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.

learn more… | top users | synonyms

2
votes
1answer
59 views

The work-energy theorem

Well here's the question. From some previous excercises we know that from \begin{align} A&=\int F\;ds,\\ &=\int ma\;ds, &&(F=ma)\\ &=\int m \frac{dv}{dt}\;ds, ...
1
vote
2answers
51 views

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 the time of: $$T=a V^b$$ $a$ and $b$ are some known constants. Having this, can we reproduce the ...
0
votes
2answers
55 views

Why is the potential energy for a body raised up by a height negative?

I tried deriving the potential energy of a body when raised at a height $h$ above the earths surface, using the formula: $$PE = -W_\text{conservative}$$ where $W_\text{conservative}$ is the work ...
1
vote
1answer
28 views

Relationship between momentum and energy for rocket-powered aircraft

I'm trying to write a problem for my students in an algebra-based physics class. We have a flight simulator and I've got a glider in the simulator that has a couple rocket boosters attached. Students ...
1
vote
2answers
63 views

My total potential energy?

The potential energy in a uniformed gravitational field is $mg \cdot \Delta h$. This assumes of course that $g$ doesn't change and only gives the difference in potential energy for $\Delta h$. How ...
2
votes
4answers
71 views

What is the intuition behind “Net Work is Zero”?

I tried searching the answer to this all over the internet, but still cannot grasp this concept. So, when a book is being lifted, let's say $25 meters$ with a mass of $4kg$, with constant speed. I ...
0
votes
1answer
53 views

Classical Mechanics - Potential Energy Function [closed]

Question The potential energy function of a particle of mass $m$ is: $$V(x) = \frac{cx}{x^2+a^2}$$ where c and a are positive constants. Qualitatively sketch $V$ as a function of $x$. Find two ...
1
vote
2answers
47 views

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 ...
4
votes
5answers
84 views

Relation between potential energy and forces

Can you also explain why can't we define potential energy corresponding to a non-conservative internal force? Non-conservative forces are those which don't depend on the initial and final states but ...
1
vote
3answers
94 views

Alternative type energy storage to batteries? [closed]

When designing portable devices it is usually the battery that stores its energy, because it has a high energy density that allows even small batteries to run up to a year, given appropriate circuit ...
0
votes
1answer
41 views

Finding the potential energy of a geosynchronous satellite above earth [closed]

I am trying to find the gravitational potential energy of a 1kg geostationary satellite above the earth. So far: $E=mgh$, and $g=GM/r^2$ so substitution of $g$ into the energy equation gives: ...
0
votes
1answer
21 views

Thomson problem vs. maximizing sum of distance

Given $N$ equally charged points lying on the unit sphere ("electrons"), the Thomson problem consists of finding the configuration of these points such that the electrostatic potential energy $$ ...
0
votes
2answers
28 views

Work in electric potential

I've read that if we want to move a charge in an electric field then we need a work of an external force to move it from a low potential energy to a high one , but then I read on another source that ...
0
votes
1answer
38 views

Mathematical misunderstanding of Work-Potential Energy Theorem?

This is a relatively basic question, but I don't understand why it is the case. This is from my dynamics book and is mainly a mathematical misunderstanding. $$ \ dU = F\cos\theta ds $$ Which means ...
0
votes
0answers
10 views

Why molecules in this potential have a common average distance $r_m$ to their neighbors?

A commonly used potential describing intermolecular interactions in liquids and real gases is the so-called Lennard-Jones potential. In this model the interaction of atoms and molecules with each ...
1
vote
0answers
28 views

Generalization of Feynman's derivation of the formula for gravitational potential energy in FLP volume I

In the Feynman Lectures on Physics, Feynman derives the formula for gravitational potential energy by applying a line of reasoning he borrowed from Carnot on reversible weight lifting machines (FLP I, ...
0
votes
0answers
16 views

What does it mean to charge a length of wire up to potential v?

