All Questions
Tagged with potential-energy homework-and-exercises
395
questions
-2
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1
answer
135
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A question on Gravitational potential [closed]
For a uniform solid sphere of radius $r$ and mass $m$, if the gravitational potential on the surface is assumed to be zero, find the potential at the center.
I can't seem to figure out a way to do ...
-1
votes
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
votes
1
answer
3k
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Working out equation of motion from potential energy [closed]
A potential energy of a particle in 2 dimensions $x$ and $y$ is given by
$$V = \dfrac{k(x^2+y^2)}{2}$$
And the equations of motions for this particle are to be calculated given that the mass of the ...
0
votes
2
answers
42k
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How to get height from potential energy? [closed]
I am making a spring launcher for an RC car. but i am trying to understand elastic potential energy of a spring and hooks law. this is what i have.
The car will weigh 200 grams.
The spring has a ...
- 21
2
votes
2
answers
2k
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Central force - stable/unstable circular orbit for $V = -V_0 \exp(-\lambda^2 r^2)$
This problem is from Introduction to Classical Mechanics With Problems and Solutions by David Morin. The solution is also given in the book for this particular problem.
Problem #6.6.1
A particle ...
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1
vote
1
answer
61
views
Conceptual difficulties with work
Consider the following problem.
Assuming that we do N joules of work in raising a M kg object, how far is it lifted?
We know that $$N = Fd$$ Therefore $$d = N/F$$ Therefore, $$d = N/Ma$$
Some people ...
1
vote
3
answers
1k
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I've a problem understanding Absolute Gravitational Potential Energy?
My current concept about potential energy is that 'If work is done on a body when it is at a point (taken as zero P.E), it covers some distance. Afterward, when it is allowed to move freely it does ...
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0
votes
1
answer
93
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What is the distance in between two shells of a spherical capacitor?
I am studying Capacitance for my Physics class. We have been working with parallel-plate capacitors, which I understand perfectly. However, I’ve seen some exercises with spherical and cylindrical ...
- 309
1
vote
2
answers
307
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Deriving gravitational potential energy - why is $r_0 = \infty$?
I'm wondering about some assumptions I have to make in deriving the gravitational potential energy. This arises from the following exercise:
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Since the net force acting on the satellite is ...
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3
votes
2
answers
734
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Why is the Gravitational Potential Energy calculation requires half the total length in case of the falling chain?
In this case, please note that it's written: $\displaystyle\frac{my}{l}g\frac {y}{2}$. Isn't the length supposed to be the total height of the falling chain, i.e., $y$ instead of $\dfrac {y}{2}$ where ...
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-1
votes
1
answer
412
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How to derive spring potential formula from Hooke's law?
I found this answer in another forum:
\begin{align}
W&=\int \mathbf F\cdot {\rm d}\mathbf x \\
&=-\int_0^xkx\,{\rm d}x \\
&=\frac{1}{2}kx^2
\end{align}
I don't understand why we have to ...
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1
vote
1
answer
361
views
Friction on parabola [closed]
A block is released from $x=2, y=4$ on a wire frame with equation $y=x^2$ find its velocity when it passes through origin.
The coefficient of friction between block and wire frame is $k$.
I tried to ...
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0
votes
2
answers
2k
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Question regarding bungee jumper [closed]
A man who does bungee jump jumps by the platform. The mass of the man is 60Kg . There is 45m from the platform to the water. Without stretching the rope is 25m long. The spring constant(k)=160Nm-1. ...
- 222
1
vote
2
answers
2k
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Prove there is an equipotential sphere between two point charges
Given two point charges of opposite sign I need to prove that inside the electric field they create there is an equipotential sphere.
I'm very positive that this is more geometry than anything else ...
- 351
1
vote
2
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338
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Relative height or height from ground?
Ok so I encountered this question ->
A 10 H.P. motor pumps out water from a well of depth 20m
and fills a water tank of volume 22380 litres at a height of 10m
from the ground. The running ...
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-1
votes
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
1
vote
1
answer
184
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The energy difference between $H$ atom and $H^+$ ion in Thomas Fermi Theory
The famous Thomas Fermi theory says that we can express the total energy of a atomic system with $N$ electrons orbiting around a charged nucleus of atomic number $Z$ in terms of radial density of ...
