Questions tagged [potential-energy]

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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Energy stored in a field - isolated system

If I consider an isolated system, e.g. two masses, i know I can apply the energy conservation principle considering the kinetic energy and the gravitational potential energy of the two masses. But to ...
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Is the strong potential repulsive for high distances?

The negative region in a potential is attractive and the positive region is repulsive. At least in case of the coulomb potential: When having a look at the strong potential it is obvious that the ...
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Role of the Yukawa potential

What is the Yukawa potential converging to zero? Afaik the strong potential rises with the distance between quarks, hence, it should rise accordingly.
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Kinematics problem, only energy related approach [on hold]

I read this question: From the top of a tower, a stone is thrown up and it reaches the ground in time $t_1$. A second stone is thrown down with same speed and it reaches the ground in time $t_2$. A ...
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Why is there a 1/2 in the expression for electrostatic energy U?

The expression for electrostatic energy is $$U= \dfrac{1}{2} \times \int \rho\,\phi\, dV$$ where $\rho$ is the charge density and $\phi$ is the potential at that point in ($dV$) Let me explain what I ...
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How to solve for stable/unstable equilibrium in this question [on hold]

A solid cube of side b is at rest on curved surface of a cylinder(horizontal axis) of radius R. Assume no slipping. We have to derive condition for stable equilibrium. My approach: Slightly we can ...
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Infinitesimal Perturbation in a potential well

If I calculate $<\psi^0|\epsilon|\psi^0>$ and $<\psi^0|-\epsilon|\psi^0>$ separately fro two different intervals, viz. 0 to $\Delta$ and from $a-\Delta$ to $a$ and then add, the ...
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Work Done and Potential Energy in Electrostatics

This is a question from class 12 Physics NCERT Part 1: I am having so much trouble with this, I can't figure out where I'm going wrong. I solved part (a) here: (a) U= -27.2 eV (b) Here, the kinetic ...
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Components of Electrostatic energy to components of electric field?

I'm trying to understand the relationship between electrostatic energy and the electric field so that I can compute electric field components from electrostatic energy components. Is it correct to ...
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How does an object gain energy when it enters a potential field?

Conservation of energy says total change in energy is $0$. Let's assume a small object is in outer space (maybe like a football). It moves towards a planet (assume planet has no atmosphere for ...
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Potential Drop across Inductor VS Potential drop across Rotating coils in $B$-Field

I was trying to understand the difference between the Back emf generated across Inductor due to change in current and Back Emf Generated across a coil that is rotating in presence of B Field. ...
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Energy stored in a sphere of variable charge density

I have seen a derivation of the energy stored in a uniformly charged sphere. However, I would like to generalize this derivation to include a variable charge density (varying with radius). The ...
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Why can't $U=b\mathbf{v} \cdot \mathbf{r}$ be considered a potential for the drag force ${\bf F}=-b {\bf v}$?

Consider the function $U(\mathbf{r},\dot{\mathbf{r}})=b\mathbf{r} \cdot \mathbf{v}=bx\dot{x}+by\dot{y}+bz\dot{z}$, where $b$ is the drag coefficient. Why can't this be considered as a potential energy ...
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Transmission coefficient in step potential [closed]

I am calculating the transmission coefficient from a scattering wave coming from $-\infty$ into a step potential given by: $$ V(x) = \left\{ \begin{array}{cc} 0 & x\leq 0 \\ V_0 &...
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Manev potencial and some problems with it [closed]

Given the Manev potential by the equation below $$\ V_M(r) = - \frac{-mMG}{r} \left(1 + \frac{\gamma MG}{c^2r}\right) $$ in which: M is the Sun's mass; m is the planet's mass; G is Newton's ...
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Is mass slowly destroyed when force of gravity is applied? [duplicate]

This may seem like a far fetched idea, but consider this system. Imagine a simple system of just the Moon orbiting around the Earth, creating low tides and high tides with its gravity. Now imagine ...
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Why am I getting a negative sign in this derivation?

