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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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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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 $=\frac{1}{2}CV^{2}$...
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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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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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132 views

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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588 views

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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58 views

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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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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154 views

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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139 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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65 views

Potential Energy [closed]

I really need help with this homework question. I thought the function very stranger to be a function of a potential energy. It´s seems to be like Lennard Jonnes pontential energy function. Am I right?...
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55 views

What is the relation between ‘Electric Potential’ and ‘Electric Potential Energy’?

What is the relation between ‘Electric Potential’ and ‘Electric Potential Energy’?
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Potential vs Potential Difference for a line charge

How would I calculate potential for an infinite line of charge a distance 'r' away from it? What does the reference point for potential difference mean? I know delta v = Q/(2pi*epsilon0*L)*ln(r2/r1) ...
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95 views

Gravitational binding energy of 2D circle [closed]

I'm interested in calculating the gravitational binding energy for an object modelled by 2D circle for a small collision simulator. In the simulation, I'm using a 2D equivalents of 3D properties (e.g ...
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55 views

Finding the work done to fill the tank by pumping water over the edge? [closed]

I am really confused on how to approach the following question and how to set it up. So the question is: An open tank has the shape of a frustrum of a right circular cone. The tank is $4\:\mathrm{...
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106 views

Flow from higher potential region to lower potential region

In Thermodynamics, it is said that heat transfer takes place from higher temperature to lower temperature. Things having higher temperature have higher potential energy because of more vibratory ...
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211 views

Why do we never account for the extra mass carried by a gravitationally excited object?

The mass of a bound system is the mass of its part minus the binding energy. For instance if you put an electron and a proton together to form a hydrogen atom you get a $13.6 \text{ eV}$ photon and ...
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60 views

Why is a satellite's GPE negative? [duplicate]

Okay, so the formula for Gravitational Potential Energy (GPE) of satellites is: $$ U=-GmM/d$$ Mass and distance can't be negative, and $G$ is constant that is not negative. Why is a satellite's GPE ...
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103 views

How does the tension force of a massless string affect the speed of a mass on its end?

i,j, and k are the unit vectors in the following question, and $\omega$ is the angular velocity. Lets say you have a mass m attached to a mass-less string of length $L$ tied to a peg with no friction....
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127 views

Why does $\omega = \sqrt{V''(x_0) / m}$?

I know that in an equation such that $$\ddot{x} + \omega^2x = 0,$$ the angular frequency $ = \omega$. But why is that ever $ \sqrt{V''(x_0) / m}$? (where $x_0$ is the equilibrium point). I just saw ...
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Confused about potential energy problem

So I am trying to solve this problem: On spring hangs a 2 kg block. Spring stiffness coefficient is 400 N/m. How much spring expanded? My attempt to solve it: ...
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32 views

Work done when applying an electric field?

On these example questions from MIT in the solution to 4.1 they write the work done by applying the electric field to be: $$W=V_0 \int \vec E \cdot d \vec D$$ Where does this equation come from and ...
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How to compute Gravitational potential energy

Find the potential energy of a system of four particles placed at the vertices of a square of side $\ell$. Also obtain the potential at the centre of the square. In the question above can ...
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Work done by gravitational force!

Suppose a ball is $10m$ high from the ground. It will have $E_p = 10mg$. Now, if the ball falls freely then we know $E_k$ will be $0.5mv^2 = E_p$. But it is said that the work done by a force will ...
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164 views

Work done against gravity comes out positive

Given two points in 3-space, $A = (9, 1, 5)$ and $B=(2,8,7)$, the work done by the gravitational field $\bf{F}$ when an object is moved from point $A$ to point $B$ comes out positive, even though it ...
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346 views

Electric field for concentric spheres

I have a couple clarifying questions: (A) in $E=kq/r^2$ for the area between a sphere inside another spherical shell, the sphere inside is considered a point charge. However, the sphere inside has a ...
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478 views

Can the electric or gravitational potential be discontinuous? Why?

I was solving the Laplace's equation for the charger thin spherical shell and noticed that the field is discontinuous at the surface (inside it is zero and outside it is proportional to $1/r^2$) but ...
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139 views

Why doesn't the volume integral vanish?

I am reading Galactic Dynamics by Binney and Termaine, and I'm struggling with the following passage. According to Poisson's equation the resulting change in potential $\delta\Phi(\mathbf x)$ ...
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Why isn't the work minus the potential energy when bringing a charge in from infinity?

