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 an object in spring

Suppose we have a vertical spring of spring constant $k$ and an object of mass $m$ is tied to it. If we stretch the object by a distance $x$,the work done by the restoring force is $\frac{kx^2}{2}$ ...
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Discrete Spectrum vs Continuous Spectrum and Bounded, Scattering States

Apolgies in advance if this is a confusing ramble and multitude of questions, I'm not quite sure how to articulate myself. I am currently reading up on quantum mechanics and seem to have confused ...
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Proof of principle of stationary action when the Lagrangian is not $L=T-V$

The principle of stationary action claims that the action $S$ takes a stationary value in a real system, where: $$S = \int_{t_1}^{t_2} L dt\tag{1}$$ and $L$ is the Lagrangian of the system. It can be ...
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Velocity- and time-dependent forces can not be conservative [duplicate]

I have already seen many posts about this specific question but in only a few of those mathematically rigorous answers were given. Unfortunately none of them are accessible at my level (first year ...
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Energy conservation in elastic collisions and pendulum [closed]

This is my solution but I couldn’t find $h$ in term of $V \rightarrow M_{1} V - M_{2} V = M_{2} V_{2} \implies V \left( M_{1} - M_{2} \right) = M_{2} V_{2} \implies \frac{M_{1}}{M_{2}} = 1 + \frac{V_{...
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How do we justify that potential energy in a spring is Galilean invariant (to the extent that Newtonian mechanics holds)?

A spring can store elastic potential energy by elastically deforming and moving its atoms out of their minima potentials. The atoms themselves can be modeled as balls connected by Hooke-like springs ...
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1. A 40-kg stone is dropped from a height of 150 meters. What is its PE and KE? a. at the top? b. at t= 1s? c. when it strikes the ground? [closed]

Can someone help me with this? I tried to get the kinetic energy but it's not really the right answer And no It's not a multiple choice
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How to understand critical points of the Brillouin zone, (in)direct bands of transition-metal dichalcogenides?

In the paper Optical and Excitonic Properties of Atomically Thin Transition-Metal Dichalcogenides, it is said: 'Such calculations indicate that the direct gap occurs at the high-symmetry K and K′ ...
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Where does the stored potential energy in a bar go, when I reduce the load acting on it?

Consider a deformable bar, fixed at one end and acted upon by a load P (gradually increasing), as shown, through a rigid plate attached to its end. At the end of loading, potential energy is stored in ...
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Energy stored in capacitor over time

I know that the maximum energy that can be stored in a capacitor is: $$ U = \frac{Q^2}{2\,C}\,. $$ What I am asked is to say how much energy was stored when half of the electric charge that could be ...
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Relative signs between interaction terms

What is the interpretation / meaning of relative signs between interaction terms in a Lagrangian density? (If there is none, are they even physically reasonable?) Example: Let $\phi$ be a scalar field,...
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Why is the gravitational potential inside a hollow sphere same as that of the gravitational potential on the surface of the hollow sphere? [duplicate]

Gravitational potential inside a hollow sphere is given by $$V(r)=\frac{-Gm}{R}$$ Why is it the same as the gravitational potential on the surface of the hollow sphere, which is given by $\frac{-Gm}{R}...
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Lagrange equation of motions for a particle moving in a surface in the presence of gravity

I have to model the dynamic behaviour of a particle solid in a gravitational field.It is for a control theory course. And my background in dynamics is not the greatest. The particle can move left and ...
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Does electric current flow from higher potential to lower potential or from higher potential energy to lower potential energy?

Here, $O$ is a field charge with a $+T$ charge. $A$ and $B$ are test charges with $+T_1$ and $+T_2$ charge, and they are fixed in place. Suppose the points at which $A$ and $B$ are situated are $P_1$ ...
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Is the mass of two vertically stacked blocks greater than when they're placed side by side?

At the end of this video on mass-energy equivalence, it's states that two blocks stacked vertically have more mass than when placed side by side because they have more gravitational potential energy. ...
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Why kinetic energy is called kinetic energy and not potential even though it has a potential to do work?

