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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Understanding parallel plate capacitors [on hold]

I need help with understanding this assignment. I originally though of using the equation of Eo*A/D = Q/ΔV but I don't know how to answer this without actual numbers to plug in besides the epsilon-not ...
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Where Potential increase gets it's energy from?

Imagine there are two particles: A,B; of which, we observe A to be stationary, while B is moving towards A at velocity v. A,B has same mass; and they are charged both positive. B has a potential wrt ...
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is the potential energy of a black hole infinity

It appears like black holes posses an escape velocity greater than the velocity of light. It takes an atom infinity energy to travel at speed of light.Do black holes posses that energy to retain ...
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40 views

How does the gradient operator pick up a minus sign when the reference frame is switched from one particle to another? [on hold]

A potential between two particles, $i$ and $j$, is given as a function only of the separation distance, $$V_{ij} = V_{ij}(|r_i − r_j|)$$ It should follow that the force by $j$ on $i$ is equal and ...
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Gravity well and constant total energy in circular orbit [on hold]

According to this question, the total energy of an object in a circular orbit in a $1/r^2$ potential does not depend on the radius of the orbit. However, if you look at "circular orbits" in a gravity ...
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41 views

Why the force acting on a particle is the negative gradient of a scalar potential? [closed]

For conservative forces we can proof that it is a gradient of a scalar potential, but why we use the negative sign? In every book I searched, it said that it is like an agreement between physicists, ...
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How to efficiently cool down simulated gas by time-dependent potential?

I'm trying to simulate condensation of a highly diluted gas (a model gas, not any real one). For simplicity I restrict the simulation to 2 dimensions. To setup the simulation I take some interparticle ...
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1answer
45 views

How can energy be negative in a finite square well?

Say if the potential $V(x) < 0$ in the well but the sides or the scattered states its zero potential, anyways How is that the energy in the well is less than zero? Is it because the potential ...
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Confusion with $F=-\nabla V$, $F$ conservative

I am rather confused by the relationship $F=-\nabla V$. If a pen drops from a height it loses potential energy so $\nabla V$ is negative. From the above equation this means that the gravitational ...
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24 views

Mechanical energy of a body

What is the total mechanical energy of an air-plane flying in the sky? Does it possess both kinetic energy and potential energy,taking the zero potential energy at ground? As it is moving it will ...
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98 views

Charging by induction [on hold]

When we charge an conductor by induction and grounding, we first bring a negative charge to the conductor. As a result the mobile electrons of the conductor get repelled and stay far from the negative ...
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53 views

Equivalence between principle of least action and minimum potential energy

Are the principle of least action and the principle of minimum potential energy equivalent? How does one show that? Also, are Newton's laws of motion equivalent to the principle of least action? How ...
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38 views

Why is the potential energy minimal when the repulsion and attraction force between molecules is 0?

According to this potentialcurve and the other curve(?) the potential energy is minimal when the intermolecular forces equal zero. Why? How should I interprete negative potential energy in this ...
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32 views

How does potential energy relate to kinetic energy on a rollercoaster?

This is appearantly how the potential and kinetic energy are in the different positions of the rollercoaster, if I am not mistaking. However I don't understand why the total energy is energy and ...
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24 views

Electrical energy in a piezoelectric material

How do we define the electrical energy stored in a piezoelectric material? I'm confused about both the naming and the meaning. Are "electrostatic energy density", "dielectric energy density" and ...
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59 views

Why are the allowed energies a continuum in the region $V_{\_} < E < V_{+}$?

I'm studying quantum mechanics and I don't quite understand why there's an energy continuum in the region $V_{\_} < E < V_{+}$ in the following example: It was explained that because of the ...
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1answer
52 views

Gravitational Potential Energy misunderstandings [closed]

I'm really confused by the derivation of Gravitational Potiential Energy. I took a screenshot of the wikipedia entry below. My major confusion lies in: 1. The use of the position vector r in the ...
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23 views

Sign of elastic potential from a spring [closed]

When writing the Lagrangian of a problem, how do I determine the sign of an elastic potential from a spring?
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34 views

Gravitational Potential Energy to Kinetic Energy Confusion

Say there is an object being dropped from a distance. I can calculate the GPE of that object using $GPE = mgh$. As the object falls, the gravitational potential energy is converted into kinetic ...
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58 views

Why is there potential Energy due to lifting an object or moving when it's attached to a spring while the net work is zero?