-1
votes
2
answers
97
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What does this root represent? [closed]
Three point charges $q$, $2q$ and $8q$ are placed on a 9cm wire and I have to minimize the potential energy.
On writing $U$, doing $dU/dx=0$ and solving the resultant quadratic equation, I get two ...
- 1,096
0
votes
2
answers
2k
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Getting 2 different answers when finding spring constant $k$ when gravity is involved
OK, so I've been wracking my brain for the past hour trying to figure out how to calculate k in a problem like this:
A mass of 10 kg is attached to a spring hanging from the ceiling. It is released,...
3
votes
3
answers
133
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Evaluating Potential Energy Integral in Quantum Chemical Calculations
My question is what are the steps for taking an integral of the following form?
$$\int e^{-\alpha|\mathbf r- \mathbf R_a|^2} {1\over|\mathbf r- \mathbf R_b|} e^{-\beta|\mathbf r- \mathbf R_b|^2} dV$$
...
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1
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2
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What happens when a voltmeter is connected across two parallel circuits?
Edit: Link to question.
I'm looking at question 4.6. I cannot understand how to make sense of this arrangement of voltmeter, let alone answer the question. Any help is very much appreciated.
Are you ...
user86425
1
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2
answers
3k
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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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1
vote
1
answer
1k
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Well-defined momentum
I have a question which states:
Show that a particle can have a well-defined momentum in every energy eigenstate if and only if the potential energy is uniform in space.
I am completely unsure how ...
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2
votes
1
answer
720
views
What is the electric potential energy of a system of 2 charges? [closed]
If we have two charges of +1C a distance of 1m apart, then if we fix one and bring the other from infinity, the work done = +k. Now, if we fix the other one and bring this one from infinity, the work ...
- 254
2
votes
0
answers
174
views
Cylinder rolling on an incline with offset center of gravity [duplicate]
Consider a hollow cylinder with a dense 1kg weight affixed to one point on the inside. If placed on an inclined plane, the cylinder will not roll down if there is sufficient friction.
If we ...
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2
votes
2
answers
279
views
Assuming strong Newton's third law, why is $\nabla V(\vert {\bf r}_i-{\bf r}_j\vert)=({\bf r}_i-{\bf r}_j)f$?
I don't understand how they come up with (1.34). All I know is that $\nabla V_{ij}=-{\bf F}_{ij}$, but I've never seen this scalar function $f$ appear. Has it something to do with the absolute value ...
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-1
votes
3
answers
1k
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Potential and Kinetic energy [closed]
How do you find potential and kinetic energy? I've gotten these questions wrong on my test and I do not understand why.
a 3-kg object is thrown horizontally off a 12-m high cliff. The Kinetic energy ...
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1
vote
1
answer
902
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Derivation of potential energy for Bohr's atomic model
I am trying to derive the total energy of the electron in Bohr's stationary orbit but I am finding it hard to derive the potential energy, i.e. how the potential energy is derived from the equation $$...
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1
vote
1
answer
315
views
Finding the spring compression length for an object to reach $U = 0$ [closed]
I have a question on the following, pertaining to only parts c and d (b was shown to provide the mass of the asteroid and radius):
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I'm going to define the mass of the asteroid here as $M_A$ and ...
- 3,200
0
votes
1
answer
335
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Finding height of rope when at an angle? [closed]
The question is that Jeff swings on a 7.6m rope that initially makes an angle of 37° with the vertical. If Jeff starts at rest and has a mass of 78kg, what is the tension in the vine at the lowest ...
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votes
1
answer
273
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How do you get the height of the block 1 after the blocks collides with block 2 on a frictionless ramp? [closed]
to get the initial height of block 1, i did mgh = 1/2(mv^2) so, 9.8(1.4)= 1/2(v^2)
and ended up getting v = 5.238. I'm not sure how to go on doing the rest.
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0
votes
2
answers
1k
views
Potential at a point on axis of the ring [closed]
Suppose we have to find out potential $V$ at point $P$ in the given figure.
I know that it can be easily done as
$$dV=\frac{k×dq}{\sqrt{(x^2+a^2)}}$$ and integrating $dq$ to $Q$. Where $k$ is a ...
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votes
2
answers
2k
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Charged box and spring in uniform electric field--when does the box stop moving?
