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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Final potential difference between plates of capacitor

If the plates of a parallel plate capacitor are given charges 4Q and -2Q . The capacitor is then connected across an uncharged capacitor of the same capacitance as first one (=C) . Now we have to find ...
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As distance increase why no change in electric field in parallel plate condenser [duplicate]

If the distance between the plates of a parallel condensor is 4mm and the potential difference is 60 volts. Now if we increase the distance between the plates to 12mm, then: Why the electric field ...
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Potential Energy for dipole in Electric Field

Potential Energy is the work done by the external agent in turning the angle of the dipole from the U=0 position to another position against the influence of the electric field applied right? So if ...
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258 views

Potential energy of springs and gravity, and work of a force

I am currently really stuck on this problem and I am not sure how to actually solve it, I think I can reason it out logically but I do not know how to show it. Here it is and under I will show what I ...
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34 views

Problem with derivation of potential enery of two body in Gravitational energy

Maybe what I'm going to ask sounds stupid but it means a lot to me that's why I'm asking. I've problem with just a single step in derivation. Let's start. I'm keeping in mind the direction of each ...
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38 views

Interaction Potential for Damped Driven Pendulum

I'm trying to use the velocity Verlet integrator to simulate a damped driven pendulum (with unit mass) described by $\ddot{\phi}+\gamma \dot{\phi}+\omega_0^2 sin\phi=Acos(\Omega t)$ The Verlet ...
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33 views

How to Explain the the following situation?

I have thought a simple thing: consider a system of a planet and its natural satellite revolving around it in a perfectly circular orbit(assumed) and this is happening in an isolated space in some ...
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1answer
61 views

Springs, elastic potential energy, kinetic energy

If a ball with some kinetic energy collides with a spring, the ball doesn't lose its kinetic energy in an instant, right? it loses kinetic energy as the spring gains potential elastic energy. Right? ...
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34 views

How is gravitational time dilation different from time dilation due to differences in speed? [duplicate]

This is what I understand from what I've been reading online: In the derivation for the gravitational time dilation equation, $$t = t_0\sqrt{1-\frac{2GM}{rc^2}}$$ we use the special relativity ...
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33 views

How to find potential energy(PE) of a system in order to write Lagrangian? Is there is any unique way to write PE for different system?

for simple pendulum or spring system its very easy . we use mgl and mgh. What I need is the unique way which will help to write PE to all the systems.
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36 views

Do the energies of cosmic rays approach infinite at the event horizon of a black hole?

Let's assume an observer orbits close to a black hole, he is not alone, massive cosmic rays, like electrons and protons and other kind of space dust comes from the outer space and may hit him. Since ...
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49 views

Force and energy relation: in case of time dependent force

The equivalent problems are also found in Marion problem 7-22, and other formal classical mechanics textbook. Here what i want to know why instructor solution and some websites gives this kinds of ...
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Center of mass problem

According to the definition of potential energy, we use $U= mhg . $ In the figure below , A thin uniform rod of mass m and length h is positioned vertically above an anchored frictionless pivot ...
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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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1answer
31 views

Why do molecules in a gas not generally arrange themselves at the distance of minimum potential energy (Lennard-Jones 6-12 potential)

As the title suggests, why is this? Is it because the distance of molecules in a gas is too large (compared to in liquids/solids)? Or are there other reasons for this?
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386 views

Schrödinger equation for many body systems

$$H_{tot}=\sum \dfrac{p_i^2}{2m}+\sum\dfrac{p_I^2}{2M_I}+\sum V_{nucl}(r_i)+\dfrac{1}{2}\sum_{i\ne j} \dfrac{e^2}{|r_i-r_j|}+\dfrac{1}{2}\sum_{I\ne J}\dfrac{z_Iz_Je^2}{|R_I-R_J|} $$ with: ...
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88 views

Basic Classification of Energy [closed]

When I was still in school, I learnt that there are 2 types of energy: Potential & Kinetic Energy. When I searched Wikipedia and other sources, there were many forms of energy. There are some ...
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27 views

Is it possible to determine how many electrons there are in a plate from its voltage?

We've just stared doing voltage in school, and so I wondered if this is possible :) If I charge an insulated metal plate using an EHT to something like 5kV, then I've added electrons to the plate. My ...
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44 views

Why did Trebuchet have so long throwing arms?

Have a look at such an historical Trebuchet: As you can see, the throwing arm (left) is much longer than the weight arm (right). Law of conservation of energy says, potential energy from the ...
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1answer
27 views

Electrostatics, System of Charges [closed]

At $t=0$, a positive point charge of mass $m$ is projected toward another positive point charge of mass $m$ in free space. At the instant of minimum separation kinetic energy of the system of two ...
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2answers
33 views

How to prove that the potential of a conservative central force depends only on the magnitude of the distance & not on the direction of the vector?

If a conservative central force acts on a body then its potential only depends on the magnitude of the distance between two bodies (does not depend on direction of vector). Is there any proof of it ...
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What is the zero of potential?

