All Questions
Tagged with potential-energy homework-and-exercises
395
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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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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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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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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 ...
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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 ...
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2
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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 \,...
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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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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 $q_{3} = +e$ ...
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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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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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My question is regarding gravitational potential [closed]
If you take a spherical shell, say of mass $M$, and then you split the shell in 2 portions by a plane other than the median plane....say that the larger portion is A and the smaller portion is B.......
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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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Change in potential / potential energy of a charge in electric field [closed]
A uniform electric field of 2000 $(\frac V m)$ exists through all space (the field is in $+x$ direction). An electron is moved from the origin to the location where $x = -2.00 (m)$ and $y = +3.00 (m)$....
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Gravitational potential at the centre of Earth [duplicate]
Why does gravitational potential at the centre of the Earth is finite i.e. $V_c=\frac{3}{2} V_s$, as at the centre $r$ becomes zero so applying $V = \frac{GM}{r}$ the result must be infinity.
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Can kinetic and potential energy be converted to thermal energy? [closed]
If they can, can I use the potential energy equation to find out how much the temperature would increase if 1 kg of water is dropped to the ground from 10m height?
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The Theoretical Minimum: Lecture 5, Exercise 3. Finding equations of motion from potential energy [closed]
From Leonard Susskind's book The Theoretical Minimum.
"A particle in two dimensions, x and y, has mass m equal in both directions. It moves in a potential energy $V = \frac{k}{2(x^2+y^2)}$. Work ...
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Change in potential energy after infinitesimal variation in position
The a particle with the potential $V(x^2+y^2)$ undergoes an active transformation where
$x\rightarrow x+y\delta$
$y\rightarrow y-x\delta$
The exercise was to prove that the Lagrangian of the system ...
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Bertrand's theorem and nearly-circular motion in a Yukawa potential
The question has arisen as a result of working on part b of problem 3.19 in Goldstein's Classical Mechanics book.
A particle moves in a force field described by the Yukawa potential $$ V(r) = -\frac{...
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Force derived from Yukawa potential
This is with regards to problem 3.19 from Goldstein's Classical Mechanics,
A particle moves in a force field described by the Yukowa potential $$ V(r) = -\frac{k}{r} e^{-\frac{r}{a}},
$$ where $k$ ...
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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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Derivation of balanced torque using conservation of energy [closed]
Let mass $m_1$ be placed at a distance of $x$ from the hinge such that the the plane makes an angle theta with horizontal
Then we drop $m_2$ at a particular distance $y$ from hinge such that after ...
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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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Gravitational potential energy between a black hole and a mass [closed]
Let's think that there is a black hole with mass $M$ and matter with mass $m$. Two objects have distance $R$. What is the gravitational potential energy between the black hole and the mass? How can I ...
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Radius of electron and electrostatic energy [closed]
The classical radius of electron is obtained from the electrostatic energy of a sphere of radius $r_e$ which is: $U=\displaystyle\frac{e^2}{4\pi \epsilon_0r_e}$. For the electrostatic energy of a ...
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Solving Particle in a Box using Newtonian Mechanics [closed]
so I'm trying to solve the one dimensional particle in a box problem known from quantum physics in a classical context. So according to Wikipedia (see picture on the right) we would get a particle ...
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The amount of work needed to dig a hole in the ground [closed]
I'm trying to calculate the amount of work that is needed to dig a hole in the ground (can be very deep) between the surface of the Earth with radius $R_{Earth}$ and some surface with radius $R$. As ...
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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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How to find the equilibrium point of a system that is bowl shaped and a mass inside the bowl with given potential energy function?
Question: $z=U(x, y)=ax^2+by^2, (a,b \in R^+)$ is the potential energy function of the system. How to find the equilibrium point of this system?
We have to find the equilibrium point of this system ...
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To Calculate Kinetic Energy of slippping chain overhanging over a smooth table as a function of length of overhang [closed]
Is it even possible to do so? (With only upto highschool level knowledge of mechanics ie without the use of things like Lagrangian mechanics if that is even useful here).
I know how the mass will be ...
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Trying to figure out the potential energy of a hanging rope [closed]
I was trying to figure out the potential energy of a hanging rope. The rope is hanging from a fixed support. The mass of the rope is $m$. And the length of the rope is $\ell$. The rope has a uniform ...
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