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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Why is the gravitational potential energy of ideal uniform massive spring $mgx/2$, not $mgx$?

In this Wikipedia page, $$L= T-V = \frac{1}{2}\frac{m}{3}\dot{x}^2 + \frac{1}{2}M \dot{x}^2 - \frac{1}{2} k x^2 - \frac{m g x}{2} - M g x$$ where $mgx/2$ refers to gravitational potential energy of ...
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How does gravitational potential energy increase, if field decreases as $h$ increases?

(constants're ommitted) 1-) M=50, m=5, h=5 then Potential Energy = (50*5)/5 = 50 After increasing height 2-) M=50, m=5, h=10 then Potential Energy = (50*5)/10 = 25 Field strength decreases amount ...
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What happens to KE when lowering a raised book?

I understand the conservation of energy theorem and mechanical energy, but there is this question that confused me a bit, so I hope someone explains it. If you had a book and you raised it, you gave ...
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4answers
106 views

Kinetic energy of the object, but Potential energy of the system: Why is it so?

Examples from Principles of Physics (by Walker,Resnick,Halliday) will say it better: Let us throw a tomato upward. . .as the tomato rises, the work $\mathbf{W_g}$ done on the tomato by the ...
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Paradox of nesting black holes and release of energy

By dumping a gas cloud into a small black hole, I can produce radiation energy, this is how quasars produce energy. By dumping the previous black hole, with the gas cloud inside, into a black hole, ...
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7 views

Constructing a dc circuit with different input and output currents and voltages? [migrated]

I am trying to answer this question (at the moment I am looking at part a) only as I still have not figured it out): But what I do not understand is how you can change the input and output of dc? I ...
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1answer
47 views

Lagrange’s equation: from energies to Lagrangian form

I don't understand how we step from $$\frac{d}{dt}\frac{\partial T}{\partial \dot q_j} - \frac{\partial T}{\partial q_j} = -\frac{\partial V}{\partial q_j}$$ to $$\frac{d}{dt}\frac{\partial ...
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Has $E=mc^2$ been experimentally verified for macroscopic objects with potential energy?

In relation to this question: What is potential energy truly?, I'm wondering if $E=mc^2$ has been experimentally verified to hold true for macroscopic objects with increased potential energy? I'm ...
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18 views

Obtaining angular velocity of a general orbit

Provided you are given a effective potential function i.e. $$ V_{eff}=\dfrac{J^2}{2ml^2sin^2(\theta)} + mgl(1-cos(\theta))$$ how do you obtain the angular velocity for different types of orbits; i.e. ...
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50 views

Where is the mass energy of potential energy (such as for the universe?)

As you know, energy has mass via $E=mc^2$. If I understand right, mass must be inside of a particle, and can not just be "free floating." Gravitational potential energy (or what ever its equivalent ...
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71 views

What happens for a spoon if you carry it to the top of Mount Everest? [duplicate]

$$U=mgh$$ $$h \to \infty$$ $$U \to ?$$ The potential of a 100 gram-spoon is approximately 1 j when it's 1 meter away from the Earth's surface. It's still a spoon if you carry it to the top of ...
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72 views

Where is the potential energy saved? [duplicate]

If you increase the h (=height), potential energy will be increased given by U=mgh. Where does the energy go, into atoms?
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2answers
36 views

What will be the amount of potential energy?

Suppose, I have an object of mass $m$. By applying a force of $F=mg$, if I withdraw this object with constant velocity and place it at a height $h$ from ground level, then potential energy stored in ...
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75 views

Gravity and its energy

Where does gravity get its energy from? So, I'm taking a high school environmental science class and we just started a unit on energy. We were talking about different types of energy and one was ...
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31 views

Gravitational potential energy of a system [closed]

I don't know how the gravitational potential energy of a system of particles is defined. For example, how would one calculate the potential energy of a system of two stars, one mass $M$, the other ...
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2answers
83 views

Potential energy $= mgh$, what is $h$?

NOTE: when I say potential energy I mean gravitational PE The formula for potential energy is P.E = mgh. What is h referring to? Height, obviously. Consider the example: What is the potential ...
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1answer
54 views

I can make the mechanical energy 0 or in fact anything. Is this normal?

We let the rope fall with $\alpha = \pi/2$ (no initial velocity). if I choose the original of potential energy as the picture indicates there, this means that: $$E_m = E_{pe} + E_c = \frac12mv^2 ...
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50 views

Is electric potential a form of potential energy?

As I understand it, the concept of potential energy arises from analytical mechanics. Yet I often see the concept of electric potential $\phi$ introduced without mention of analytical mechanics. For ...
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1answer
75 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, ...
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87 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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74 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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1answer
38 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 ...
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2answers
91 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 ...
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4answers
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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 ...
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1answer
63 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 ...
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51 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 ...
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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 ...
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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 ...
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1answer
46 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: ...
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1answer
25 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 $$ ...
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31 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 ...
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71 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 ...
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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 ...
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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, ...
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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 ...
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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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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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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 ...
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76 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} ...
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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 ...
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1answer
61 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 ...
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176 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 ...
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523 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 ...
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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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3answers
182 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 ...
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1answer
80 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 ...
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1answer
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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 ...
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1answer
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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 ...
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1answer
55 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? ...
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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 ...