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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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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interpreting the dirichlet-principle

In obstacle problems (see e.g. wikipedia here) we are minimizing the dirichlet energy $$ I[u]=\int_D\|\nabla u\|^2dx\tag{1} $$ The Dirichlet-principle states that minimizing $I[u]$ is equivalent to to ...
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Why is $F=-\nabla V$?

I came across this equation $$F=-\nabla V$$ where $V$ is potential energy. I do understand that $$F(r)=-\frac{dV}{dr}.$$ Hence does this mean the nabla operator in this case means derivative? Because ...
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How far up an object is its gravitational potential energy taken from? [on hold]

This is quite a brief question but, Is the $h$ value in $mgh$ taken from an object's base, middle of top. For example, if a person was $1.5m$ in height and they were standing on a hill of height ...
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30 views

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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37 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 ...
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106 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 ...
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81 views

Rolling down an arbitrary hill with friction

I had in mind this physical situation of a point mass rolling down a hill of some arbitrary shape ($y=y(x)$, for instance a parabola about $x=0$), with a peculiar friction force whose "expended work" ...
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65 views

Is there an example of a situation where you need a continuous spectrum?

If you had a hydrogen atom you could say that you want to be able to ionize them. But if you then add the potential due to the earth, e.g. ...
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19 views

Work done by flow of a fluid

I'm looking at the power a flow of steam when used by a turbine. I originally assumed that the kinetic energy of a moving section of steam was equal to (let $V$ be volume, $\rho$ be density, and $v$ ...
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122 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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105 views

How this formula for work follows from the definition?

If a particle moves along a path $\gamma : I\subset \mathbb{R}\to \mathbb{R}^3$ then the work done by a force $\mathbf{F}$ is defined by $$W = \int_{\gamma} \mathbf{F} = ...
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175 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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52 views

What is minimum total energy?

I thought that the energy for a system is constant. But in a question in my physics book we have been asked to determine the minimum total energy from a graph of potential energy vs position? What ...
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35 views

Question about defining potential energy of a magnetic dipole placed in a magnetic field

We know that magnetic field is a non-conservative field, since it exists in closed loops. Then how can we define the potential energy of a magnetic dipole placed in a magnetic field ?
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What was the amount of energy released in the 9/11 terrorist attacks?

I read somewhere on the internet that the amount of energy released by the terrorist attacks on the twin towers on 9/11 should have been of the order of 100 tons of TNT. This number surprised me, ...
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295 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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142 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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67 views

Can't a hydrogen electron have net positive energy?

This page http://www.physicspages.com/2011/06/07/hydrogen-atom-series-solution/ is the 2nd half of a solution to the hydrogen atom Schrödinger equation. They derive that $E = -1/n^2 *$ (bunch of ...
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342 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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How to solve this energy problem using trends related to impulse and momentum? [closed]

The question runs a 1kg block moves with a speed of 10 m/s. It strikes a spring that has a spring constant of 25 N/m. Determine the maximum compression of spring. The energy way of solving ...
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127 views

How to reconstruct the dependence of the potential from a coordinate?

An ion moves along the x-axis of a black box with a speed $V$ and returns in a time $$T=a V^b$$ where $a$ and $b$ are some known constants. Having this, can we reproduce the dependence of a field ...
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125 views

Does a mass falling towards the earth obey conservation of energy?

I'm trying to grasp basic concepts of energy and I have a question regarding conservation of energy. According to Feynman's book and Wikipedia, the law of conservation of energy states that ...
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58 views

On the connection between forces and the principle of stationary action

Feynman tries to account for the relation between the principle of stationary action, which is a statement about the whole path of a particle, and Newton's second law, which is a statement about the ...
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34 views

Slingshot Energy into traveled distance [closed]

If I have a slingshot and I am told that when pulled it has about $E$ joules of energy, how do I compute the height at which an object of mass $m$ would travel if the slingshot is released in the ...
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36 views

Approximate Electric Potential $V$ so that it is of the form $V(r) + V(\phi) + V(z)$

I'm trying to simulate the conductivity of a nanowire that is modeled by a cylindrical shell of infinite potential with benzene rings in the core of the wire. (This is based on a coiled-coil protein ...
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27 views

Of the two variables (Q and V) in the equation of capacitor energy, which is better to take the average of?

$U_c = \frac{1}{2}QV$ I understand from the graph which it should be one half but not quarter, or taking the average of both. But it doesn't really matter to me which variable is on y or x axis? ...
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61 views

Why is the equation for electric potential energy so counter-intuitive?

The equation: $U_E = Vq$ or $(Eq)d$. This works the same way as the equation for gravitational potential energy: $mgh$ But to me, for charges of different signs, the potential energy also varies. ...
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66 views

What is the definition of potential energy? [duplicate]

I have problems with this equation: $$U_G ~=~ G\frac{m_1m_2}{r}.$$ It's for potential energy of say something placed on Earth. But it intrigues me. $r$ is the distance from the very center of the ...
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20 views

Can the electric potential corresponding to the negative plate ever be equal to anything bigger than zero?

I am doing my homework. I read my textbook. It says that the negatively charged plate is the low potential plate. It also shows a example of lower plate equal to 0V, I guess for simplicity. But what ...
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93 views

A little confusion in the derivation of potential energy of a shell

This is a paragraph and a figure from The Feynman Lectures, He's trying to prove the Shell theorem for gravity: If we rearrange $dm=2\pi y \mu ds$ we obtain $\dfrac{dm}{2\pi yds}=\mu$. In this ...
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427 views

A confusion regarding an example in The Feynman Lectures

In The Feynman Lectures, In the chapter entitled Work and potential energy, Feynman states: The work done in going around any path in a gravitational field is zero. This is a very remarkable ...
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How does The work done in going around any path in a gravitational field is zero implies conservation of energy?

In The Feynman Lectures, Feynman states: The work done in going around any path in a gravitational field is zero. This is a very remarkable result. It tells us something we did not previously ...
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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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69 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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33 views

does $Q_AV_{AB}=Q_BV_{BA}$ in this case

Sorry fo unclear title but I can't find any suitable on for this question. Here is what my text book says about how to find out the energy of a system of charge of n particle. What I don't know is ...
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What is an effective potential in classical mechanics?

What is an effective potential in classical mechanics? I have read the wikipedia article and David Tong's lectures notes, but I didn't understand how an effective potential simplifies a situation or ...
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Does the mass of an object change as it moves away from the earth?

The mass of a helium nucleus is less than the mass of two isolated protons and two isolated neutrons. When the component hadrons are assembled, this mass is lost as energy ($E=mc^2$). This makes it ...
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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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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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66 views

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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84 views

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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48 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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90 views

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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60 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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323 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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694 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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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 ...