I lift a block of mass $m$ by a height $h$ in gravitational field. I have done a work of $mgh$ on the block. This energy is stored in the block when it is at height $h$. At height $h$, the block has ...
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Deformation of gradually applied load vs impact loads?

When a load P is applied gradually on an object, the work done on it is the average of the initial and final loads, which is generally P/2 multiplied by the deflection Δ1. In the case of impact load, ...
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In general relativity, assuming a spherical uniform mass distribution, what is the total energy value of the gravitational field inside the sphere?

In Newtonian mechanics, assuming a spherical uniform mass distribution, the total gravitational potential energy (gravitational self-energy) inside the sphere is $$U_{gs}=-\frac35\frac{GM^2}R.$$ In ...
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What would be the outcomes in this arrangement? would potential varies along a conducting wire? [closed]

Two conducting solid sphere,one with charge Q1 and radius R1 and the other with charge Q2 and radius R2 are kept far away $$Q_1=5Q_2 \text{ and } R_1=5R_2 $$ If these spheres are connected with ...
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Is energy infinite in an electric field?

Energy is defined as the capacity to do work. Work in turn is defined as force x displacement. An electric field exerts the field in all directions infinitely (even though the strength of that force ...
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Using Variation of Energy for a Dielectric to define the Electric Field

I have been reading through Zangwill's Modern Electrodynamics on my own, and I am confused about something in section 6.7.1, concerning the variation of total energy $U$ of a dielectric in the ...
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Work done on a probe

When moving a probe from the radius of a planet to a new orbit of radius 2R, do we find the work done by subtracting the final potential energy from the initial potential energy? That would give GMm/...
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How to Derive Potential Momentum?

The only derivation/definition of potential momentum I've seen is using the fact that: $$E^2-p^2c^2=m^2c^4$$ And if you add a potential, you must subtract something else from the momentum called the ...
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Where should I apply the harmonic spring function in the case of polymer simulation?

I need to simulate the off-lattice movement of a polymer chain in a 3D space using Monte Carlo simulation. Note this is not a simulation of polymer growth; rather this is about polymer movement/motion....
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Does the 'internal potential energy' (created by charge separation) of a dipole have any physical meaning?

If you have a dipole with charges $Q_+$ and $Q_-$ separated by a distance $d$ you could calculate the work done of separating these two charges the distance $d$ $$ \Delta U = q \Delta V = - \vec{F} \...
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Infinite gravitational potential question

For this question I use Newtonian gravity only. Relativistic gravitational/kinematic effects are ignored. It is known that the gravity surrounding a point particle of mass $M$ can be described by ...
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Potential Energy defined for internal conservative forces

Will potential energy be always defined whenever internal conservative forces come into play? for example in case of electrostatic interaction between two charged particles potential energy is defined ...
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Cyclotron: why is there no work during the polarity shift?

From what I understand, the point of cyclotrons is to accelerate charges without requiring a huge potential difference: e.g. to accelerate a proton to 10 MeV, instead of using a single 10-megavolt ...
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Potential energy for uniform sphere doubt

For a sphere of radius $R$, with electric charge distributed in uniform way $\rho=Q/V$, we have $$U_e=\dfrac{3K_CQ^2}{5R}$$ However, when substituting the charge $Q=\rho V=\rho 4\pi R^3/3$, we get $$...
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Spring attached to a block [closed]

CONCEPTUAL DOUBT: Consider an ideal spring of length $l$, one end of which is fastened to a wall and the other attached to a block. Take the spring as the system. Now as the block is elongated by a ...
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A block starts from rest at the top frictionless slide at a height $h_1$ above the ground and leaves the slide perfectly horizontally

A block starts from rest at the top of a frictionless slide at a height h1 above the ground. The block leaves the side moving perfectly horizontally at a height h2 above the ground. The block ...
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Why gravitational potential away from a planet increases?

textbooks---- "potential increases towards infinity and is maximum at infinity" But that is true only when we are seeing potential w.r.t Earth EXPLANATION--------- So , as we know that ...
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Would it be correct to interpret $\hat{A} V \neq \hat{A} \hat{V}$?