Consider that you lift an object a height h vertically, if the body happens to move with uniform velocity this means that net force acting on it is zero. The same is true for a body attached to a ...
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69 views

To derive the relation between work function and potential energy

I'm reading "The variational principles of mechanics- Lanczos", The author mentions a relation between Work-Function $U(q_1,q_2,\cdots,q_n,\dot q_1,\dot q_2,\cdots,\dot q_n)$ and the potential ...
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Why don't they use springs as an energy source for cell phones?

I know they used springs for clocks way back in the day and now it's all lithium ion batteries. For reference, consider the Iphone that has a battery with a capacity of 5 Watt hours (18,000 joules). ...
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168 views

How to show period is defined by $T=dS/dE$ (V.I. Arnold Mathemtical Physics)

I'm looking at a book by VI Arnold on mathematical physics and I've hit a roadblock pretty early on. I'll quote the question: "Let $S(E)$ be the area enclosed by the closed phase curve ...
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Why are gravity and spring-force conservative forces?

I know that the amount of work does not depend on the followed path but on the position when speaking about conservative forces. But could someone please prove/explain why exactly those two are ...
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Why can't we define a potential energy for a non-conservative force? [closed]

We could define potential energies for non-conservative forces too and then we could conserve it with kinetic and potential energy as we know it. But no one does that. Why is this? Please explain. Any ...
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45 views

Spring Potential Energy [closed]

A spring whose spring constant is $k$, having an initial "free" length is $l$, is being pressed by $2$ hoops on a metal(the parabola) on his both sides. (see image below) I want to calculate the ...
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Why does the gravitational potential energy decreases as balloon filled with hydrogen ascends up?

As body ascends height increases from the formula $mgh$ the increasing height should increase magnitude of P.E. but some say we should take height negative as it is going up against gravity.
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Why is the potential independent of the generalized velocity?

In Goldstein, Classical Mechanics, Chap. 1.4 we derive Lagrange's equations from D'Alembert's Principle. My question is regarding the last part of the derivation, specifically the part where he ...
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62 views

Potential energy in gravitation

The gravitational potential energy of a two particle system is: $$ U = -G \, \frac{m_1 \, m_2}{r} $$ where $r$ is the distance between the two particles with mass $m_1$ and $m_2$, and the potential ...
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40 views

Hamiltonian average of energy of two stationary states

In quantum mechanics, the description of the infinite square well is given with the potential energy defined as $$V(x) = \begin{cases} 0 & \text{if } 0 \leq x \leq a,\\ \infty & ...
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How much energy does an electron have when it is situated right next to a negative point charge?

The formula for potential energy regarding point charges is $E=kQq/r$. If $r=0$, then will the energy be approaching infinity? But what about an electron in a parallel-plates situation where it is ...
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Infinite square well physical interpretation

In quantum mechanics, the description of the infinite square well is given with the potential energy defined as $$V(x) = \begin{cases} 0 & \text{if } 0 \leq x \leq a,\\ \infty & ...
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Dilemma About Energy : Can You EXPLAIN? [closed]

PROBLEM 1 : A 2.14 kg block is dropped from a height of 43.6 cm onto a spring of force constant k = 18.6 N/cm as shown in fig:12-19.find the maximum distance the spring will be compressed. solution ...
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Transform QM radial equation to spherical Bessel equation

I'm currently learning about spherical potentials (ex. hydrogen and hydrogen-like systems) and am trying to work through the problem of a generic spherical potential well such as: $$V(r) = ...
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1answer
70 views

How much work can the human body do before dying of exhaustion [closed]

If we could assume: We don't increase our energy from absorbing food. Our human example in scope isn't starving or suffering from malnutrition. I mean how much work can we do until the body would ...
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1answer
39 views

Minimum energy required to remove the satellite from its orbit to infinity?

