All Questions
61
questions
0
votes
1
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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 ...
- 103
0
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
views
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
-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? ...
1
vote
2
answers
380
views
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 ...
- 493
0
votes
2
answers
815
views
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 ...
- 141
0
votes
1
answer
42
views
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 ...
- 62
6
votes
2
answers
2k
views
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 $$ V(r) = -\frac{...
- 1,031
1
vote
1
answer
2k
views
Force derived from Yukawa potential
This is with regards to problem 3.19 from Goldstein's Classical Mechanics,
A particle moves in a force field described by the Yukowa potential $$ V(r) = -\frac{k}{r} e^{-\frac{r}{a}},
$$ where $k$ ...
- 1,031
0
votes
1
answer
106
views
Feynman Lectures, Chapter 4, Fig 4-3
From the Feynman lectures Chapter 4, Fig 4-3
"We lifted the one-pound weight only three feet and we lowered W pounds by five feet. Therefore W=3/5 of a pound."
If there is a change of 3ft in ...
- 171
2
votes
2
answers
1k
views
Change in Energy when placing an object on the ground
It seems like a simple question but I was wondering where does the energy go when I place an object from a height on the floor.
Initially it's all stored as potential energy, and as I'm moving the ...
- 131
1
vote
1
answer
383
views
Weight and potential energy for a spring pendulum
Consider a spring pendulum like in this figure
suppose the spring is arranged to lie in a straight line and its equilibrium lenght is $l$.
Consider the unit vectors $e_1, e_2$, $e_x, e_{\theta}$ like ...
- 145
0
votes
2
answers
783
views
Classical period of Morse potential [closed]
A particle of mass $m$ and energy $E<0$ moves in a one-dimensional Morse potential:
$$V(x)=V_0(e^{-2ax}-2e^{-ax}),\qquad V_0,a>0,\qquad E>-V_0.$$
From the only other question I have ...
0
votes
1
answer
78
views
Approximating the time it takes for a particle with a potential $-Ax^4$ to approach the origin [closed]
Here's the problem I'm solving:
A particle of mass $m$ can only move along the $x$-axis and is subject to an interaction described by the potential energy function $U\left(x\right) = -Ax^4$, where $A ...
user113773
0
votes
4
answers
102
views
Potential Energy of Conservative Forces [closed]
For a conservative force, its associated potential energy at position $\mathbf{r}$ is
$$U(\mathbf{r}) = - \int_{\mathbf{r}_{0}}^{\mathbf{r}} \mathbf{F}(\mathbf{r'}) \cdot \text{d} \mathbf{r'}$$
...
- 1