I want to derive a formula for calculating the final velocity of an object that falls from rest as it reaches the surface of the Earth. I want to take the change in acceleration into account and hence ...
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Can I use the expansion of the universe to create or destroy energy?

Imagine I have a setup like this: (The objects are not attached to each other. The red objects are much heaver than the black one, and the setup is balanced.) This setup has a non-zero ...
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From a potential energy equation, how can we determine whether or not the particle undergoes circular motion?

(I realise this may be considered a homework question but I have read the rules.) I'm working through an introductory book on classical mechanics and there is this question: Consider a particle of ...
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The pair potential different that $r^{-1}$

As I know, the potential between two particles of the form ~ $r^{-1}$ ($r$ is distance between particles) is special, because it solves the Poisson's equation in 3D. My question is: If I consider for ...
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Can a cat be non-Lagrangian?

It is obvious to regard a cat to a system of masspoints (particles) with forces acting between point-pairs satisfying Newton's third law, and assuming that these forces can be arbitrary functions of ...
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Reference request: Langevin dynamics of particle in high dimensional quenched random potential

I would like to have some reference (either papers or books) for the study of the Langevin dynamics (out of equilibrium, non asymptotically) of a particle $X(t)\in \mathbb{R}^N$ in a quenched random ...
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Potential energy of electric dipole

While deriving the formula for potential energy of electric dipole I almost every time see that while the torque was demanding the dipole to rotate in one direction , we let the dipole to rotate in ...
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Potential barrier, vertically shifted

I'm attempting to solve the 1D Schrodinger Equation, approaching a potential barrier defined as follows: $$V(x) = \begin{cases}-V_0&\quad\text{for}\quad x<0 \\0&\quad\text{for}\quad x>0\...
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What's wrong with this argument that the potential energy of an arbitrarily heavy object at arbitrary height is $0$?

Consider an object with mass such that there is a gravitational force downward of $1N$. Also assume the environment is a perfect vacuum. Now assume that we exert a force of $1+\epsilon $ Newton upward ...
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Potential Energy Graph for Nuclear Force

when you draw PE energy graph wrt to distance between two interacting nucleons, at distance $r$ around 1 fm, graph has the lowest PE and is point of stable equilibrum. For $r >$ around 1fm, nuclear ...
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Is there a need to consider the relativistic mass when calculating gravitational potential energy?

The equation for gravitational potential energy is: $$V(r) ={GMm\over r}$$ In the reference frame where $M$ is stationary. I am wondering for mass $m$ here do we need to consider its relativistic ...
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Solution Cahn-Hilliard 1d for a domain of finite size

I'm trying to get the solution of the Cahn-Hilliard equation in 1d with a certain mass $C$. We have two components, and let's assume we have the relation $c_1+c_2=1$.Hence we take only the variable $c=...
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What is the work done in bringing a charge from infinity to the location of another point charge?

Consider a positive charge $Q$ at the origin.What is the work done in bringing a unit positive charge from infinity to zero. We know that the work done in bringing the charge from infinity to $r$ is ...
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Regarding the definition of the electrical potential energy

Let us say we have two charge positive $q_{1}$ and $q_{2}$ very far away from each other. Suppose also that $q_{1}$ is stuck in its place. If we want to bring them closer to some distance $b$ apart, ...
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Potential energy of an object (with non-negligible size compared to distance from ground level)

Let's say I have a cylindrical water tank (with area $A$ and height $h$), and the bottom of the tank is $H$ meter from the ground. So what is the potential energy of the water tank? If the $h$ is ...
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Potential and potential energy

I know when a negative charge moves in the direction of a uniform electric field its potential energy increases and its potential decreases. For example, its potential energy changes from $0.9\ \rm{mJ}...
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How does gravitational potential energy work in Relativity?

According to relativity, the universe is expanding, at an accelerating rate. Far away planets and stars will soon leave our observable universe. But as planets and stars leave our observable universe, ...
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Where does the energy used to fight gravity go?

