All Questions
Tagged with potential-energy homework-and-exercises
50
questions with no upvoted or accepted answers
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Energy of a spherical shell
System: spherical shell with surface density.
Objective: calculate potential energy.
I found energy through potential.
Next, I found the formula for energy through the field, which gives two ...
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2
votes
1
answer
156
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Intuiting qualitatively the shapes of the eigenfunctions of a finite well-like potential, using the infinite well eigenfunctions as an inspiration
Consider, for example, the third excited state of an infinite square well:
Now consider the following potential:
If we wanted to sketch the rough shape of the third excited eigenfunction of this ...
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2
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0
answers
710
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Gravitational potential of an infinite plane
In this link http://www.feynmanlectures.caltech.edu/I_13.html#Ch13-S4 , Feynman first computes the gravitational field generated by an infinite plane of constant density, and then he computes the ...
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2
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Position equation of $U(x)=-U_1[(\frac{x}{x_1})^3-(\frac{x}{x_1})^2 ]$
If $U(x)$ is given by $$U(x)=-U_1\left[\left(\frac{x}{x_1}\right)^3-\left(\frac{x}{x_1}\right)^2 \right]$$ can I find the position equation without harmonic aproximation?
I'm having problem with the ...
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0
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187
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Potential energy and atomic units in the Bohr model
I have a question regarding the final sentence written in the solution to part iii) (found below) for the question given below.
In the Bohr model of the hydrogen atom, the radius of the electron ...
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1
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3
answers
136
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Velocity not affecting heat produced by impact
A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with an uniform speed of 7 $\text{m s}^{–1}$. It hits the floor of the elevator (length of the elevator = 3 m) and does not ...
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0
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77
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A pendulum consists of a rod with length L and a coin of mass m
A pendulum consists of a rod with length $L$ and a coin of mass $m$. The pendulum is held in a horizontal position and then is released with a minimum velocity needed to make a full circle.
What's the ...
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527
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Particle in electromagnetic field Lagrangian
Given the two definitions of $\vec E$ and $\vec B$ by scalar potential $\phi$ and vector potential $\vec A$:
$$\vec B=\vec \nabla \times \vec A$$
$$\vec E=-\vec \nabla \phi -\frac 1 c\frac {\partial \...
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1
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0
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474
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Potential energy on a spherical capacitor
I have been having some trouble understanding the storage of energy
inside a spherical capacitor composed of two concentric spherical
shells where the inside shell has radius $a$ and charge $2q$, ...
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0
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98
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Potential energy stored by an elastic circular loop on deformation to an ellipse
This question is related to an origami circular loop that I built. This structure is elastic and I intend to find the elastic potential energy stored by it when I deform it to an ellipse.
My actual ...
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2
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Hanging mass from spring/ Setting potential to 0
I'm working a problem from Taylor's Classical Mechanics Book, and it's highlighted a couple issues I never quite wrapped my head around (despite getting good marks in advanced undergrad mechanics and ...
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0
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215
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Effective potential in Lagrangian
I have two question related to the steps in equations 3-7 in this paper:
Question 1 They find the effective potential in eq. (5) as the negative of the effective Lagrangian (eq. (3)). I don't see how ...
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0
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78
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Perihelion precession for general potential
I'm trying to show that for the perihelion precession $\Delta\phi$ follows:
$$\Delta\phi=2\int_{r_\textrm{min}}^{r_\textrm{max}}\frac{L}{r^2(E-U_\textrm{eff}(r))^{1/2}}~\mathrm dr$$
where $L$ is the ...
user137707
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0
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249
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Work to assemble charge distributions in the presence of a dielectric
I am asked by a problem to:
Find the potential energy of a point charge in vacuum a distance $x$ away from a semi-infinite dielectric medium whose dielectric constant is $K$.
I wish to approach ...
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1
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0
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163
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Potential Energy of two masses
If two particles with masses $m_1$ and $m_2$ interact and are located at $\vec{s_1}$ and $\vec{s_2}$ have their potential energy $U$ defined by the modulus of their position vectors, how would I ...
