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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Physics of every-day life: rotating bag of tea
Whilst studying for my physics courses, I like to drink tea. Today, I noticed that if you pull a bag of tea out of a hot cup of water, it gradually starts to rotate, picking up speed as time ...
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Potential on a Charged Sheet
I know the field difference across a charged sheet-but what's the potential on a charged sheet? Is it just asymptotic?
If we had a thin cylindrical sheet would it be the same? Zero field inside the ...
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Potential energy sign conventions
Almost every book on physics that I read have some weird and non-clear explanations regarding the potential energy. Ok, I do understand that if we integrate a force over some path, we'll get a ...
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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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2answers
60 views
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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Center of mass problem
According to the definition of potential energy, we use $U= mhg .
$
In the figure below ,
A thin uniform rod of mass m and length h is positioned vertically above an anchored frictionless pivot ...
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101 views
Negative potential energy of gravity
Does the negative potential energy in the gravitational field have to be considered in calculating the total mass of the system in question (because of $E=mc^2$)?
If so it seems to me that the ...
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49 views
Escape velocity to intersection of two gravitational fields
Find the minimal velocity needed for a meteorite of mass $m$ to get to
earth from the moon. Hint: the distance between the center of earth
and the center of moon is $\approx 60 R_E$, and the ...
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219 views
In the Lennard-Jones potential, why does the attractive part (dispersion) have an $r^{-6}$ dependence?
The Lennard-Jones potential has the form:
$$U(r) = 4\epsilon\left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6} \right]$$
The (attractive) $r^{-6}$ term describes the ...
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77 views
Gravitational potential energy of mass between two planets
Suppose I want to launch a rocket from earth to some point $O$ between the center of earth and the center of moon (on a straight line connecting their centers), where the gravitational force of the ...
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37 views
Maximum Height of Potato [closed]
I have a bit of a problem. We made potato launchers and launched the potato's into the air. I need to find out what the maximum height my potato reached was. The givens I have are the following:
Mass ...
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Electrostatic Potential Energy Derivation
How is the boxed step , physically as well as mathematically justified and correct ?
Source:Wiki http://en.wikipedia.org/wiki/Electric_potential_energy
As work done = $- \Delta U $. for Conservative ...
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Given a potential energy function, find expression of the force of a particle?
This comes from an AP review packet. I'm given a potential energy functon, $$U(r)=br^{-3/2} + c,$$ where $b$ and $c$ are constants, and need to find the expression for the force on the particle.
...
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51 views
Electrostatic Potential Definition
In the book, Introduction to electrodynamics by David J. Griffiths, he introduces potential separately as a function and potential energy through that function.
How can potential be defined before ...
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4answers
191 views
Energy Gain with capacitor?
I have a question about energy gain in capacitors. Assume the following system:
As the electron gets accelerated inside the capacitor, it will have more kinetic energy coming out than going in. But ...
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1answer
66 views
Orbital mechanics and rocketry: Is it ever a good idea to intentionally lower periapsis?
tl;dr: Hohmann Transfer appears to be the optimal way to achieve a circular-to-circular orbit, but is it possible to lower the periapsis in order to achieve a more elliptical orbit with apoapsis at ...
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Let F(x,y,z)=−c(r/||r||3) be the force resulting from the inverse square law… [closed]
c is a constant and r=(x,y,z). Show that f(x,y,z)=c/sqrt(x2+y2+z2) is a potential function for F. What can be concluded from any path from point A to point B in F? What can be concluded about a simple ...
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How do you find the total electric potential energy? [closed]
Examine the charge distribution shown in this system (see below). Sphere 1 has a charge of +3.0 × 10-4 C; sphere 2 has a charge of –3.0 × 10-4 C; and sphere 3 has a charge of +3.0 × 10-4 C.
Here is ...
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What is the mathematical justification for the quadratic approximation to the energy of a spring in a one-dimensional lattice?
It follows easily from this draw, the length $l$ of this spring as a function of the vertical distance $x$, as $l(x)=\sqrt{1+x^{2}}$
Now, $l$ can be expressed as a MacLaurin expansion:
$$l(x) = ...
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1answer
72 views
Electrostatic Potential Energy Calculation (Sign Problem)
In the derivation of electrostatic potential energy ,
how is $ds=-dr$ step justified ?
Why we use a differential position vector ? Why doesn't directly work and potential energy give the correct ...
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2answers
68 views
Potential energy during vertical fall
Suppose I have a weightless spring connected perpendicularly to the ground, and it has on top of it some weightless surface. Now, I release some sticky object from height $h$ above the system of light ...
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About electrostatic potential energy
I consider an electron (charge $-e$) in $x=0$ and a constant electric field $E(x) \equiv E $. If the electron has initial velocity $v_0$ with the same direction of $E$, then its potential energy is
$$ ...
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Gravitational potential outside Lagrangian points or Lagrange points
The diagram in Why are L4 and L5 lagrangian points stable? shows that the gravitational potential decreases outside the ring of Lagrange points — this image shows it even more clearly:
If I ...
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1answer
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Work done by gravity on Water
Now according to me we would see change in potential energy of system and equate it to the work done by gravity.
But when we see this the first column lowers by $H/2$ and right one rises by $H/2$ ...
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45 views
Gravitational potential energy
Consider two places next to each other: Place 1, where there is a gravitational field whereas Place 2 - there's no field.
Now if we lifted a box in place 1, it gains potential energy. Then, we move ...
