All Questions
Tagged with potential-energy homework-and-exercises
395
questions
-1
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1
answer
280
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Configuration corresponding to lowest potential energy [closed]
Figure shows a small magnetised needle P placed at a point O. The arrow shows the direction of its magnetic moment. The other arrows show different positions (and orientations of the magnetic moment) ...
- 33
0
votes
1
answer
55
views
Functional force in raising a block upright [closed]
Here $5$ blocks of equal dimensions are placed one on another in two ways:
The $1^{st}$ way is by placing one upon another individually and the $2^{nd}$ is done by considering the $5$ blocks as one ...
- 1,179
0
votes
1
answer
266
views
Finding energy of a rubber band
I'm solving a thermodynamics exercise and at one point I'm asked to find the energy if a rubber band. The rubber band has temperaturte $T$ lenght $L$ and tension $J$. I'm given the following ...
- 185
-1
votes
1
answer
833
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Find Potential energy of a hanging chain
A chain of Length L is fixed at one end to a point and the rest of the chain is hanging such that the other end of the chain just touches the ground. Find the potential energy of the chain given its ...
0
votes
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 ...
1
vote
1
answer
34
views
Bar released from upright position rotates about a lower hinge before being caught by a steel cable, how to calculate the tension on the cable? [closed]
I wish to check the safety factor of a steel cable that I've designed to catch a heavy bar that rotates freely due to the gravitational force acting on it.
From the upright position, I'm assuming that ...
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3
votes
1
answer
537
views
Doubt in the expression of Lagrangian of a system [duplicate]
There is a problem given in Goldstein's Classical Mechanics Chapter-1 as
20. A particle of mass $\,m\,$ moves in one dimension such that it has the Lagrangian
\begin{equation}
L\boldsymbol{=}\...
- 436
0
votes
1
answer
86
views
Is the product between proportionality constant and vector defined?
$$
\delta {U} = - \int F \cdot ds
= -k \int s \cdot ds
= -1/2 ks^2 \tag{i}$$
In ($i$) is there is a dot product between spring constant $k$ and deviation $s$?
Correct me if I am ...
1
vote
1
answer
619
views
Redistribution of charge spherical capacitor
In a spherical capacitor, we have two concentric spherical shells, the inner one carrying a charge $Q$ and the outer one carrying charge $-Q$. If the inner shell is displaced from the center without ...
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0
votes
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, ...
- 101
0
votes
2
answers
156
views
Energy stored in a Capacitor with dielectric [closed]
We have a parallel plate capicitor with capacitance C ($ C= \epsilon°A/d $) when no dielectric is inside it.
The charge on it is Q(+Q on left and -Q on right).
Now a dielectric slab of dielecteic ...
2
votes
2
answers
128
views
How to show that interaction potential depends only on separation of particles in system with position translation symmetry?
System
2 particles with mass moving in one spatial dimension $x$. Positions of particles are $x_1$ and $x_2$ respectively and they are only acted on by a conservative interaction force corresponding ...
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0
votes
1
answer
227
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Electrostatic Potential, Potential Energy, Method of Images [closed]
I am a beginner in problem solving in the field of electrostatics. Well equipped with basic strategies and use of gauss' law. I wanted to analyze the situation below and couldn't wrap my head around (...
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0
votes
1
answer
112
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Potential Energy of a Lagrangian System Involving a Mass and Spring [closed]
If you were to calculate the potential energy term of the Lagrangian for this system, would there be an mg term included, or would it be unnecessary as the change in potential energy of the mass would ...
- 3
1
vote
1
answer
824
views
Work done for conservative forces is path independent Proof
So I’m looking at the proof for work that is path independent.
There is a line were the integral
Partial derivative V dr from r1 to r2 becomes
Partial derivative V r’ dt from t1 to t2
I’m a bit ...
0
votes
0
answers
162
views
Hooke's law and elastic potential energy [duplicate]
A mass $m$ is attached to a vertical spring of elastic constant $K$ and length $L$. The spring is supposed to be of negligible mass. Due to the attached mass $m$ the spring reaches a new ...
0
votes
0
answers
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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0
votes
1
answer
263
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Taylor Example 4.8. Is my reasoning sound? [closed]
This problem has been giving me all sorts of fits. For one, Taylor states that because the frictional force and normal force are forces of constraint, they produce no work. I'm trying to figure out ...