My book says that minimum energy required to remove the satellite from its orbit is equal to its total energy (K.E+P.E). But shouldn't it equal to only the potential energy difference of satellite in ...
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29 views

Why is the energy lost due to the internal resistance always equal to $(1/2)CV^{2}$ in a simple capacitor battery circuit? [duplicate]

Suppose we have simple circuit in which a battery of EMF $E$ is connected to a capacitor of capacitance $C$. Work done by battery $W_{b}=CV\times V$ and energy stored in capacitor ...
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Effective potential kerr solution

In Newtons mechanic we obtain $E=V_{eff}(r)+\frac{1}{2}mv²$ with $V_{eff}(r)=V(r)+\frac{1}{2} \frac{L²}{mr²}$ for the effectiv potential. The first equation is easy to interpret the total energy ...
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Odd question on potential energy [closed]

A particle with mass $m$ is acted on by a conservative force and moves along a path given by $x = A\cos\omega t$ and $y = B\sin\omega t$, where $A$, and $B$ are constants. Find the potential energy of ...
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What is exactly gravitational potential energy and explain P.E. $= -GMm/r$? [duplicate]

I was studying gravity and I came to know about $P.E.= -\frac{GMm}{r}$ which is derived by $GMm(\frac{1}{\infty} - \frac{1}{r})$ which the work done by the body to displace it from infinity to $r$. ...
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Deriving Kepler's First Law from Newton's Law of Universal Gravitation: Interpretation of the $u = 1/r$ change of variable

I'm working through a somewhat unsatisfying derivation of Kepler's First Law from Newton's Law of Universal Gravitation. The key to obtaining the equation of motion that you can solve lies in making ...
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Does really a spring compresses placed between two blocks when one block is given force on a frictionless surface?

When Spring is placed between two bodies on a frictionless surface it gets compressed when one block is given kinetic energy as told by my physics teacher. But it should not compress as there's no ...
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Electric Potential, Work Done by Electric Field & External Force

I did lot of searching but couldn't find any textbook nor any webpage which could clarify my doubt. Maybe my doubt is insanely stupid and I was dumb for not realizing it at the first place. The ...
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System of potential energy

Is potential energy calculated between a system? More specifically, if we say 'potential energy of a ball with respect to earth', does it mean that the Earth + the ball is a system?
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35 views

Capacitance question

A capacitors capacitance, C is equal to Q/V right? If Q was somehow cut in half, would the potential difference also be cut in half, since V is directly proportional to Q? And if so, Its C would be ...
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Is gravitational potential always defined for a system?

I have studied about Gravitational potential energy ($GPE$) and Gravitational potential ($GP$). ..while everywhere it is said that $GPE$ is always of a system as it depends on the configuration of the ...
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Integration path with opposite direction from the unit vector

The task is to calculate the voltage between points $M$ and $N$ if the electric field vector is known to be $\vec{E}=\frac{V_0\cdot x^2}{a^3} \cdot \vec{i} + \frac{V_0 \cdot y}{a^2} \cdot \vec{j}$, ...
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Energy forms of a charged particle in an electric field?

I am thinking an explicit list of all energy forms in a system of charged particle (take electron or proton, for instance). It has at least potential energy and kinetic energy by Newton. ...
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129 views

Defining gravitational potential

I recently came across the definition of gravitational potential where ..... Suppose a particle of mass $m$ is taken from a point $A$ to $B$. Let $U(A)$ and $U(B)$ denote the gravitational ...
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Finding equilibrium points in two dimensional potential [closed]

Ok so suppose I have a two dimentional potential. I want to find the stable and unstable equilibrium points and to decide which is which. So I know that I can derive them by finding the gradient of ...