

Calculating change in gravitational potential energy [closed]

A satellite mass $500\ kg$ is elevated from altitude $10000\ km$ to altitude $20000\ km$. Radius of earth is $6378\ km$. Mass of earth is $5.97 \cdot 10^{24}\ kg$. Gravity is given to be $9.81\ m/s $ ...
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67 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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43 views

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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163 views

Energy to reach the moon

I've been stuck on this question for a couple of days now. Given that the potential energy of a 930 kg object on the Earth's surface is -58.7GJ, calculate the minimum energy required for the 930 ...
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75 views

How to meaningfully describe the practical effectiveness of one large bomb versus a series of many small bombs, all else constant? [closed]

Background: Given two sets of conventional bombs (constituted of fuel which explodes by way of chemical decomposition reaction) : Set 1 - One shell of a given volume encasing a given amount of fuel. ...
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1answer
56 views

Picturing Feynman's argument about perpetual motion

So, there is a certain paragraph in Fenyman's book that I'm struggling with for quite some time. It says: "We imagine that there are two classes of machines, those that are not reversible, which ...
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Why airports are generally near sea? [closed]

The generic way to measure the height is from the sea-level. If the airport is near the sea i.e. not at a very height from the sea, then the fuel required to make the air-plane above the sea level ...
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Does a pulled rubber band contain as much energy as a twisted rubber band?

lets say I take two similar rubber bands. One of them I pull until it almost reaches its breaking point. The other I twist until it almost reached its breaking point. Do both of these rubber bands ...
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Is there a way to measure the energy stored in a twisted rubber band?

I am building an energy storage device using rubber bands. It contains 24 bands which are twisted by a set of gears. I would like to measure (or predict) the amount of energy that the device can ...
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71 views

Gravitational potential energy and Center of Mass

I've been reading about the Nordtvedt effect, and how Gravitational Binding Energy (GBE) affects total mass. According to the WP article, experimental evidence rules out the existence of this effect. ...
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1answer
39 views

Where does elastic energy come from?

I vaguely remember reading that the elastic potential energy of a spring, $\frac{1}{2} k x^2$ comes from mass which is turned into energy according to the law $E=mc^2$. I also remember hearing that ...
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62 views

Bound states, scattering states and infinite potentials

I am doing my first semester of Quantum Mechanics and we're using Griffith's Introduction to Quantum Mechanics. As he is introducing the Dirac delta function potential he explains bound and scattering ...
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63 views

Why does the work done by an internal force differ from the work done by external force?

Let's consider the following situation. We put a body of mass $m$ at a distance $A$ from the center of Earth. We let the Earth attract the body and analyze the situation at a point $B$, closer to the ...
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25 views

Comparing work done for two accelerations

Suppose at a time $t_{0}$ a car goes from 0 to 30mph at time $t_{1}$, and then maintains a speed of 30mph until $t_{2}$. After that minute it accelerates, reaching 60mph at time $t_{3}$. I want to ...
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54 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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1answer
200 views

Derivation of formula of potential energy by a conservative force [duplicate]

the formula for potential energy by a conservative force is given by: $$ F = -\nabla U(r), $$ which in one dimension may be simplified to: $$ F = -\frac{dU}{dx} .$$ My question is how is it ...
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370 views

How does escape velocity relate to energy and speed?

I have several confusions regarding escape velocity. I am sure I am missing something(s) obvious or maybe I am taught wrong. Lets say we throw an object of any mass at exactly escape velocity of ...
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1answer
317 views

What is the cause of the large damage by atomic bomb?

I recently read in the Feynman Lectures that when the nuclei like that of uranium which are at the crucial level of balance between strong nuclear forces and electrical repulsive forces are taped ...
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109 views

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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1answer
46 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 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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312 views

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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48 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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71 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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283 views

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 ...