I'm having a lot of trouble trying to figure this out: a box of mass m and positive charge Q is attached to a spring of spring constant k, which is in the equilibrium position. They sit horizontally ...
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3
votes
3
answers
3k
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Work done involving friction and other external forces
A block of mass $1$ kg is placed at the point A of rough track shown in figure. If slightly pushed towards right, it stops at B of track. Calculate work done by frictional force on the block during ...
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0
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3
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3k
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Is my derivation of the potential energy formula $m*g*h$ correct?
I've just wondered where the formula $E_{pot} = mgh$ you learn at school comes from so I've tried to work it out - is my reasoning correct?
The change in energy is given by
$$\Delta E=\int_{e}^{e+h}G\...
- 1,012
2
votes
1
answer
207
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Calculate distance of launched particles from a rotating disk
At my education we are busy with creating a small device that can spread thaw grains.
Our plan is as follows:
The particles should be spread by launching them from a fast rotating disk.
The particles ...
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0
votes
2
answers
1k
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Potential energy in cylindrical coordinates [closed]
I am having trouble deriving the elastic potential energy in cylindrical coordinates for this problem:
We have $|AP| = 2R\cos(\phi/2)$ (elongation) and $\theta = \phi/2$. The projection axes (defined ...
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0
votes
0
answers
118
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From Lagrangian of Electromagnetic field to the Lorentz force? [duplicate]
The dynamics of a charged particle with velocity $\textbf{v}$ in electromagnetic field is dominated by the Lorentz force
$$\textbf{F} = q(\textbf{E}+{\textbf{v} \times \textbf{B}}), \tag{1}$$
and ...
- 1,757
1
vote
4
answers
98
views
Faced a contradiction while calculating the work done by an outside agent from two different ways
I solved this problem in two ways.
Since $dV$ and $dy$ are given, we sum the work done on the hydro-static system and the change in the potential energy of the spring.
$$\delta W=-PdV+\frac12 k ...
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1
vote
0
answers
215
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Effective potential in Lagrangian
I have two question related to the steps in equations 3-7 in this paper:
Question 1 They find the effective potential in eq. (5) as the negative of the effective Lagrangian (eq. (3)). I don't see how ...
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0
votes
2
answers
70
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Calorimetry problem [closed]
The second picture shows the textbook solution which I don't find convincing and the third picture shows my work.
I don't understand why will the block fall 40 cm toward the bottom of the vessel as ...
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2
votes
1
answer
315
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How is it possible to define a potential energy of a magnetic dipole if $\bf{B}$ is not conservative?
The magnetic field $\mathbf{B}$ is not conservative (it is not even irrotational). Nevertheless, considering a small loop (of area $S$ ) with electric current $i$ (equivalent to a magnetic dipole) in ...
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votes
2
answers
1k
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Question related to Potential Energy - Mass Spring System [closed]
The P.E stored by a mass spring system at an extension of 2cm is 10J. The P.E stored by the same system at an extension of 4cm will be?
Someone please provide an extensive answer if possible.
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3
votes
4
answers
2k
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Meaning of transmission coefficient greater than one in a potential well problem
Consider the finite 1D wedge-shaped potential well given by
$$V(x)=V_0\left(\frac{|x|}{a}-1\right) \hspace{10pt}\mathrm{for}\hspace{3pt} |x|<a;\hspace{6pt}V(x)=0 \hspace{10pt}\mathrm{for}\hspace{...
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votes
2
answers
4k
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Potential energy of an Atwood Machine [closed]
The two weights on the left have equal masses $m$ and are connected by a massless spring of force constant $k$. The weight on the right has mass $M=2m$, and the pulley is massless and frictionless. ...
- 171
-2
votes
2
answers
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 ...
- 823
1
vote
0
answers
78
views
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
1
vote
1
answer
13k
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Problem in Proving the potential due to concentric shells between the shells
Imagine a spherical shell having charge Q. The Electric Field exists outside. I bring a test charge from infinity to the surface of the shell (I bring it radially to simplify the calculation and ...
- 2,797
-1
votes
1
answer
1k
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Maximum height mass attached to a vertical spring with conservation of energy
There are various methods to find anything we like for a mass attached to a vertical spring, however I wanted to use the conservation of energy.
Suppose $m$ hangs from the spring of normal length $l$ ...
- 247
1
vote
1
answer
868
views
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. ...
- 19