Questions tagged [potential-energy]
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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The magnetic force is conservative when the magnetic field is static, what is its potential function then?
The magnetic force $\vec{F}$ can be conservative when the magnetic field is a static. That is $\vec{\nabla} \times \vec{F}=0$, so it follows that there is a scalar function $f$ such that $\vec{F}=q \...
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What is the difference between GPE and gravitational self energy in GR?
What is the difference between gravitational potential energy and gravitational self energy in General Relativity? Are they both the same in Newtonian gravity?
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How does gravitational potential energy work in a very large distance?
I have a question that I made up when I was in high school in first year when we started physics and potential energy and something like that. The question goes like this:
Imagine the universe has ...
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Expression for Potential energy of a hanging mass
If the acceleration due to gravity is $g$ and a mass $m$ is hanging from a fixed support with a thread of length $l$, then it's potential energy ($U$) is given by:
$$U = -mgl;$$
This was stated by my ...
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Why isn’t electric potential energy involved in the calculation of pair production?
When I learned about energy conservation in pair production, we only considered the energy of matter and light. Why isn’t the electric potential involved? Also why isn’t the gravitational potential ...
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How to calculate magnetic force using differentiation of magnetic energy?
I tried to calculate the magnetic force between two circular current loops using numeric integration and differentiation of magnetic energy:
$$ \int d^3\vec{r} \frac{1}{2 \mu_0} \vec{B}^2 \,\,\,\,\,\,...
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When we say a body is at high potential compared to the other, what can we interpret from this and why flow of electrons takes place? [closed]
When we say electron flow from low potential to high potential when connected, what is the reason behind it. I am bit confused whether it is due to the excess of +ve charge on one body compared to the ...
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Can work be 0 but the potential energy still increase?
Let's say that we have two point charges of same magnitude charge, $+Q$ and $-Q$, separated by distance $d$, and charge +Q is fixed in place. If I move -Q away from the +Q charge by giving it an ...
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Gravitational potential energy of a galaxy
How can the total gravitational potential energy of a galaxy be calculated?
Lets assume for simplicity that the entire galaxy follows an exponential mass density function for an infinitely small ...
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Should we regard a capillary tube as a source of potential energy?
When a capillary tube is inserted into a large body of water, there is an increase in potential energy (PE) of the system. This is because the increase in PE of the rising water in the capillary is ...
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Understanding the physical interpretation of the third virial coefficient's peak and zero-crossing point
In the figure posted below (source: doi.org/10.1021/ie00077a027), the third virial coefficient of water shows some interesting features: it crosses the origin around 590K and exhibits a peak at ...
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Some books write $V(\vec{r})$ instead of $V(r)$ as a notation for the electric potential, so which one is right? [closed]
Some books write $V(\vec{r})$ instead of $V(r)$ as a notation for the electric potential, so can the electric potential depends also on the direction?
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Tetrahedral Geometry and Potential energy
Intuitively, I'd think it possible to use potential energy to find the bonding angles in methane, but I'm not getting the right answer. Am I missing something?
In a tetrahedral, the faces are ...
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Potential energy of a charge?
Whilst answering a question I read the Wikipedia article Potential Energy and was quite surprised to find the following statements:
In physics, potential energy is the energy held by an object
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Ownership of potential energy in thermodynamics
Consider an object falling under gravity. To make this an "equilibrium problem", let's say the object has attained terminal velocity (due to air drag). In this situation, how do we apply ...
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If you pick an object from ground and place it at bookshelf.. it has gained potential energy
If you pick an object from ground and place it at bookshelf.. it has gained potential energy but no change in kinetic energy.. does it violate law of conservation of energy
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Electric potential difference due to gravity [duplicate]
A colleague asked me an interesting question: If you have a copper bar, let's say 1 meter long, and stand it upright: Is there an electrical potential difference between top and bottom due to gravity?