A satellite of mass $m$ is travelling at a speed $v_0$ in a circular orbit of radius $r_0$ around a fixed mass at $O$. Taking the zero of potential at $r=\infty$, show that the total energy of the ...
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1answer
266 views

Finding the components of the tensor for potential and kinetic energy

I have a rather poor understanding of what a tensor is, but enough to apply it to the biggest part of the classical mechanics I'm studying. However, I've run into a small problem while studying "Free ...
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1k views

How much energy can be extracted by lowering something into a black hole? [duplicate]

If an object is in orbit around a star, the object has gravitational potential energy that could possibly be extracted. For example, when we perform gravitational slingshots around Jupiter, our ...
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4answers
246 views

How is energy converted when massless spring is attached to a rigid support

Say a massless spring of length $l$ is attached to a rigid support. It is extended to length $l + x$. Now at this position, the force extending it is removed. How will its potential energy be ...
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2answers
940 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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39 views

Why we can use partial derivatives to tell if a force is conservative? [duplicate]

Let us, initially, analysis only a two dimension situation. Assume that $F(x,y)$ is a force dependent on the particle position (give by $x,y$) is proposed that if \begin{equation} \frac{\partial ...
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2answers
149 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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3answers
66 views

how could Kinetic energy increase if no energy was there in the system?

i was reading Physics-Halliday, Resnick, Krane(fifth edition) there on page 638 it is written: if the external agent does positive work in assembling the charge ...
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1answer
25 views

Why is force negative if PE increases?

I'm looking at the PE vs force graphs for gravity, and it doesn't make sense to me. As potential energy increases (and the object goes higher above the ground), F=-mg. But if I'm raising an object up, ...
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15 views

Where is the zero electric potential energy point?

Does the point of the electric potential energy of zero is defined by human or dominated by the indefinite integral of the electric force?
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55 views

Understanding potential energy

I am self-studying the classical mechanics using the book by Taylor, and I have a question about the potential energy. The book (pg 111) says: If all forces on an object are conservative, we can ...
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154 views

What does energy represent in $E= mc^2$?

Due to energy-mass equivalence, any object with mass can be said to have a corresponding amount of energy. So in a 5kg object there are 450,000,000,000 joules. A joule as I understand it is the ...
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30 views

What is the relationship between potential energy and electrical potential?

I actually always thought this was trivial, now I am not so sure. For a potential $\phi$ the potential energy is $V=q\phi$ where q is a test charge. Now I am thinking this may work differently in two ...
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23 views

Working with the problems related to potential energy

Consider a spring mass system. A block is attached to a light vertical spring which is stretched under the load of block and this system is at a height $h$ from the ground. Now my problem is ...
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131 views

If systems minimize their potential energy, why do people climb mountains?

A person climbs a mountain. They convert the stored chemical energy of food in their body and back pack into heat energy on the mountain, and gravitational potential energy as they move towards the ...
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Understanding electric potential in the context of gravitational potential?

I'm trying to understand the concept of electric potential and the significance of an electric field being related to the gradient/derivative of an electric potential. I found this question that ...
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1answer
159 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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2answers
67 views

Does contracted spring weigh more than stretched one?

(One of examples that potential energy contributes to mass.) Does hot object weigh more than cold one? (One of examples that kinetic energy contributes to mass.) If these are true and justified by ...
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450 views

Mass in special relativity?

Is the mass of a object at rest defined by $$E=mc^2$$ where $m$ is the rest mass. I.e. does the rest mass include every thing from thermal to gravitational potential energy and every other possible ...
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49 views

What is the difference between the potential difference and potential energy of an electron?

What is the difference between the potential difference and potential energy of an electron? Let's take an example the potential difference (PD) across a resistor. if there's a current flowing, the ...
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67 views

Whats the meaning of this equation relating electric field and potential energy?

My electrodynamics teacher was explaining that it is required to apply some energy (or do some work) on charges in order to arrange them in space. When he stated an example about energy in a capacitor ...
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19 views

Does a charge difference necessitate a potential difference?

Consider two metal objects, X and Y that when connected by a conducting wire results in a transfer of electrons from Y to X. What can be concluded about X and Y before the connection was made: ...
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21 views

Problem involving Energy Method and Non-conservative Forces [closed]

I've got a problem in my physics I class that's got me stuck at the moment. A box is placed onto an angled plane so that it compresses a spring. When released, how far up the plane does the box go? ...
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29 views

Trouble understanding non-conservative force and work

I am having some trouble defining whether a force is conservative or not. In the example that we are working on a mass on a pulley system is used to cause a slender bar to rotate from rest to a ...
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6answers
151 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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2answers
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Potential Energy of Point Charges in a Square [closed]

So, an AP Prep book for the Physics 2 test has the following problem: My reasoning is as follows: The total potential energy = the sum of the PE of each of the 4 charges Which will equal 4x the PE ...
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What is the physical meaning of potential energy in a band diagram of a semiconductor?

According to this slide (from this website), the potential energy of an electron in a semiconductor is defined by the difference between the Energy level of the conduction band and the fermi level. ...
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Why does positive work done by internal conservative forces $\implies$ decrease of potential energy?

Potential energy can be thought as the amount of work that the force can potentially do on the point because of its position. $$W=-\Delta U=U_{initial}-U_{final}$$ A positive work done by a force ...
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40 views

Energy diagram of a planet with fixed mechanical energy

Consider the following energy diagram for the motion of a planet about a star. The centrifugal potential curve can be represented once I fixed the angular momentum $\vec{L}$ of the planet. To fix the ...