All Questions
Tagged with potential-energy homework-and-exercises
35
questions
5
votes
2
answers
4k
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Shape of a string/chain/cable/rope/wire? [closed]
The height of a string in a gravitational field in 2-dimensions is bounded by $h(x_0)=h(x_l)=0$ (nails in the wall) and also $\int_0^l ds= l$. ($h(0)=h(l)=0$, if you take $h$ as a function of arc ...
- 1,550
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,...
-1
votes
2
answers
639
views
Electric Potential produced by Hollow Sphere
Let there be a hollow sphere (Throughout the question we will ignore the thickness of the sphere) which is positively uniformly charged,q of radius, R. Suppose there to be a test positive charge, q' ...
- 356
3
votes
3
answers
2k
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Potential energy of an infinitesimal length of elastic rod
I am having an embarrassingly hard time with the derivation for the potential energy of an infinitesimal element of an elastic rod of area $A$. The picture shown below is an element of the rod that ...
- 423
1
vote
1
answer
334
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Why does $\omega = \sqrt{V''(x_0) / m}$?
I know that in an equation such that $$\ddot{x} + \omega^2x = 0,$$ the angular frequency $ = \omega$. But why is that ever $ \sqrt{V''(x_0) / m}$? (where $x_0$ is the equilibrium point). I just saw ...
- 171
3
votes
2
answers
3k
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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
537
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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
1
vote
2
answers
845
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Elastic potential energy and equilibrium position when mass changes in vertical mass-spring system
I'm a bit stuck with this situation:
Suppose that an object $A$ with mass M=8 kg at 10 mt above the floor falls from rest tied to an 2 mt elastic rope, which does not exert any force since $A$ falls 2 ...
- 21
0
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 ...
-1
votes
2
answers
2k
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Potential at Center of Earth
If using the surface of the earth as a reference point how much work is needed for gravity to pull me to the center. Is it negative infinity or am I wrong? Also is a single value of potential ...
- 53
5
votes
3
answers
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 ...
- 559
4
votes
0
answers
1k
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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 ...
4
votes
2
answers
7k
views
Why is the gravitational potential inside a hollow sphere same as that of the gravitational potential on the surface of the hollow sphere? [duplicate]
Gravitational potential inside a hollow sphere is given by $$V(r)=\frac{-Gm}{R}$$ Why is it the same as the gravitational potential on the surface of the hollow sphere, which is given by $\frac{-Gm}{R}...
- 43
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
2
votes
1
answer
1k
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What is the energy of interaction between a point charge and an infinite cylinder?
I don't remember enough from my electromagnetism course and I can't find any simple, full example on this subject.
I know, that I can consider the cylinder as a wire with the same charge density (...
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