All Questions
Tagged with potential-energy homework-and-exercises
395
questions
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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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2
votes
0
answers
711
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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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1
vote
1
answer
383
views
Weight and potential energy for a spring pendulum
Consider a spring pendulum like in this figure
suppose the spring is arranged to lie in a straight line and its equilibrium lenght is $l$.
Consider the unit vectors $e_1, e_2$, $e_x, e_{\theta}$ like ...
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4
votes
2
answers
1k
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Can Potential Energy be found by Energy Density? [closed]
I wanted to find a creative solution to the problem:
Find the electric potential energy of a uniformly charged sphere of radius $R$ possessing a charge $Q$.
My attempt at a solution:
Consider a ...
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3
votes
4
answers
712
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Rocket Leaving Earth's Gravitational Field
I stumbled across this seemingly simple question that really stumped me on further thought:
A rocket is intended to leave the Earth's gravitational field. The fuel in its main engine is a little ...
0
votes
2
answers
783
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Classical period of Morse potential [closed]
A particle of mass $m$ and energy $E<0$ moves in a one-dimensional Morse potential:
$$V(x)=V_0(e^{-2ax}-2e^{-ax}),\qquad V_0,a>0,\qquad E>-V_0.$$
From the only other question I have ...
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votes
2
answers
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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101
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To consider or not to consider potential energy of a mass attached to a spring in oscillation? [closed]
For the above system I have the following expressions for kinetic and potential energy:
$$
V = \frac{1}{2}\,k\,x^{2}+m\,g\,l\,(1-cos\,\theta)-m\,g\,x\\ T = \frac{1}{2}\,m\,\dot{x}^{2}+\frac{1}{2}\,m\,...
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0
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130
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Charging two spheres by induction n times
There is a conducting sphere $S_1$ of radius 'r' mounted on an insulating handle. The sphere is given a charge Q. Another uncharged conducting sphere $S_2$ of radius R mounted on an insulating handle ...
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1
answer
78
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Approximating the time it takes for a particle with a potential $-Ax^4$ to approach the origin [closed]
Here's the problem I'm solving:
A particle of mass $m$ can only move along the $x$-axis and is subject to an interaction described by the potential energy function $U\left(x\right) = -Ax^4$, where $A ...
user113773
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4
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102
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Potential Energy of Conservative Forces [closed]
For a conservative force, its associated potential energy at position $\mathbf{r}$ is
$$U(\mathbf{r}) = - \int_{\mathbf{r}_{0}}^{\mathbf{r}} \mathbf{F}(\mathbf{r'}) \cdot \text{d} \mathbf{r'}$$
...
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votes
2
answers
127
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Work done in circular expansion of a rubberband or an elastic wire
What will be the work done in radially stretching a rubberband it can't be zero as there is potential energy being stored in it
All I came up with it that there would be increase in overall length so ...
0
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1
answer
767
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Two point charges
Is it possible to have an arrangement of two point charges separated by a finite distance such that the electrical potential energy of the arrangement is the same as if the two charges were infinitely ...
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1
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1
answer
55
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2 body problem question
I am taking a classical mechanics course and i am struggling to determine the equilinrium points for this potential $$Q= -(k/r) + ar + (L^2/mr^2).$$ The problem is that i have to solve a cubic ...
4
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2
answers
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Proof of total energy is constant in a central force field
I saw many proofs of total energy is constant in a central force field. But all the proofs end up showing this formula $$m[{\dot r}^2 + r ^2{\dot \theta}^2 ]+ \int f(r)dr = E$$ is constant. But ...
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2
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Why do we include $x$ in this Spring Equation?
I am currently in Physics 1 and we are learning about Energy. This may sound like a dumb question but I am currently trying to understand this. Here is the question of the problem:
A 10kg block is ...
1
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2
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680
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Accurate Equation for Earth's Gravitational Binding Energy
This is a relatively important question for anyone who can answer it. I am trying to find the equation that accurately solves for Earth's Gravitational Binding Energy. The information below is from ...
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1
answer
315
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Finding G.P.E. of a system of particles
we want to calculate the P.E(potential energy) of a system containing 3particles p1,p2,p3.the point of observation is P.so now we should add up the P.E at P due to p1,p2,p3 to get the net potential ...
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1
answer
646
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Problem regarding finding work done
This problem is given in my physics book. How much work will be done if anyone wants to stack up 12 bricks? Given that each brick is $10 cm$ high and each brick's mass is $2 kg$. ($g=9.8$)
Now in ...
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Motion of an electron near a proton [closed]
Statement of the problem:
Consider an electron and a proton that are initially at rest separated $a$ meters. Do not take into account the movement of the proton, because its mass is much greater ...
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votes
1
answer
376
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Change in electric potential energy after sphere splits in two
The problem:
Consider a uniformly charged sphere of radius $R$ and charge $Q$ and then they separate into two spherical halves of equal volume and charge, and both get to stabilize. Determine the ...
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votes
1
answer
576
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What is the largest radius that the circular track can have such that the car remains in contact with the track? [closed]
A car is travelling at $u$ as it enters a vertical loop of radius $r$.
What is the largest value of $r$ that the track can have such that the car goes up and around the track whilst remaining in ...
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3
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7k
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Electric Potential Energy of a charged conductor
My physics textbook asks (I translate):
A sphere of copper with a radius of 0.72 metres is charged with a Potential of 270,000 Volt. Find its charge and the electric energy it holds.
I found the ...
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votes
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
58
votes
15
answers
13k
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When a balloon pops and lets a brick fall, where does the energy come from?
Let's say a scientist attaches a 1 kg brick to a large helium inflated balloon, lets the balloon go, and then it reaches an altitude of 10 000 meters before it pops, dropping the brick.