Define $V=V(\mathbf{r})$ as the potential function, $\hat{A}$ is some differential operator, then for an arbitrary function $\psi$ $$\hat{A} \hat{V} \psi \iff \partial (V\psi) $$ whereas $$\hat{A} V\...
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Potential energy in Schrodinger eq

In the Schrodinger eq what does potential energy $V$ mean? In harmonic oscillation, it is the potential energy of the particle itself. However, At potential well, it looks like the potential is an ...
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Convert horizontal wind movement of a swaying tree into vertical movement under the tree

How to efficiently convert the horizontal wind movement of a swaying tree into vertical movement under the tree? One way I can imagine is by tying a rope to a point in the ground some distance from ...
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Why didn't we account for kinetic energy of two stars in conservation of mechanical energy

Two stars of masses 3×10^31kg each, and at distance 2×10^11m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star's rotation plane. In ...
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Decrease in average kinetic energy at Lennard-Jones phase transition

I have written a molecular dynamics simulation to model argon using the Lennard-Jones potential. I am investigating the behaviour of the system near it's melting point for a specific pressure and ...
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Intuition behind gravitational potential

Gravitational potential at a point is equal to work done in bringing a unit mass from infinity to a particular point That was the text book definition $$V_{p} = -\frac{GM}{r}$$ If we calculate $V_p$ ...
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Change in gravitational potential energy when the work is zero

I may be misunderstanding the whole concept , but my doubt is this. Let us say there is an isolated system comprising of a rock and the Earth. If I was to lift the rock up with a force equal to the ...
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Coulomb potential vs Coulomb potential energy

I know that the Coulomb potential in a hydrogen atom is $V(x)=\frac{-e^2}{4 \pi \epsilon_{0} r}$. Usually the potential is given by the potential energy divided by the charge, so I would expect $V(r)=\...
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Nearest Neighbor Entropy Estimate Differentiation

I am interested in differentiating an effective potential based on the following nearest neighbor estimate from [1]. $$H_n = \frac{1}{n}\sum_{i=1}^n \ln(n\rho_{n,i})$$ where, $$\rho_{n,i} = min_{j \...
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What is the meaning of external work in electric potential?

We learned that $$-Work = \Delta U = q(Va-Vb).$$ However, we write that $$W = q(Va-Vb)$$ in this question. Why don't we write the minus sign in the equation? How does external work affect the minus ...
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Different result when deriving electric force as $dW/dr$ and $-dU/dr$

Work done by electric field, $W$ is the negative of the change in electric potential energy, $U_r$. $$W=-\Delta U$$ By considering an infinitesimal change in EPE, we can deduce that electric force, $...
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Magnetic potential energy solenoid explanation

When the solenoids magnetic field is disaligned completely with the external magnetic field, it is said to have a higher potential energy associated with it. This makes sense since there is a ...
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Why does gravity seem to get energy out of nowhere?

Most of the forces have an end point. A positively charged object, when it touches a negatively charged object, becomes neutral and stops attracting other negatively charged objects. We need energy to ...
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Why does the incline angle not affect how high a launched object will slide up a frictionless ramp?

I am seeing a problem with the solution given in this book. How did the height of the box have nothing to do with the incline of the ramp? Intuitively it would seem the higher the incline the higher ...
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Can you use the water flow exiting a hydroelectric generator to generate more energy?

In videos of hydroelectric generators I often see that the water that exits a turbine is still moving with significant velocity. Example of a turbine that has exit water flow with significant velocity:...
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What is the relation between potential energy and the no. of charges travel from one place to another?

if potential difference is just a quantity which tells us about how much more energy is needed by the particle to travel from one place to the other then how does the increase in potential difference ...
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Intuition for the negative sign of gravitational potential energy

The gravitational potential energy is introduced to us as $U = mgy$. We usually set $U = 0$ on ground level and hence, for an object at height $y$, we have a potential energy equal to $U = mgy$. I ...
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How to use the equations for electrostatic work?

I was reading Griffith's Introduction to Electrodynamics (3rd ed.) when I stumbled upon two equations. In electrostatics, the work required to move a charge $q$ between two points with different ...
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