Imagine the following scenarios: A. We have a spaceship at x distance from a star. It faces directly away from the star, and fires its engines such that it ...
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What is in physical term meaning of penetration of a potential barrier?

While solving the quantum mechanical case of potential barrier meaning - $$\text{E} <\text{V} $$ The transmission coefficient is nonzero. My problem is what is happening with particle motion Has ...
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Why internal energy in Lagrangian is treated as a potential energy?

To obtain Euler fluid equations of motion one can do variational principle on the following Lagrangian density where $\rho_0$ is reference density, $\Phi$ is displacement vector field and $u$ is ...
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Definition of non-conservative force [duplicate]

In defining conservative force, we say that "The potential energy difference is path independent." However, as far as I understand, potential energy only exists when there is a force field. ...
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The sign of $d\mathbf{r}$ when integrating the universal gravitational force in order to define gravitational potential energy [duplicate]

I am trying to find gravitational potential energy by integrating the gravitational force: $$\mathbf{F}(\mathbf{r}) = - \ G \frac{Mm}{|\mathbf{r}|^2} \ \hat{\mathbf{r}}$$ where $\mathbf{r}$ is the ...
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Mechanics of a particle problem (potential energy vs. work approach)

I'm trying to reconcile two methods of approaching a problem, see picture below: Disregarding the angle of the surface and any friction, calculate the velocity $v$ of a particle pulled back a ...
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Elastic (Young's) modulus and shear modulus derived from interatomic potential

Based on figure shown here, a theoretical elastic modulus can be derived by considering the interatomic potential and taking the derivative of the potential energy with respect to the distance (x-...
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Lagrangian, central forces and conservation of angular momentum [duplicate]

When studying central forces it is possible to propose the Lagrangian: $$ L = T-U=\frac{1}{2}m \dot{r}^2+\frac{1}{2}mr^2 \dot{\theta}^2 - U(r)$$ Then we can solve the equation of motions for $\...
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Heating a ball tied to a string so that its potential energy decreases as Center of mass goes down

Suppose I have a ball hanging from a thread and I start heating it. The ball is tied from the upper end and as the ball starts to heat it expands and ultimately its centre of mass which is the centre ...
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Collision of particles [closed]

I read in a book that in both elastic and inelastic collision, the interacting forces after the collision become effecitively zero, the potential energy of the system remains the same both before and ...
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Why definition of potential energy and law of conservation of mechanical energy is misleading several times?

I regularly see 1 or 2 questions on this website about the definition or application of potential energy.The users fundamentally ask the same thing in every question. What I have learned till now is:-...
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In a circuit having one resistor why do the electrons lose all their potential energy across that resistor and not do so if there are many resistors

In a simple circuit which consists of a battery and one resistor, why do electrons lose all their potential energy across this one resistor regardless of the magnitude of the voltage or the resistance?...
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How does the battery do work on the electron although the speed of electrons is constant

In a simple circuit how does the battery do work on the electrons of the wire although their speed is constant . Imagine I want to take a body which has 5 Newtons weight from the ground to 10 meters ...
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Does increasing the length of wire increase the work (energy) needed to move electrons from the negative terminal to the positive one?

Imagine a circuit which consists of a battery and a resistor with a certain wire length. Suppose that the batter supplies 9 Volts. I know that it is the electromotive force which pushes the electrons ...
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Electric potential energy in a system

According to my notes, electric potential energy of a charge at a point is the work done in bringing a charge from infinity to that point. So say, two electrons are brought from a point that's far ...
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Is net work always equal to the change in kinetic energy?

I know that $$W_{net}=\Delta K\tag{1}$$ However, I don't know if this is only true in a system where only kinetic energy is present, or if it's also true for a system in which there's potential ...
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Allowed energies for a particle inside potential barrier

The allowed energies for a particle inside a potential well are discrete ones, and for a particle outside the well, the energy specrum is continuum. But what for a particle inside a potential barrier? ...