This is an example in my physics textbook, and there is just one step that I don't understand. Two point charges are located on the x-axis, $q_1 = -e$ at $x = 0$ and $q_2 = +e$ at $x=a$. Find ...
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206 views

Does the rest mass energy include the potential energy of the particle?

The potential energy (as far as I have studied - that is, mainly classical physics) depends on the reference level, since its absolute value cannot be calculated. It can therefore be negative as well. ...
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148 views

Hamiltonian of coupled oscillators

Let's say I have a system of coupled oscillators which are described by the coordinates $\{x_1,...,x_N\}$ and $\{\dot{x}_1,...,\dot{x}_N\}$. The equation of motion for each oscillator is $$\ddot{x}_n ...
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60 views

Gravitational potential and intensity

Why don't we calculate gravitational field/intensity of a point due to a disc directly? We first calculate the potential then calculate the field by differentiating with respect to $dr$. Why don't we ...
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Potential Energy in a System and its Relation to the Total Energy

In this answer it was stated that potential energy is a property of a system and not an individual particle. If we have two particles (1 and 2) interacting via a conservative force, we can write an ...
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Lagrange: when a potential force, when a generalized force?

Consider the following case of a drum unrolling a mass that is on a massless string wrapped around the drum: According to my professor, here we must consider the mass $m$ being in a gravitational ...
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93 views

How do I found the Kinetic Energy of a mass being lifted?

I did an experiment where I lifted a mass and measured the force. I know the change in height, the mass, and the work of the pull. How can I use the work-kinetic energy theorem to find the final and ...
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Potential Energy of two masses

If two particles with masses $m_1$ and $m_2$ interact and are located at $\vec{s_1}$ and $\vec{s_2}$ have their potential energy $U$ defined by the modulus of their position vectors, how would I ...
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Gravitational PE lost v Elastic PE gained in mass - spring

If a spring has a load $m$ added to it (and so is extended by $x$), the gravitational potential energy lost by the mass will be $mgx$. The elastic potential energy gained by the spring is $\frac{1}{2}\...
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Multiple Definition For Gravitational Potential Energy?

This may just be a simple Misconception Question, here goes: Definition for Gravitational Potential Energy: The work done by gravity to pull an object to the ground. $E=-(\frac{GMm}{r}-\...
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What has the potential energy: the spring or the body on the spring?

Particles have gravitational potential energy due to its position in the gravitational field. We say the particle has potential energy and not the Earth (the body doing the work). Why is it not the ...
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Work done by a non-conservative force and change in potential energy

I know that the work done by a non-conservative force is equal to the change in total mechanical energy (from Work-Energy Theorem). But I read in a place that "Non-conservative forces don't affect PE"....
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A question on Rolly polly dolls

I was reading on rolly-polly dolls when the following questions crept into my mind How exactly does center of gravity play a role which helps rolly-polly doll to stand up on its own? Can a rolly-...
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What is meant by saying the work done by a conservative force is -(change in PE)?

I read through all related questions, and they are almost the same, but I still didn't understand this and so am asking again. What is meant when we say that the work done by conservative force is = -...
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Why isn't energy stored in a capacitor equal to just $QV$ when it is fully charged? [duplicate]

I just learned that the energy stored in a capacitor is electrostatic potential energy. Also potential energy is a state function and is independent of the path. So, when the capacitor is fully ...
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Strain energy density (potential energy of elastic continua)

This question has to do with writing down the potential energy of an elastic body, which obeys a generalized Hooke's law [; \sigma_{ik} = \sum_{klm} \lambda_{iklm} u_{lm} ;] Where $\sigma$ is the ...
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The “potential energy” degree of freedom?

I'm reading Schroeder's "An Introduction to Thermal Physics" and he mentions the vibrational degrees of freedom of a diatomic molecule: A diatomic molecule can also vibrate, as if the two atoms ...
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Is potential energy frame dependent in special relativity?

In newtonian mechanics, As far as I'm aware, only kinetic energy is dependent on frames of reference, since kinetic energy is a function of velocity(squared) and velocity is dependent on frames of ...
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177 views

Where does the energy go when you stretch a rubber band?

There is resistance when you stretch a rubber band. That makes sense to me because the energy you exert is turned into potential energy of the rubber band, but if you hold the rubber band in the same ...