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 electrostatic energy of a Capacitor [on hold]

They give me the area ($0.06m^2$), the separation between the plates ($0.001m$) and the capacitor is charged at $150V$. At this point is really easy to find Q $\frac{V}{d} \rightarrow ...
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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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80 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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307 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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1answer
80 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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45 views

Mechanical energy? [closed]

A particle of mass $2\,\mathrm{kg}$ is attached to one end of a model spring that is hanging vertically from a fixed point O. The spring has stiffness $4$ and natural length $1\,\mathrm{m}$. ...
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42 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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761 views

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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162 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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43 views

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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90 views

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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1answer
38 views

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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101 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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1answer
67 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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1answer
121 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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42 views

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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1answer
143 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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1answer
242 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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41 views

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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66 views

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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1answer
318 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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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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52 views

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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103 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 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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128 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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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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59 views

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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1answer
87 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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116 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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42 views

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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1answer
151 views

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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65 views

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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97 views

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 ...
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118 views

Electric potential energy and signs

I know that electric potential is negative near a negative charge and positive near a positive charge. But does this mean a small positive 'test' charge has a negative electric potential energy near a ...
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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 ...
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Why should Conservative forces have their curl equal to zero?(intuition)

There are several conditions that must be met in order for a force to be conservative. One of them is that the curl of that force must be equal to zero? What is the physical intuition behind this? If ...
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71 views

Are black holes an infinite source of energy? [duplicate]

Black holes are considered particularities because in a determined point in time they are pointless, as consequence there are some mass in a null space so the density become infinite. Finally if ...
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1answer
46 views

Metric in Lagrangian and the minimum total potential energy principle

I was wondering why physical systems "like" to go to the minimum of potential energy and I found this question, that tries to justify the minumum total potential energy principle. I was also reading ...
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73 views

Potential Energy in modified Atwood Machine

The initial length of the spring is $l_0$. I need help understanding how the potential energy of this system comes to be. I know the answer: $$ U = ...
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117 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 ...
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Why is the total energy of an orbiting system negative?

Assume it's an circular orbit. Object A orbits around object B. Take object B as frame of reference. .$E=KE_a + GPE$ .$E=\frac 12m_av_a^2 +(-\frac {GM_bm_A}r)$ .$E=\frac 12m_a(GM_br)+(-\frac ...
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90 views

How does potential energy work out for floating things?

Seeing a ship canal lift in TV spawned the following thought: "Oh my, this sure is a heavy ship and it can be lifted by simply adding water. What a marvellous machinery. After all, I could lift that ...
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1answer
55 views

Lagrange equation and a force derivable from a generalized potential

I was reading the solution of this exercise and I have a doubt: A point particle moves in space under the influence of a force derivable from a generalized potential of the form $$U(r,v) = ...
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197 views

Is it possible to prove that planets should be approximately spherical using the calculus of variations?

Is it possible to use the Lagrangian formalism involving physical terms to answer the question of why all planets are approximately spherical? Lets assume that a planet is 'born' when lots of ...
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1answer
60 views

What is this equation $f^e = f^a - \nabla U$?

Recently in a mechanics class my prof scribbled down something looked like $$f^e = f^a - \nabla U.$$ Where he claimed $f^e$ is the external force on an object, $f^a$ is the applied force on the ...
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60 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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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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Water in a U-tube [closed]

I'm currently working on a problem that states: a U-tube has vertical arms of radii $r$ and $2r$.... The U-tube contains liquid up to a height $h$ in each arm. The liquid is set oscillating and at ...
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34 views

Buckling of a slender column - total energy

I'm following Goldbart's Mathematics for Physics book, and I ran into a problem with exercise 1.4 (page 43). We have a formula for the energy stored in a slightly bent rod aligned on the $z$ axis: $ ...
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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: $$U = \frac{\epsilon_0}{2}\int_V E^2 dV .$$ ...