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Mass Conversion from Potential Energy in Merging Black Holes
I am considering a hypothetical system of two black holes, each with a mass of 10 solar masses, uncharged and without spin (for the sake of simplification). Initially, they are separated by a distance ...
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How can mechanical energy be preserved if the potential energy is negative? [closed]
If I set the upwards direction as positive, the gravitational acceleration $g$ will be negative (and thus, $mgh$ will be negative if $h$ is positive). Thus, the potential energy will be negative, but ...
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Is gravitational binding energy or gravitational self-energy a source of gravity?
The gravitational binding energy or self-energy of a system is the minimum energy which must be added to it in order for the system to cease being in a gravitationally bound state. Equivalently, the ...
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Energy gained by a black hole [duplicate]
Consider a massive particle falling into a black hole with a very high kinetic energy, for instance, an a particle with travelling at 99.9999999999% of the speed of light towards it.
The mass-energy ...
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Velocity-Dependent Forces and Generalized Potential
Is there any theorem about for which velocity-dependent forces a velocity-dependent generalized potential of the form
$$F_k=\frac d {dt} \left(\frac {\partial U}{\partial \dot q_k}\right)-\frac {\...
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Minus sign in Force potential relation, a convention?
The usual defination of force in terms of potential energy is
$$\vec F=-\nabla U$$
This definition leads to
$$K_1+P_1=K_2+P_2\rightarrow \Delta K + \Delta P =0$$
Where $K$ and $P$ are kinetic and ...
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Can kinetic and potential energy of a swinging pendulum both be zero?
I am currently reading Jakob Schwichtenberg's No-Nonsense Classical Mechanics for some review, and I can't seem to reconcile one of the claims in the beginning of the book. He states that the total ...
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Does Elastic Potential exist?
In gravitation, we have gravitational potential energy U and gravitational potential Φ where: $$Φ = \frac{U}{m}$$
In electrostatics, we have this instead: $$Φ = \frac{U}{q}$$
In a spring-mass system, ...
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How to define the potential energy, and conservative forces? [closed]
I understand that there are multiple questions under this name, but as far as I have seen, none of them answers what I am about to ask. If you came across a duplicate, please feel free to share the ...
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Why Does equipotential surfaces gets father apart in the regions of weak electric field?
If we consider a charge in space then we can draw infinite number of spheres (taking the distance between the spheres equal) around the charge and these spheres act as equipotential surfaces. Now, As ...
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Violation of energy conservation due to Lorentz Force?
We know that work done by Lorentz Force $q(\vec{v}\times\vec{B})$ is $0$ on moving charge in magnetic field as velocity is always perpendicular to the force. This means that kinetic energy remains ...
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Does negative charge move from lower potential to higher potential?
This image implies that charge flows from a higher potential to lower potential….but if we attack a battery to a circuit then the current will flow from lower potential (positive terminal) to higher ...
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Understanding potential energy abstractly and its connection to entropy? [closed]
From what I understand, each particle has an energy called kinetic energy. When we consider a system of particles, in addition to their individual kinetic energy, there is an energy associated with ...
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Quantum physics problem [closed]
Challenging Quantum Physics Problem
Consider a particle in a one-dimensional potential well defined by the potential energy function:
$$V(x)=V₀x²+(V₀/4)x⁴$$
where V₀ is a positive constant. This ...
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How to write the force on a test particle as the negative gradient of potential energy in relativity?
In newtonian mechanics, the gravitational force on a test particle can be expressed as the gradient of the potential energy ($\phi$) as
$$\vec{F}=-\nabla\phi.$$
Now, if we consider a relativistic ...
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Potential inside a Charged Conductor near another Charge
Let's say that we have a solid conducting sphere with radius r and this conductor is given a positive charge of q1. We know that the charge will get distributed on the surface to reduce field inside ...
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What is the significance of a reference point in calculating the potential?
The gravitational potential is given as $$U(r)=-\frac{GMm}{R}$$ where $G$ is the universal gravitational constant $M$ is the mass of the earth and $m$ is the mass of an arbitrary object and $R$ is the ...