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840
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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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0
answers
254
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Deriving the curve of a cantilever
Essentially, there is a beam of length L and negligible mass sticking out of a wall with a mass Mg hanging at the end of it. We are given an equation for elastic energy (which I don't think needs to ...
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1
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1
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868
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Shooting an arrow straight up, forces in play
Okay, I'm a little confused with this question here.
Someone shoots an arrow straight into the air, we'll ignore friction, the arrow has a hardness of $1.0 kN/m^2$. The arrow itself weighs 12g. ...
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1
answer
61
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Deriving expression for gravitational potential energy around a mass, $M$, using vectors
(I think my question will be somewhat related to this one: Deriving gravitational potential energy using vectors .)
I know the change in the potential energy associated with a conservative force, $\...
0
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1
answer
58
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Question about Problem $12$ in Chapter $11$ from Kibble & Berkshire's book
I write again the problem for convinience:
A rigid rod of length $2a$ is suspended by two light, inextensible strings of length $l$ joining its ends to supports also a distance $2a$ apart and level ...
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0
answers
27
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About reference of potential energy
I have an exercise with a pendulum starting at horizontal position, then we give it a velocity of 5m/s pointing down, $z=0$ at this horizontal position and potential energy = 0. This confuses me ...
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0
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108
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Finding the Equation of motion for a vertical rotating disc with an added mass
I have been trying to figure out the equation of motion of a rotating disc with an added mass fixed on the surface of the disc at a certain distance $r$ from the disc's centre point.
I have ...
0
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1
answer
93
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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 $...
0
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1
answer
49
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How do I visualize total potential energy of charges?
In the following exercise from University Physics with Modern Physics (Young, Hugh D.; Freedman, Roger A..)
Two point charges are at fixed positions on the $x$-axis, $q_1 = -e$ at $x = 0$ and $q_2 = ...
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44
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Why didn't we account for kinetic energy of two stars in conservation of mechanical energy
Two stars of masses 3×10^31kg each, and at distance 2×10^11m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star's rotation plane. In ...
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1
answer
380
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Gravitational Potential Energy Lab Confusion
I had a lab that tested the dependence of gravitational potential energy on its position and the goal out of each exercise was to see if kinetic energy equaled potential energy. A cart was on a flat ...
0
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1
answer
178
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Goldstein equation 1.33
I am trying to read from Goldstein for self-study but I am stuck on equation 1.33. Let me restate some of the lines from Goldstein (with some modification):
If $\textbf{F}_{ij}$ (internal force, ...
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40
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Motion near the local maximum of potential energy
Particle is moving along the $x$ axis in the field with potential energy $U(x)$. $U(x) $has local maximum at $x=0$, and the total energy of particle is equal to $E=U(0)$.
I'm supposed to find how the ...
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1
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60
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How do I intuitively draw phase portrait from pseudopotential vs $x$ plot?
I am struggling with the process of deducing a phase portrait from pseudopotential vs $x$ plot. Is there a resource that would be helpful in understanding it better?
Given the pseudopotential(V) vs $x$...
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48
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Potential energy of a system of three charges question
Two point charges are located on the $x$-axis, $q_{1}=-e$ at $x = 0$ and
$q_{2} = +e$ at $x = a$.
(a) Find the work that must be done by an
external force to bring a third point charge $q_{3} = +e$ ...
0
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0
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320
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Potential energy distribution near a cube with negative charges at 8 corners and one positive charge at its center
What is the potential energy of an arrangement of eight negative charges on the corners of a cube of side $b$, with a positive charge in the center of the cube? Suppose each negative charge
is an ...
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1
answer
106
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Feynman Lectures, Chapter 4, Fig 4-3
From the Feynman lectures Chapter 4, Fig 4-3
"We lifted the one-pound weight only three feet and we lowered W pounds by five feet. Therefore W=3/5 of a pound."
If there is a change of 3ft in ...
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1
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145
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Question about principle of minimum total potential energy
So this question is really basic compared to some others on this website.
I was reading professor povey's perplexing problem, a book on physics problem solving. I came across a problem which is below....
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From a potential energy equation, how can we determine whether or not the particle undergoes circular motion?
(I realise this may be considered a homework question but I have read the rules.)
