All Questions
61
questions
58
votes
15
answers
13k
views
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 ...
- 1,298
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 ...
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 $$ V(r) = -\frac{...
- 1,031
5
votes
1
answer
1k
views
How to show period is defined by $T=dS/dE$ (V.I. Arnold Mathemtical Physics) [closed]
I'm looking at a book by VI Arnold on mathematical physics and I've hit a roadblock pretty early on. I'll quote the question:
"Let $S(E)$ be the area enclosed by the closed phase curve ...
- 130
4
votes
2
answers
3k
views
Proof of total energy is constant in a central force field
I saw many proofs of total energy is constant in a central force field. But all the proofs end up showing this formula $$m[{\dot r}^2 + r ^2{\dot \theta}^2 ]+ \int f(r)dr = E$$ is constant. But ...
- 1,149
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, ...
- 43
4
votes
2
answers
1k
views
The "stationary potential energy" condition for static equilibrium in mechanical systems
I've often read that, for a mechanical system which can be described by $n$ generalized coordinates $q_1,...,q_n$, a point $\mathbf{Q}=(Q_1,...,Q_n)$ is a point of equilibrium if and only if the ...
- 4,654
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}
...
- 1,704
4
votes
0
answers
1k
views
Hamiltonian function for classical hard-sphere elastic collision [closed]
I'm trying to find the Hamiltonian function for a system consisting of a single particle in one dimension colliding elastically with a wall at $x = 0$.
Everything I've read on the topic (e.g. this ...
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{=}\...
- 436
3
votes
2
answers
3k
views
Charge, velocity-dependent potentials and Lagrangian
Given an electric charge $q$ of mass $m$ moving at a velocity ${\bf v}$ in a region containing both electric field ${\bf E}(t,x,y,z)$ and magnetic field ${\bf B}(t,x,y,z)$ (${\bf B}$ and ${\bf E}$ are ...
- 1,133
3
votes
1
answer
2k
views
Finding potential energy of a solid hemisphere on top of another solid hemisphere [closed]
A solid hemisphere with radius $b$ has its flat surface glued to a
horizontal table. Another solid hemisphere with radius $a$ rests on top
of the hemisphere of radius $b$ so that the curved ...
- 111
2
votes
2
answers
2k
views
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 ...
- 592
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
2
votes
1
answer
125
views
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 ...
- 123