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153 views
Proof that flux through a surface is independent of the inner objects' arrangement
$$\Phi=\iint_{\partial V}\mathbf{g} \cdot d \mathbf{A}=-4 \pi G M$$
Essentially, why is $\Phi$ independent of the distribution of mass inside the surface $\partial V$, and the shape of surface ...
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1answer
135 views
Electron volt and Voltage
Voltage is the work done per unit charge. Given by:
V = W/q
Electron volt is the maximum kinetic energy gained by the electron in falling through a potential difference of 1 volt. Given by:
K.E ...
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1answer
66 views
Electric potential energy and speed
If we have electric field and we put electron there , the electron will move in the opposite direction as the electric field.
My question is electron in that direction will speed up or slows down ? ...
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1answer
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Locally every force admits a potential?
I have a little doubt about a force being or not conservative. Well, as I understood, some forces cannot be expressed as exterior derivative of some scalar potential because the work done by the force ...
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2answers
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Higher To Lower Electric Potential
The question I am working on is:
"An electron moving parallel to the x axis has an initial speed of $4.65 \cdot 10^6~m/s$ at the origin. Its speed is reduced to $1.27 \cdot 10^5 ~m/s$ at the point ...
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Particle coming across a step potential barrier
My quantum mechanics textbook says that when a particle (in the classical case) comes across a potential-step barrier of finite height, if it has sufficient energy to surmount the barrier, it will ...
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How do I correctly express the work required to put an object with positive buoyancy down into a certain depth (of water)?
It seems to me that I can express the work required to put an object under water in the same way that I express lifting an object up against gravity. I. e., in both cases I increase the potential ...
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Potential energy of a spring
I'm puzzled about the potential energy of a spring. A spring is a conservative system. So the potential energy should be defined only up to a constant -- can be defined to be 0 anywhere. However, ...
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1answer
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How much (usable) potential energy is stored in a compound bow?
I have done a bit of reading about the energy stored in bows, but I haven't seen anywhere a description of how much energy actually is stored. Clearly there are many factors, bow design being ...
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Shape of a string/chain/cable/rope?
The height of a string in a gravitational field in 2-dimensions is bounded by $h(x_0)=h(x_l)=0$ (nails in the wall) and also $\int_0^l ds= l$. ($h(0)=h(l)=0$, if you take $h$ as a function of arc ...
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Why is the spring constant $W_p''(0)$?
According to my physics book, the spring constant can be calculated from knowing the potential energy, with the formula $k = W_p''(0)$.
I don't really understand why, and the book doesn't explain it ...
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Potential energy of a spring
I have a little problem with the potential energy of a spring... I hope you can help me!
I have two coupled pendula, given by two masses $m$ fixed to two rigid bars (that haven't any mass) and with ...
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2answers
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Measuring work done by gravity over non-constant gravitational acceleration
A question from an example from a MIT Classical Mechanics Lecture on Work.
Here's the given definition for gravitational potential energy (~32:00): "The ...
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1answer
81 views
exercise concerning the inclined plane
I have an exercise to ask yourself.
A ball of mass m = 5 g starts at rest and travels 50 cm along a ramp
inclined at 45 ° to the horizontal. a) If we imagine frictionless motion
of the ball along the ...
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3answers
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Potential energy in $E_f^2=(mc^2)^2+(pc)^2$?
Let's consider
$$E_f^2=(mc^2)^2+(pc)^2$$
where the $mc^2$ is the rest energy due to the rest mass -- in Finnish "lepomassa".
$$ \sqrt{(mc^2)^2+(pc)^2} - mc^2~=~(\gamma-1)mc^2$$
is the kinetic ...
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Elastic potential
I have a doubt:
elastic potential energy is given by: $U=\frac{k}{2}x^2+K$
but does elastic potential exist? (for example: potential gravitational energy is given by $U=mgz+K$ and gravitational ...
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1answer
165 views
What is the energy of interaction between a point charge and an infinite cylinder?
I don't remember enough from my electromagnetism course and I can't find any simple, full example on this subject.
I know, that I can consider the cylinder as a wire with the same charge density ...
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5answers
265 views
Is there a mathematical derivation of potential energy that is *not* rooted in the conservation of energy?
For simplicity I'll consider only gravity, but in general this question only applies to conservative forces.
As per my understanding, the way one gets to the equation for gravitational potential ...
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1answer
229 views
Potential Energy in General Relativity
I often hear about how general relativity is very complicated because of all forms of energy are considered, including gravitation's own gravitational binding energy. I have two questions:
In ...
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1answer
295 views
Derivation of the self gravitational potential energy of a sphere
I have been searching on the Internet but have not found a derivation of the formula for the self gravitational potential energy of a sphere. Can someone show how to do this? I assume it involved 6 ...
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279 views
What is meant by potential energy for a particle in a field?
Potential energy is usually defined using a field and a particle that experiences the field force, as the work down in moving a unit particle from infinity to a position in that field.
But some ...
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Meaning of subscript in $V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$
This is probably a simple question, but what does the subscript $0$ mean in the following expression?
$$V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$$
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1answer
50 views
Is more energy required to magnetize based on its distance to other objects?
I have had this question since I was in college physics, but never could figure out how to express it. Well, now I think I have it.
Let's imagine two scenarios A and B. Both scenarios start with two ...
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1answer
69 views
Do field and potential energy always come together?
Is energy directly due to a field always potential energy?
Is potential energy always due to a field?
From the two Wikipedia links:
a field is a physical quantity that has a value for each ...
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Lever Mechanics - How to formulate an ideal lever launch
Let's say I have a simple lever as shown below, and the lever is massless and the pivot is frictionless and there is no air resistance. I'm thinking the cradle for the projectile would have to have a ...