0
votes
1
answer
129
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Why have we assume that the there should be no acceleration in deriving the Electrostatic potential energy
In the NCERT textbook grade 12, it is mentioned before deriving the work done in moving a charge $q$ from point $R$ to $P$ in presence of an electric field at Origin, $O$ by charge $Q$
Two remarks ...
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1
vote
1
answer
962
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Cylinder gravitational potential
I have a question about infinite cylidner. I wanted to calculate a gravitational potential that it creates, but I've stumbled across some difficulties.
From Gauss's Law we know, that force on an ...
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0
votes
2
answers
451
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Gravitational potential in a system of two particles
Suppose two particles with masses $m_1$ and $m_2$ are interacting via a central force. Lets work in the center-of-mass frame, and let $r$ be the distance from the masses to the center of mass which ...
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0
votes
1
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148
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Particle in a cylinder with a spring, sign convention in potential energy (Lagrangian multipliers)
I'm trying to get the force of constraint. The problem I have is when defying the sign of the potential energy using cylindrical coordinates $(\rho,\phi,z)$, what I have is:
$$
V=mgy-\frac{1}{2}k\left(...
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1
answer
239
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Potential energy of two point charges of opposite sign (exercise)
I'm trying to do this exercise, but I don't understand how the textbook does it:
I don't understand, how they get a positive $27V$ and a got a few more doubts:
First thing, you can only measure ...
- 299
1
vote
1
answer
387
views
Why do we evaluate the gravitational potential energy relative to the middle of the rod?
Here is the diagram for the problem and the question is asking me to find the angular velocity of the rod when it is completely vertical. I used the conservation of energy but I was wondering why I ...
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1
answer
38
views
Change in electric potential energy [closed]
I am trying to find the velocity of a charged particle $+q$ as it moves away from a charged shell of charge $+Q$ to a distance of $2R$. I know I need to find the change in electric potential energy ...
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2
votes
2
answers
1k
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Why can't energy be below the minimum of the potential in a bound state? [duplicate]
I just stumbled across the problem and have no idea how to solve it:
"Considering the Time-Independent Schrodinger Equation for a stationary state $\psi$ with energy $E$, that is $$\psi '' = \...
- 418
0
votes
1
answer
569
views
Potential energy of a mass bewteen two springs with pendulum hanging [closed]
I need some help with this problem.
A particle of mass $m_1$ hangs from a rod of negligible mass and length $l$, whose support point consists of another particle of mass $m_2$ that moves horizontally ...
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3
votes
2
answers
277
views
Help interpreting equipotential line diagram
I immediately understood that this question is about how work done to get a test charge from one equipotential line to another doesn’t depend on the path taken but this diagram seems a little strange ...
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1
vote
2
answers
678
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How do we find the average value of gravitational potential energy over one orbit?
We just completed orbital dynamics in my university astrophysics class. The textbook we are using is Carroll and Ostlie. In the textbook, it is mentioned that the average gravitational potential ...
1
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0
answers
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
answer
4k
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Lennard-Jones potential, distance $r$ for minimum energy
I'm sorry if the question seems stupid. I found (wikipedia) that the Lennard-Jones potential has it's minimum at a distance of
$$r = 2^{\frac{1}{6}}\sigma.$$
If $U(r)_{min} = -\epsilon$
$$U(r) = 4\...
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1
vote
1
answer
570
views
How to compute the self-energy of a sphere? Electrostatics [duplicate]
Not just the formula, how to derive it as well, im lost in this topic any help would be great.
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votes
2
answers
130
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Finding total mechanical energy, given the potential [closed]
The average kinetic energy of a particle in a potential of the form
'$V(x, y)=x^{4}+4 x^{2} y^{2}+4 x^{3} y-2 y^{4}$'
is equal to $T$.
How can we find the total energy of the particle?
My attempt:
I ...
- 1,270
0
votes
1
answer
188
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Elastic potential energy during elastic collisions
While working with problems on elastic collisions, I have come across this observation, that the elastic potential energy of a two-body system is the maximum when the relative velocity equals zero. In ...