I have to study the text "On the Theory of the Electric Telegraph," By William Thomson, 1855. I am having trouble gaining a conceptual understanding of the opening: "Let c be the electro-statical ...
1
vote
1answer
70 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 ...
17
votes
4answers
778 views

How is potential energy actually stored in a steel spring at the atomic level?

Elasticity is one the most intriguing phenomena, wiki gives a summary explanation of what happens in a steel spring: the atomic lattice changes size and shape when forces are applied (energy is ...
0
votes
1answer
28 views

Ballistic Pendulum question?

I am answering a question regarding the ballistic pendulum, and the teacher gave this worksheet. I have figured out both t (time) and the change in y. Where I am getting confused is where he wrote out ...
0
votes
1answer
61 views

Violation of conservation of energy… or not?

The work done by surface tension is double the increase in potential energy. This is a clear violation of conservation of energy. What is the flaw here? Work done by surface tension is \begin{align} ...
2
votes
0answers
46 views

Modelling gravitational potential of a galaxy

I am interested in modelling the gravitational potential of a disc-shaped galaxy with radius $R$, i.e. solving the 2D Poisson equation numerically by Gauss-Seidel relaxation: $$\nabla^2 \phi = 4\pi G ...
0
votes
1answer
59 views

Is there anything interesting about an n-body system whose potential energy is constant?

I am curious about a system of gravitating bodies with particular characteristics. Before describing the characteristics of the system, let me say what I want to know about it: Can this be a ...
0
votes
2answers
61 views

How to find height, when given the velocity at that location, starting height, and mass of object? [closed]

The question: A roller coaster is 100m above the ground, and weighs 1000kg. At one point of the roller-coaster-ride, the velocity is 28 m/s. What is the height of the roller-coaster at that ...
2
votes
6answers
493 views

Can energy be created and destroyed?

The indroduction of the principle of conservation of mechanical energy has been tremendously useful from the practical point of view. But .. Consider the case in which we shoot an electron up in the ...
0
votes
2answers
46 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 ...
2
votes
3answers
125 views

Conceptual Question on Work and Potential Energy

I'm confused by classic description of work and negative work. If someone pulls (slowly) on a rope to lift a bucket in a well, I understand that the person is doing work on the bucket and gravity is ...
2
votes
1answer
69 views

Finding potential energy of a solid hemisphere on top of another solid hemisphere [closed]

A solid hemisphere with radius $b$ has its flat surface glued to a horizontal table. Another solid hemisphere with radius $a$ rests on top of the hemisphere of radius $b$ so that the curved ...
2
votes
1answer
59 views

Confused about gravitational potential energy [duplicate]

So learning the concept of gravitational potential energy, my professor says that when lifting an object without any acceleration, the force we exert on the object to lift it is the same as the force ...
2
votes
1answer
42 views

Separating the potential energy of a system of particles.

Assuming all forces derive form a conservative source and that all forces observe the strong form of the third law, how do we arrive at the following equation? \begin{equation} V=\sum _i V_i+\frac ...
1
vote
1answer
51 views

Hooks Law and acceleration [closed]

A 435 gram sharpened piece of iron rebar into a spring loaded device. It takes a force of 355 Newtons to compress the spring by 27.5 cm. With what speed does the rebar shoot out of the device? ...
1
vote
1answer
47 views

Which inertial observer should I choose when using $\Delta U = -\Delta K$?

I just read and undertood that For any conservative force $F$ (which is not necessarily constant), we can define a potential energy change $\Delta U$ of an object on which the force exerts as ...
1
vote
1answer
39 views

Show the equivalence of two electrostatic energy

$$U = \frac{1}{2}\iint_{all space}^{ } \frac{\rho(1)\rho(2)}{4\pi\epsilon_{0}r_{12}}dV_{1}dV_{2} $$ and $$U = \frac{\epsilon_{0}}{2}\int_{allspace}^{ } \vec{E} \cdot \vec{E} dV.$$ In the left ...
1
vote
2answers
83 views

Conservative force as a potencial energy gradient

A conservative force $\vec{F}$ is apparently defined as the gradient of a potential energy $U$: $$\vec{F} = -\nabla\ U$$ I am curious if this definition was originally used to describe a ...
2
votes
2answers
144 views

The Delta-Function Potential

I'm reading through Griffiths Intro to QM 2nd Ed. and when it comes to bound/scattering states (2.5) they say: $E<0 \implies$ bound state $E>0 \implies$ scattering state Why doesn't this ...
1
vote
0answers
23 views

Can anyone give me a simple proof for the sign change of electronic wavefunction when taken around a loop containing a conical intersection?

