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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Elastic potential energy and equilibrium position when mass changes in vertical mass-spring system

I'm a bit stuck with this situation: Suppose that an object $A$ with mass M=8 kg at 10 mt above the floor falls from rest tied to an 2 mt elastic rope, which does not exert any force since $A$ falls 2 ...
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Would this be a practical way to convert tidal energy into electrical energy?

Imagine a structure that is held above the water by pylons that are grounded on the ocean floor. In between these pylons is a pontoon that, when tides are rising holds and lifts a heavy weight. When ...
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Prove that gravitational potential energy of a body of mass m at a height h is mgh

Many introductory physics books just write that potential energy of a body of mass $m$ at a height $h$ as $U_g=mgh$. However, they never show how this was derived. I'm interested in knowing this ...
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How to find speed of rotation of gears from kinetic energy of falling body?

A pulley is fitted to the first driven shaft of compund gear train. Last driven shaft of gear train(gear 8) is fitted to the 12V DC generator (6W).Now to the rope extension at the one end of the ...
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Deriving the formula for energy stored in a spring without using geometry (determining the area under a curve)?

Using Hooke's Law, we know that the force applied is proportional to the extension of the spring. Therefore by plotting a graph of force against extension, through the area under the curve we are able ...
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Is this thought regarding work and potential energy correct?

I am really confused about this. The potential energy acquired by an object is equal to $mgh$, if we are on any planet, where $g$ is the planet's gravitational acceleration, which directly comes from ...
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65 views

Period on the phase plane (small oscillations)

I have this formula to calculate the period of a motion in the phase space (plan, in this case) along a phase curve. \begin{equation} T(E)=\int_{x_1}^{x_2}\frac{dx}{\sqrt{2(E-U(x))}} \end{equation} ...
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Energy of a body in circular motion?

I'm confused about energy of a body in circular motion. In particular I'm having trouble to find the correct answer to this question. Consider the body in the picture that is set in motion from ...
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22 views

Relation between gravitational field and gravitational potential

gravitational field is the negative differential of gravitational potential . now gravitational potential due to a particle at a distance r is -Gm/r where m is the mass of the particle . If i take the ...
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44 views

Electric Potential from separating charges [closed]

Say there are 2 charges, one of charge C, and the other with a charge of -2C. C=1.5*10^-6 C. Initially, they are right next to each other. I pull them apart to a distance of 15 cm. So I can use the ...
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1answer
77 views

Gravitational potential energy lost by an object falling on the earth [closed]

I am stuck on this simple question: g is the strength of the gravitational field at the surface of the Earth; R is the radius of the Earth. Show an equation describing the potential energy ...
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39 views

Potential Elastic Energy between two carts [closed]

I have a problem in which two carts are attached by a compressed spring. I have found that cart $A$ moves at $1.1~\mathrm{m/s}$ to the right and has a mass of $0.39 ~\textrm{kg}.$ Cart $B$ has a mass ...
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54 views

Calculating Potential Energy

I'm familiar with the potential energy equation, but I'm concerned with the value of 'g' in it. I know that, at sea level, earth's gravitational acceleration is 9.81 m/s/s. So I know that within the ...
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1answer
18 views

electric potential and other potentials

We know that without potential difference no electric current can flow.If two conductors carrying positive and negative charge respectively then the first one will have positive and the rest one will ...
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27 views

Does a potential of interaction produce also torque?

I have a system of particles (spheres with masses and radii), with $6$ degree of freedom (they are free to move and rotate as they wish). Between each couple there is an interaction potential $V(d)$, ...
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148 views

When we write that $F = -\nabla V$ , what would happen if we ommit the (-) minus sign

I have had this question for a long time. In classical mechanics, if we choose $\mathbf F = -\mathbf \nabla \, V,$ with the minus sign, we can proof the work - kinetic energy theorem. What are the ...
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125 views

Understanding parallel plate capacitors [closed]

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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182 views

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

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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1answer
45 views

Gravity well and constant total energy in circular orbit [closed]

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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46 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
133 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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130 views

Charging by induction [closed]

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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1answer
64 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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1answer
71 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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58 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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30 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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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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60 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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25 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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119 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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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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76 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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186 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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167 views

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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1answer
50 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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1answer
65 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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1answer
46 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) = ...