- 1,638
0
votes
1
answer
96
views
How do I integrate this function? [closed]
I have an exercise where I have to calculate the potential energy function $U(x)$ of this force $F$. I know the function is given by integrating $-F$, but how do I do this? $c$ is a constant, and a ...
0
votes
2
answers
423
views
Work-Energy Theorem, conservation of energy, and Elastic Potential Energy problem [closed]
So I'm having some trouble with this problem can anyone help me out on how to solve it?
A 3.0 kg block is released from rest at the top of a 3.4 m high frictionless incline. At the bottom of the ...
1
vote
3
answers
93
views
An object which is thrown up rises to a height $h$ and and is stopped at height $h/2$. What is the work done?
So, I had this question in mind for a few days now, suppose an object of mass $m$ is thrown up by a person.
Now, work done on the object would be stored in the form of potential energy, now it rises ...
- 356
0
votes
2
answers
327
views
What is the work done in pushing an object up a slope of mass $m$ to a height $h$?
What would be the work done when an object is pushed up a slope, My teacher recently said that work done on the object would be greater than PE, can someone explain it to me if this is right or ...
- 356
0
votes
1
answer
60
views
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$...
-1
votes
1
answer
150
views
Falling Chain help! [closed]
I was going through Example 9.2 in Thornton and Marion's Classical Dynamics, and I am stuck on the Potential Energy part of the Question. How do they get the term at the top of the page on the right? ...
0
votes
1
answer
515
views
Potential energy of a particle moving in a circle [closed]
Consider a particle under the influence of a conservative force field such that that it moves in a circle of radius $r$. Its potential energy is a function of $r$ and the angle $\theta$ made by the ...
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3
votes
1
answer
849
views
Need help creating the Lagrangian for a coupled pendulum [closed]
I know that for 2 separate single pendulums, the kinetic and potential energies are:
$$KE = \frac{1}{2}I(\dot\theta_1^2 + \dot\theta_2^2)$$
$$PE = 2mgl - mgl(\cos\theta_1 + \cos\theta_2)$$
But I don't ...
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1
vote
2
answers
380
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Why is the work done by a block into a spring the same from the work done by the spring on the block?
In the following situation:
A 700 g block is released from rest at height h 0 above a vertical
spring with spring constant k = 400 N/m and negligible mass. The block
sticks to the spring and ...
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votes
2
answers
131
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Verifying $W = \int \vec{F} \cdot d\vec{x}$
Verifying formula for Work;
$$W = \int \vec{F} \cdot d\vec{x} \quad(i)$$
Let us consider a very simple scenario; I will solve first by simple Maths and then by calculus.
Scenario 1: (Force vector is ...
- 439
0
votes
2
answers
37
views
Potential energy for an amount of time [closed]
a mass of 10kg is maintained at 1m above the ground for 25s. What is the work done during this time interval?
i know this formula :
$ W = F * d * cos(a)$
but I don't find a formula with the time and ...
1
vote
2
answers
143
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Part of physics answer I didn't understand, and don't have reputation to ask them. $10\,\text{ms}^{−2}$
When you lift your $2.5 \,\text{kg}$ laptop (a 15-inch Apple MacBook Pro, for example) by a foot, you do work of approximately $2.5 \,\text{kg} \times 10 \,\text{ms}^{−2} \times 0.3 \,\text{m} = 7.5 \,...
3
votes
3
answers
2k
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How to calculate the potential energy of coupled oscillators?
The equations of motion that describe the above situation is given by:
$$ m \ddot{x_1} = -2kx_1 + kx_2 $$
$$ m \ddot{x_2} = -2kx_2 + kx_1 $$
Now I want to work out the potential energy of this system. ...
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0
votes
0
answers
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 $q_{3} = +e$ ...
4
votes
3
answers
678
views
In this problem, why is the work done by the spring not equal to the line integral of the spring force over its displacement?
Problem statement:
In the given figure, two blocks A and B, each having a mass of 320 grams are connected by a light string passing over a smooth light pulley. The horizontal surface on which block A ...
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0
votes
1
answer
43
views
Potential energy to gain elevation
I did a calculation to see how high the energy in a cell phone battery could lift an adult assuming perfect efficiency but something seems way off.
...
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