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Where would the extra mass due to mass-energy equivalence for a system of two charged particles come from? How could that statement make any sense?
Suppose we have two point charges of rest masses $m_{1}, m_{2}$ and charges $q_{1}, q_{2}$. The electrostatic potential energy of the two objects is $U = k\cdot q_{1}q_{2}/r$ where $r$ is the distance ...
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Very Basic Question: Relationship between Potential, Conservative Forces and Path Independency
I am studying for my exam and wanted to clarify if the following I got from Taylor are true, because we have written something different in my lectures:
$$\nabla\times\vec F=0\ \ \Leftrightarrow\ \ \...
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How can we define Magnetic Potential Energy if it is non-conservative?
I recently learnt that for a circular wire carrying electric current or for a magnetic dipole, if it is kept in a uniform magnetic field, we can define its magnetic potential energy. This would mean ...
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How do you calculate the power needed to pump water with a hand water pump?
I have a doubt about the way in which I could calculate the power requiered to pump water with a hand water pump like the next one:
I´ve seen that many people use the equation below:
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Where does an object get its energy from and what does it mean?
It is stated that an object in motion acquires "kinetic energy" while an object under the influence of gravity when raised to a height acquires "potential energy" but I have a ...
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Lagrangian function of a mass-spring-system with deflections in 2D
I’m looking for the lagrangian function of the following problem (as seen in the picture). We have a mass connected to two springs. We can deglect the mass in two dimensions.
My main problems are:
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How can the equation for generalized force be derived assuming the system is in equilibrium?
I have been going over sections 1.4-1.5 of Goldstein's Classical Mechanics where the equation for generalized force
\begin{equation}
Q_j=-\frac{\partial U}{\partial q_j} +\frac{d}{dt}\frac{\partial U}{...
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How to calculate gradients in dihedral/torsion bond?
Given 4 consecutively bonded atoms (A-B-C-D), how do i calculate the vector along which a force should be applied for the interior 2 atoms?
The dihedral is described by vectors r1, r2, and r2 between ...
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Gravitational potential energy of pendulum below pivot [closed]
The author wants to write potential energy of the ball attached to pendulum. He says that pivot is at $y=0$, so $y$ component is $-\ell\cos\vartheta$ so $U=-mg\ell\cos\vartheta$.
But why don't we ...
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Is Hamilton’s principle valid for systems that are not monogenic?
I have read in Goldstein that Hamilton’s principle works only for monogenic systems. Is it true? I thought that the action principle is universal?
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Question about condition for oscillation of a physical system in Lagrangian mechanics
I can't answer the following question about a (simple) physical system I have studied using Lagrangian mechanic techniques.
So, we have a straight rigid rod in a horizontal plane, symmetrically fixed ...
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Potential energy involving both elastic and gravity
A block of mass $m$ is placed against an ideal spring as shown. Initially the spring (of force constant $k$) is compressed by a distance $s$. The block is then released and slides a distance d up the $...
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Does potential energy actually exist? Or is it just a useful mathematical model? [closed]
The title basically covers it. I've actually thought about this question for a while now, and I am still not sure if I have a definitive answer. Most potential energies seem to just be the work that ...
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Potential energy of a one-dimensional mass
The potential energy of a one-dimensional mass $m$ at a distance $r$ from the origin is $$U(r) = U_0 \left(\frac{r}{R} + \lambda^2\frac{R}{r} \right)$$ for $0 < r < \infty$, with $U_0$, $R$, $\...
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Elastic Potential Energy of spring
Suppose I stretch an ideal spring by distance $x$ then we know that the potential energy stored in the spring during elongation is $kx^2/2$. Now if I leave the spring it returns back to its natural ...
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Why Doesn't the Amount of Work Determine the Elastic Potential Energy in Springs and Gravitational Potential Energy? [closed]
Why isn't the amount of work done on the spring the determining factor for the amount of elastic potential energy stored in a spring?
I learned that the change in potential energy is a result of the ...
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