All Questions
61
questions
0
votes
3
answers
80
views
Question regarding gravitational force as external force
So, I was watching a lecture on YouTube for problems on conservation of energy and momentum and I don't quite understand this:
In this question, mass $M$ is released from the peak of the smooth ...
0
votes
1
answer
58
views
Question about Problem $12$ in Chapter $11$ from Kibble & Berkshire's book
I write again the problem for convinience:
A rigid rod of length $2a$ is suspended by two light, inextensible strings of length $l$ joining its ends to supports also a distance $2a$ apart and level ...
- 54.5k
1
vote
1
answer
164
views
Why is there a *minimum* energy for a particle to be captured in a $r^{-3}$ potential?
I was stuck in a central force problem from David Morin's Book "Introduction to Classical Mechanics".
The problem states that suppose there is a particle of mass $m$ moving under the ...
- 207k
4
votes
2
answers
5k
views
Problem $\S12$ $2(b)$ of Landau & Lifshitz "Mechanics" Integration of the Equations of motion [closed]
I'm studying Landau, Lifshitz - Mechanics. Could someone help me with this problem ? =)
Problem $\S12$ $2(b)$ (Page 27 3rd Edition) Determine the period of oscillation, as a function of the energy, ...
- 219
1
vote
2
answers
65
views
Position equation of $U(x)=-U_1[(\frac{x}{x_1})^3-(\frac{x}{x_1})^2 ]$
If $U(x)$ is given by $$U(x)=-U_1\left[\left(\frac{x}{x_1}\right)^3-\left(\frac{x}{x_1}\right)^2 \right]$$ can I find the position equation without harmonic aproximation?
I'm having problem with the ...
- 1,940
0
votes
2
answers
195
views
Marble "rolling" on the graph of a function
Consider a guide for marbles whose profile locally coincides with a function $f(x)$, for example
$f (x) = - \frac{1}{2} x ^ 4 + x ^ 3 + x ^ 2-2x + 1.$
Suppose that the reference system is chosen in ...
- 2,536
1
vote
0
answers
50
views
Potentials that prevent the phase flow of the system [closed]
I am trying to solve a question that my professor gave.
When a particle moves in one dimension $x$ in a potential $U(x)$ , the resulting motion over a very short time interval is specified by Newton’...
- 207k
0
votes
1
answer
332
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Doubt from Arnold; Mathematical methods of classical mechanics (page 20)
I am trying to do a problem from Arnold; Mathematical methods of Classical mechanics.
But I didn't get the desired result mentioned by the author.
Let $E_0$ be the value of the potential function at ...
- 6,235
13
votes
5
answers
4k
views
Why does the incline angle not affect how high a launched object will slide up a frictionless ramp?
I am seeing a problem with the solution given in this book. How did the height of the box have nothing to do with the incline of the ramp? Intuitively it would seem the higher the incline the higher ...
- 626
1
vote
0
answers
71
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Verifying the equation of motion, expressions of kinetic energy and potential energy and how to examine whether motion confined to a plane or not [closed]
A particle is moving in space such that it is attracted towards a fixed point and is proportional to the distance from the fixed point. Derive the Lagrangian and Hamiltonian of the system. Examine ...
- 111
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{=}\...
- 25k
4
votes
1
answer
442
views
Period on the phase plane (small oscillations)
I have this formula to calculate the period of a motion in the phase space (plan, in this case) along a phase curve.
\begin{equation}
T(E)=\int_{x_1}^{x_2}\frac{dx}{\sqrt{2(E-U(x))}}
\end{equation}
...
- 12.1k
0
votes
1
answer
178
views
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, ...
- 207k
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 ...
- 207k
0
votes
0
answers
40
views
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 ...
- 207k