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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Derive frequency given potential using Newton's laws

A mass with mass $m$ has a potential energy function $U(x)$ and I'm wondering how you would find the frequency of small oscillations about equilibrium points using Newton's laws. I started by finding ...
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How to reconstruct the dependence of the potential from a coordinate?

What is known is that an ion sent along the X-axis of a black box with a speed $V$ returns in a time: $$T=a V^b$$ $a$ and $b$ are some known constants. Having this, can we reproduce the dependence of ...
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142 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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53 views

Deriving Gravitational Potential Energy using Vectors

Here is my attempt at derivation: First you must find a vector function for the gravitational force. By the inverse square law, the magnitude of gravitational force between two bodies of mass $m$ ...
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Feynman Lectures: Why a non-reversible weight lifting machine cannot lift higher that a reversible one?

Consider weight-lifting machines—machines which have the property that they lift one weight by lowering another. Let us also make a hypothesis: that there is no such thing as perpetual motion ...
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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 ...
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Hooke's Law Problem [closed]

This question assumes that the spring obeys Hooke's law. Say we have a spring Length $L$. The energy of said spring when extended will be $E=(kx^2)/2$. The extension $x_1$ of said string would be ...
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What is the binding energy in General Relativity?

In general relativity, the potential energy is given by $$V(r)=\frac{h^{2}}{2r^{2}}\left(1-\frac{2M}{r}\right)-\frac{M}{r}.$$ Solving $V^{\prime}(r)=0$, there are two points where circular orbits ...
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What is the meaning of this definition of potential energy?

The isolated system of particles is being observed. In the coursebook, $\vec F_\mu$ is by definition the vector sum of forces of all other particles acting on $\mu$-th particle. Usually, potential ...
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92 views

Isolation of a Physical System and Energy

I'm trying to grasp basic concepts of energy and i have a little doubt regarding conservation of energy. According to Feynman book and Wikipedia, the Law of Conservation of Energy states that ...
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36 views

Differential form of the law of gravitation potential

I have problem understanding transaction (operations and methods applied) for one equation to other equation. It is about gravitational potential. $${\vec F_{grav}=\frac{GMm_{obj}\vec R}{R^3}}$$ If we ...
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Definition for potential energy

I came across this definition for potential energy: If we let $T$ be the Kinetic energy, we have that: $$T = \frac{1}{2}mv^2 \implies T = \frac{1}{2}m{x'}^2$$ $$T'= mx'x'' = F(x)x' \implies \\T = ...
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Mechanical Equivalent of Heat

Recently I have been looking up James Joule's experiment regarding the mechanical equivalent of heat. After viewing some drawings of the apparatus, I assumed that the lines holding the weights would ...
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39 views

Resistance and potential difference across it

I have this question that has baffled me for hours now. My question is what really happens when charge passes from one point to another in a circuit for eg what happens when it passes over a ...
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288 views

Picturing Feynman's argument about perpetual motion

So, there is a certain paragraph in Fenyman's book that I'm struggling with for quite some time. It says: We imagine that there are two classes of machines, those that are not reversible, which ...
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606 views

Potential energy curve for intermolecular distance

I'm trying to understand this curve better, but I can't quite figure out what "negative potential energy" means. The graph should describe a molecule oscillating between $A$ and $B$, however where ...
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114 views

Is the Einstein Energy-Momentum equation $E^2 = p^2c^2 + m_0^2c^4$ valid only for Free Particles?

Is the energy -momentum relation $$E^2 = p^2c^2 + m_0^2c^4$$ satisfied only by free particles or even bound particles? Does the Energy refer to total Energy(including potential) or only (kinetic ...
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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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24 views

Electrostatic potential due to two charge system

When we calculate electric potential energy of a two particle system, say first I bring $+q_1$ and then I bring $+q_2$ against $q_1$'s electric field. Say I get that $q_2$ charge to a point $r$ ...
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344 views

Why is a conservative force defined as the negative gradient of a potential?

I'm learning about work in my dynamics class right now. We have defined the work on a particle due to the force field from point A to point B as the curve Integral over the force field from point A to ...
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326 views

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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159 views

What happens to gas molecules after ionization?

I know that gas molecules conduct electricity after they get ionized but what will happen if we keep increasing the voltage even after ionization? Will it explode? If it will then how much energy ...
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Sign of an electric field in electric potential energy problem

I was wondering why the electric field E in this problem is negative. Is it because the earth is negative? We can assume that near the Earth’s surface, a uniform electric field is set up thanks to ...
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258 views

Why potential energy of external force on particle attached to spring is equal to full force multiplied by full displacement?

I am having quite difficult time to understand the meaning of total potential energy on spring. All references I read say that the total potential energy on particle attached to spring is: ...
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Why are L4 and L5 lagrangian points stable?

This diagram from wikipedia shows the gravitational potential energy of the sun-earth two body system, and demonstrates clearly the semi-stability of the L1, L2, and L3 lagrangian points. The blue ...
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Turning points of particle

A particle of mass $m$ and energy $E<0$ moves in a one-dimensional Morse potential: $$V(x)=V_0(e^{-2ax}-2e^{-ax}),\qquad V_0,a>0,\qquad E>-V_0.$$ Determine the ...
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Why is intermolecular potential energy given in 'per mole'?

