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 Energy = Voltage x Charge, and how to prove that?

As you know the equation $\mathbf{E=V\times Q}$. Where: $\mathbf E$ is the energy measured in joules, $\mathbf V$ is potential difference (Voltage), $\mathbf Q$ is the charge. So my qustion is: ...
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Why does negative energy imply that a system is bounded? [duplicate]

I wanted to know why "negative energy" of a two particle system implies that it is bounded. That is what happens in the case of a hydrogen atom; my textbooks say so, but they do not give any reason ...
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Bounce height of ball on Mars vs Earth

I understand that if a ball is dropped on mars and on earth the ball will bounce back to basically the same height on both planets thanks to the law of conservation of energy. But can anyone prove ...
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Pendulum point in polar coordinates for Lagrangian

So I'm really stumped with this. I have a particle in a cone, like pictured. The particle orbits the z axis on the dotted line for $r$. So knowing that $\alpha$ and $r$ remain constant in this ...
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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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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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Can we define the zero potential at an imaginary point?

Consider a force field defined as $$\vec{F}(x) = \left(\frac{A}{x^2}-B\right)\hat{i}\space$$ where $A, B$ are positive constants. We want to get the potential energy function for this field. We can ...
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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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Understanding the relationship between electric energy and force

I'm trying to do the following problem: One of the three types of radioactive decay is "β decay", during which protons decay into neutrons or vice­versa, emitting either electrons (β­) or positrons ...
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Violation of conservation of energy… or not? [on hold]

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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Why the gravitation potential in a uniform field has 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 the point in a gravitational field. But why the work is ...
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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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Velocity increase calculated from kinetic energy in different frames

Say we have an aeroplane cruising along at constant height with velocity $v_0$. It dives by height $h$ and levels out, at a new velocity $v_1$, in a gravitational field of strength $g$. If all the ...
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Potential Energy of Interaction Between a Sphere and a Particle Formula Derivation [closed]

A sphere of radius R has density described by ρ=ρ(r). Derive equation for pontetial energy of interaction between the sphere and some point particle of mass m which is at distance r from the center of ...
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119 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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Hooke's Law vs. Elastic Potential Energy

I am currently learning about elastic potential energy and this is a question that was given to us by my teacher: When a 13.2-kg mass is placed on top of a vertical spring, the spring compresses ...
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What's the Relation between Potential of mechanics and electricity?

As we know that for a conservative force field, there is associated a Potential with the force. But we know there is a potential in electricity (That's voltage). My question is that is there any ...
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Can the momentum eigenstates be non-orthogonal?

Consider the Hilbert space of a particle, whose position domain is confined to $q\in[0,1]$ (e.g. a particle in a box with unit width). Using $$ 1=\int_0 ^1 dq |q\rangle\langle q| $$ and the position ...
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What is the meaning of the negative sign in $W = -\Delta U$?

What is the meaning of the negative sign in $W = -\Delta U$ ? As far as I understand, $W = -\Delta U = -(U_f - U_i) = U_i - U_f$. While $U_i$ is the initial potential energy (before applying the ...
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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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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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Kinetic energy on macro and micro situation

I just have this random question in my mind. If you drop something in deep space, and it falls due to a gravitational pull. As it's falling, its kinetic energy increases. I just wonder, is the average ...
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Determine the value of $g$ with rolling ball

At first, I thought the value of $g$ ($9.8m/s^2$) could be determined simply by placing a ball at the top of a ramp at a known height. The ball was released with no initial velocity, and the final ...
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Is work needed to bring a test charge from a higher potential to a lower potential?

I don't understand whether work is needed to bring a test charge from a higher potential to a lower potential. It seems that no work is needed because the positive test charge will be under the ...
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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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Conservation and forces/energy

Are there really non-conservative forces in actuality ? Feynman states in his book that in fact, all forces are conservative ( originating from conservative vector-fields ), provide we look close ...
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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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Using Electric Potential to Float an Object

I've been trying to answer the following question but I'm stuck at one step. The question essentially states that a magician is trying to perform a "floating objects" act, for which she has a thin ...
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Energy density in electrostatics

Imagine two hollow spheres with radius $R$ with charges $q$ and $-q$. $L>2R$ is distance between them. Potential energy of the each sphere is \begin{equation*} W_1=\frac 1{8\pi \epsilon_0}\frac ...
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How do I correctly introduce time into this equation?

So, for the past few years it's been my goal to create an equation that would give me the position of an object in a gravitational field at time $t$, given it's initial position and velocity. At first ...
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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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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: $$U = \frac{\epsilon_0}{2}\int_V E^2 dV .$$ ...
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Why is the objective function used in Nudged Elastic Band method reasonable?

In Nudged Elastic Band (NEB) method, which is used to find reaction pathways when both initial and final states are know, an objective function is first constructed and then minimized to find reaction ...
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How much energy does it take to hold a bag? [duplicate]

I'm holding a bag with some mass $m$. The force required for not letting it fall is equal to its weight $m \cdot g_L$ (where $g_L$ is the local gravity, assuming Earth this is $\approx 9.8 \; \text{m} ...
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How can energy be partitioned equally when energy is relative?

According to the Equipartition theorem in a system at equilibrium the energy should be on average be divided equally between the available degrees of freedom. The most common examples are the three ...
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How does gravitational potential energy increase, if field decreases as $h$ increases?

(In the following constants are ommitted) Let $ M = 50, m = 5, h = 5$. Then $$ \text{Potential Energy} = \frac{50\cdot5}{5} = 50.$$ While after increasing the height $h$: $ M = 50 , m =5, h =10 ...
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In atoms, what is potential energy?

I was reading about how potential energy in atoms is measured by how far apart they are from one another. From what I have heard of potential energy, it's a way of showing how fast an object could ...
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What starts the conversion between GPE and KE?

When researching GPE and KE conversion, lots of websites say that as an object with GPE (Gravitational Potential Energy) falls, that GPE is converted into KE (Kinetic Energy), so there is less GPE and ...
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Do magnets violate the 1st Law of Thermodynamics?

A magnet can increase an object's gravitational potential energy without any energy input right? or wrong?
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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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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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Potential energy of a charged ring

Consider a ring of radius $R$, and charge density $\rho$. What will be the potential energy of the ring in its self field? The best I can do: $$dq = \rho R \cdot \, d \alpha $$ $$E_p = 2 \pi R \cdot ...
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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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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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What is potential energy truly?

I have a problematic question for which I have been unable to attain a satisfactory answer. What is potential energy truly? - I have read about how potential energy can be seen as the "highering" ...
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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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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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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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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. ...