I'm working through an introductory book on classical mechanics and there is this question:
Consider a particle of ...
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1
answer
61
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The work due to friction given an influential force
Statement: I am trying to work through Chapter 8, Problem #70 of OpenStax University Physics Volume 1 and I cannot figure out what I'm doing wrong. The problem statement is as follows:
A particle of ...
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1
answer
459
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Gravitational potential energy of an isothermal sphere
I am trying to calculate the gravitational potential energy, W, defined as:
$$W = -\frac{1}{2}\int\rho(r)\Phi(r)\mathrm d^{3}r$$
for an isothermal sphere. I am given that the density profile varies ...
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130
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Charging two spheres by induction n times
There is a conducting sphere $S_1$ of radius 'r' mounted on an insulating handle. The sphere is given a charge Q. Another uncharged conducting sphere $S_2$ of radius R mounted on an insulating handle ...
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1
answer
49
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Decreasing energy but at expanse of what
question : A hollow spherical shell with radius R has charge Q uniformly distributed
over it.
(i) show that the energy
stored in this system is $\dfrac{Q^2}{8\pi \epsilon_{0}R}.$
(ii) Now imagine ...
user182868
0
votes
1
answer
67
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Why is this height used for potential energy?
"In a hydro-electric scheme the catchment area is 57 km2 and the annual rainfall for the area is 1720 mm. The
reservoir for the scheme is 380 m above sea level, and the power station is 50 m above sea ...
user193025
0
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0
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175
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Calculating Electrostatic Energy from Capacitance Matrix
Let's say I have two spherical conductors and I put some charge on each. As I understand it, the electrostatic energy $W$ in the fields will be equal to
$$W = \frac{1}{2}C_{11}V_1^2 + \frac{1}{2}C_{22}...
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2
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296
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How do I find the energy difference between two points of a gravitational gradient?
What I'm ultimately trying to figure out is how to calculate only the potential energy attributed to the differences in the force of gravity at two distances from the Earth's center of gravity.
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1
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82
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Can the electric potential corresponding to the negative plate ever be equal to anything bigger than zero?
I am doing my homework.
I read my textbook. It says that the negatively charged plate is the low potential plate. It also shows a example of lower plate equal to 0V, I guess for simplicity.
But what ...
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2
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993
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Electrostatic energy of "a spherical dielectric shell and a point charge at the center"
The inner radius of the dielectric shell is $a$, and the outer radius is $b$. I tried to use the formula involving the square of the electric field, and found $E$ in three regions. But when I evaluate ...
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2
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369
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How can a system of Atwood machine lose gravitational potential energy?
The heavier block in an Atwood machine has a mass twice that of the lighter one. The tension in the string is 16.0 N when the system is set into motion. Find the decrease in the gravitational ...
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1
answer
193
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Potential and Kinetic equality with scalar and vector potentials
I have to prove that:
$$\frac{d}{dt}\left( T+q\phi \right)=\frac{\partial}{\partial t}\left[ q\left( \phi - \vec{v}\cdot\vec{A}\right)\right] $$
Where $T=\frac{1}{2}mv^2$ is the kinetic energy and ...
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-1
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1
answer
1k
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Conservation of energy in a uniform electric field
Say you place a positively charged particle between two plates with an uniform electric field between them. The particle will accelerate towards the negatively charged plate with a constant ...
- 1,307
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3
answers
4k
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Confusion in the derivation of the potential of a magnetic shell
I am reading an old book on electromagnetism (THE MATHEMATICAL THEORY OF ELECTRICITY AND MAGNETISM) and I have some confusion in the following pages:
First let me clarify what a "magnetic shell" is:
...
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-1
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1
answer
438
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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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2
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696
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Total potential energy for two charged particles
I'm trying to formulate a Lagrangian equation for a system of two charged particles. They have respective masses $m_1$ and $m_2$, and respective position vectors $\vec{x_1}(t)$ and $\vec{x_2}(t)$.
...
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2
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3k
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How to solve a spring question?
What is the difference between the distance a spring is stretched using $F=kx$ formula vs the distance using the work formula? They seem to give different answers.
Doesn't distance stretched using ...
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