I was just wondering that if intermolecular potential is the interaction potential energy of two atoms/molecules, then why do we give its value in J/mole? I don't understand why 'per mole' ...
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Proof that oscillations in 1d potential well occur between certain points

In >>this<< situation, a particle with energy $E$ will oscillate between the positions $x_1$ and $x_2$ indicated on the diagram. This simple fact is taught in many introductory courses however I ...
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23 views

Change in Potential energy moving toward line of charge

I'm analyzing the energy involved with charges moving in an electric field and I'm getting caught up here and I must be missing something. So given that an infinitely long line of charge produces a ...
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312 views

Point charge potential (sign problem)

I'm a bit embarrassed, but I'm not able to compute the electric potential at point $P$ (at a distance $R$ from the origin) generated by a positive unitary point charge in the origin with the right ...
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59 views

Can KE and PE of a small element of a transverse progressive wave be maximum simultaneously?

Maybe a string can be taken as an example to produce the transverse progressive wave.
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169 views

Simple harmonic oscillator, calculate the trajectory in real space

Potential of a simple harmonic oscillator: $$U=\frac{1}{2}k x^2$$ I'm asked to calculate the trajectory of a particle moving in this potential, with initial conditions $x(t=0) = 0$ and $v(t=0)=v_0$. ...
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A captious work problem: same paths but same forces?

A man jumps onto a chair. A man climbs onto a chair by putting a leg first and then the other. In both cases, the work has been the same. TRUE or FALSE...? Spoiler!: The path is the same, so the ...
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What makes an orbit stable or unstable?

I have an assignement, where I have a given central potential $V(x)=-\frac{K}{6r^6}$ and object with an angular momentum $L$. I've calculate the radius of a circular orbit, which I've done by ...
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How to calculate the period of the movement from a potential?

I have an assignment, where I have an object moving in 1-D with a given mass and energy, and the potential V(x), and I'm supposed to calculate the period of the movement as a function of the energy ...
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87 views

Why does the gravitation potential in a uniform field have negative values?

As we know the gravitational potential is the work done per unit mass in taking a point mass from zero potential (at infinity distance) to a point in a gravitational field. But why is the work ...
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134 views

Positions and corresponding terminology of “acoustics energy”?

From limited knowledge, decades ago, dating back to the nineteenth century: Ohm's law of specific acoustic energies was the first biological application of Fourier's theorem. Actually, it was ...
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Gravitational potential difference

in my revision guide it defines gravitational potential difference as: The gravitational potential difference is work done in moving a unit mass. It then goes on to explain the gravitational ...
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Gravitational field strength and potential different signs

In my revision guide the gravitational field strength is given as $g=GM/r^2$ whereas gravitational potential is $V=-GM/r$. Why does potential have a minus sign but field strength doesn't?
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Graph of electric potential

In my AP physics guide the graph for electric potential (for a radial field, i.e. point charge) and gravitational potential (for radial field, i.e. point mass) slightly differ from each other and I ...
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Potential Energy of a Molecule

A generic problem asks that we find the total potential energy of a water molecule. Potential energy is given by $\Sigma \ kQ_{1}Q_{2}/r$ where $Q_{1}$ and $Q_{2}$ are the charges of any one bond ...
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The amount of potential energy at the height of h [duplicate]

When we lift an object upwards with a constant velocity for a distance of $ h $ the work that we've done is $mgh$ and the work done by the force of gravity is $-mgh$. So the net work on the object is ...
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Why is potential energy negative when orbiting in a gravitational field?

I had to do a problem, and part of it was to find the mechanical energy of satellite orbiting around mars, and I had all of the information I needed. I thought the total mechanical energy would be the ...
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Total Energy of Inverted Pendulum

I have to find the total energy $V$ of an inverted pendulum (rod). The following parameters and their values are given: Mass $m$ and length $l$ of the pendulum $\theta$ as the angle of the ...
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146 views

Derivation of Interaction energy of Dipole - Induced Dipole Interaction

I see that the formula giving the potential (interaction) energy of a dipole and an induced dipole is $$V=-\frac{C}{r^6}$$ where $$C=\frac{\mu_1^2 \alpha'_2}{4 \pi \epsilon_0}$$ and that the formula ...
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135 views

Susceptibilities and response functions

It is often confusing whether a susceptibility is the same as a response function, specially that often they are used interchangeably, in the context of statistical mechanics and thermodynamics. Very ...
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What is the difference between the potential $V$ and the effective potential $V_{eff}$?

What is the difference between the potential $V$ and the effective potential $V_{eff}$? Some times when solving problems, an effective potential $V_{eff}$ is defined and its usually equal to the ...
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How did Feynman prove that energy cannot be extracted from electric field?

In the Feynman Lectures, vol. II, chapter 4, Feynman discusses electric potential and says: If we carry a charge from point $a \to b$, $$W = -\int_{a}^{b} \mathbf{F} \cdot ds.$$ Now, in general, ...
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Is potential energy an energy exists or potentiality of energy? [closed]

I want to ask whether Potential Energy is truly existing Energy - though i know the energy concept is abstract and we do not know what is energy truly as Feynman said - or it is the potentiality that ...
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Is negative energy a consequence of gravitational energy? [closed]

Assumption Treat all objects as a point. Gravitational constant = 6.67384 × 10^-11 m^3 kg^-1 s^-2 Acceleration of the object is 1 ms^-2 The setup Imagine there are 2 identical objects with mass of ...