How and why does the sign of the electronic wavefunction changes when it is taken around a contour? For example, suppose the initial wavefunction is $f(s;S_0)$ at nuclear configuration $S_0$ and now ...
3
votes
2answers
92 views

Food calories vs gravitational potential energy [closed]

Imagine you could use all of the energy you have ever extracted from your food as a source of propulsion. Is the energy contained in the food you’ve eaten over the course of your lifetime enough to ...
1
vote
2answers
38 views

Confusion with Grounded Conductor: bringing in a point from infinity

Suppose, for sake of argument, we have a spherical grounded conductor at the origin. Additionally, let our reference voltage be at infinity. Now, I view the potential of a point in space as being the ...
0
votes
1answer
32 views

trying to understand the electricl potential and potential energy

I am trying to understand some facts on electrical potential and potential energy. It is quite confusing in the text to say that the zero potential could be freely chosen for convenience. In that ...
1
vote
1answer
78 views

Integrals and Legendre Polynomials

I was told by a professor that this equality: $$\frac{1}{2\pi}\int_0^{2\pi}\frac{1}{|r-r(\varphi)|}d\varphi = \frac{1}{r}\sum_0^{\infty} \bigl(\frac{a}{r}\bigr)^n{|P_n(0)|}^2$$ ( where: $a$ is the ...
0
votes
2answers
172 views

Particle in a Box: Energy Less than the Potential Energy

I am reading quantum mechanics from Shankar's Principles of Quantum Mechanics. On page 157 he defines the box potential $V(x)$ as $$ V(x) = \left\{ \begin{array}{rl} 0 &\mbox{ if $|x|< L/2$} ...
1
vote
1answer
170 views

Using gravitational potential energy and elastic potential energy in a problem?

This is a problem my professor worked on in class: The first thing he said was that we would use position 2 as the "reference height" and I'm not sure what that means exactly. He goes on to say ...
0
votes
2answers
63 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 ...
2
votes
1answer
91 views

Confusion with Newton's Second Law : Position & Time Dependence of Force

For a conservative force $\vec{F}(x,y)$ we have $$\vec{F}(x,y) = - \vec{\nabla}\phi(x,y)$$ where $\phi(x,y)$ is a potential function for $\vec{F}(x,y)$. Again, Newton's second law states that $$ ...
0
votes
1answer
95 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 $v(t=0)=v_0$. ...
2
votes
3answers
92 views

How come we talk about gravitational potential energy and not gravitational potential?

With regards to gravity the equation learned is $$U=-\frac{GMm}{r}$$ And the relationship to force is $$F=-\frac{dU}{dr}$$ In electrostatics we instead talk about electric field and electric ...
2
votes
1answer
100 views

Electrostatic Potential Energy Integral

I'm trying to calculate the total energy of a simple two charge system through the integral for electrostatic energy of a system given in Griffiths' book: $$U = \frac{\epsilon_0}{2}\int_V E^2 dV .$$ ...
0
votes
1answer
64 views

Calculating change in gravitational potential energy [closed]

A satellite mass $500\ kg$ is elevated from altitude $10000\ km$ to altitude $20000\ km$. Radius of earth is $6378\ km$. Mass of earth is $5.97 \cdot 10^{24}\ kg$. Gravity is given to be $9.81\ m/s $ ...
2
votes
2answers
190 views

Energy to reach the moon

I've been stuck on this question for a couple of days now. Given that the potential energy of a 930 kg object on the Earth's surface is -58.7GJ, calculate the minimum energy required for the 930 ...
0
votes
1answer
86 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 ...