The brick ...
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Gravitational potential energy and kinetic energy
I have a question that has been bugging for quite some time now. The quesiton is from a textbook by Bostock and Chandler on Mechanics.
It says:
Water is being raised by a pump from a storage ...
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2
votes
1
answer
125
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Potential energy and conservation law
I'm preparing for my masters entrance exam on pure mathematics (thought some problems are devoted to classical/lagrangian mechanics). I would be grateful to clarify some basics regarding the ...
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0
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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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1k
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Finite square well bound states
Let's suppose I have a finite potential well: $$
V(x)=
\begin{cases}
\infty,\quad x<0\\
0,\quad 0<x<a\\
V_o,\quad x>a.
\end{cases}
$$
I solved the time-independent Schrodinger equation ...
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2
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217
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Gravitational potential energy in CM frame
If the centre of mass is taken as the origin, then the gravitational potential energy of two bodies is
\begin{equation}
V=-\frac{Gm_{1}m_{2}}{(r_{1}+r_{2})}
\end{equation}
where $r_{1}$ and $r_{2}$ ...
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1
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271
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Lagrangian of a massive particle in an electromagnetic field
I am trying to find the Lagrangian of a massive particle in an electromagnetic field using the Lorentz force: $$ \vec F = q ( \vec E + \vec v \times \vec B)$$ with $$\vec E = - \nabla \phi - \frac{\...
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30k
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How to calculate speed, given potential energy and mass? [closed]
A question from a CIE IGCSE Physics past paper:
[A train, travelling at speed $v$, is approaching a buffer.]
The train, of mass $2.5 \text{kg}$, is stopped by compressing a spring in the buffer. ...
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-1
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1
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106
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Direction of infinite plate when calculating the potential difference [closed]
Given the setting,
What is the potential difference between point $Q, ( {q ~\rm cm} , {0~\rm cm} )$ and point $P, ( {p~\rm cm} , {0~\rm cm})$? Let $q = 17.2~\rm cm$ and $p = 2~\rm cm$.
When ...
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690
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Why does mass increase when gravitational potential energy increases?
I saw a solved example in a book (Concepts of Physics by H.C. Verma, volume 2), where there is a body near surface of the earth, the problem is to calculate the increase in mass of the body when it is ...
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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
1
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0
answers
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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2
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75
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Potential energy function
I've been given
"A particle of mass m moves under a force $F = −cx^5$, where $c$ is a positive constant. Determine the potential energy function."
I've obtained:
Is this correct? I've separted ...
1
vote
1
answer
4k
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Potential energy of a mass-spring system
I'm having trouble with determining the potential energy of the mass-spring system depicted below. We assume that the extensions of all 3 springs are zero when $x_1=x_2=0$. The potential energy that I ...
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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 ...
0
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1
answer
1k
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Work done against gravity by a man climbing up a rope [closed]
Question:
A man of weight W hangs at the end of a light extensible rope whose modulus is $nW$. The other end of the rope is fastened to a fixed point. He proceeds to climb up the rope. Prove that ...
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2
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Perturbation theory with infinite potential
I'm trying to solve an excercise that involves first order perturbation theory and an infinite potential. To ease the problem, I tried to consider an easier one dimensional model. Consider an infinite ...
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2
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3k
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If the difference in pressure is zero between two points of a horizontal constant-radius pipe, why isn't flow rate zero?
In a straight pipe of uniform cross-sectional area filled with a nonviscous, incompressible fluid, the pressure at one end is equal to the pressure at the other end. Which of the following statements ...
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139
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Final state of a two-block system with friction on a smooth ground
I was working on a modified version of this problem (which I solved):
The modification is as follows:
Consider the following system with two masses, $M$ and $m$, with the length of the body $M$...
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-2
votes
1
answer
400
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How to calculate the potential energy and acceleration in a fixed pulley [closed]
This is my first post here so I want to give a disclaimer. I study in Slovenia so maybe my terminology won't be proper. Sorry in advance!
So I came accross an excersise that is giving me a lot of ...
-1
votes
1
answer
143
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Spring-mass problem [duplicate]
Question: A spring-mass system hangs vertically from a fixed support. The natural length of the spring is l. The block is displaced from the equilibrium position and constrained to move horizontally. ...
-3
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1
answer
67
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Frequency of vibration from potential field [closed]
I have an equation:
$$V = 200x^2 + 150 ergs/gm$$
How can I get the frequency of its vibration? (I have the mass of object which is 4gm)
I don't know where to start to solve this. Please help.
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5
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How can we determine stable and unstable equilibrium points from a potential energy versus displacement graph?
In this question, how can we comment on the position of stable/unstable equilibrium if we don't know the total energy of the system? We know force is zero at points 'a', 'b', 'c' and 'd' but there ...
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-2
votes
2
answers
481
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In this question of elastic potential energy, why doesn’t the answer of compression come negative? [closed]
A smooth curved track terminates in a smooth horizontal part. A spring of spring constant $400N/m$ is attached at one end of a wedge fixed rigidly with the horizontal part. A $40g$ mass is released ...
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votes
3
answers
499
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How do I get the negative sign in the expression for Gravitational Potential Energy?
From universal law of gravitation, gravitational force exerted on a body of mass m by another body of mass M is
$$ \mathbf F = \frac{GMm}{x^2} $$
where x is the distance between the ...
77
votes
8
answers
27k
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Does a thrown ball have kinetic energy at the top of the curve?
I'm going through physics with my 5th grade child. There is a question and answer that indicates that a airborne ball at the top of the trajectory does not have kinetic energy.
The diagram below ...
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