All Questions
11
questions
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Finding the Equation of motion for a vertical rotating disc with an added mass
I have been trying to figure out the equation of motion of a rotating disc with an added mass fixed on the surface of the disc at a certain distance $r$ from the disc's centre point.
I have ...
0
votes
1
answer
98
views
Triple integral gravitational potential between point and sphere [closed]
Problem for self-study: Gravitational potential between a point $\mathbf a$ and a uniform sphere, leaving out gravitational and density constants
$$
V(\mathbf{a})=\int\int\int\dfrac{1}{\vert\mathbf a -...
- 95
0
votes
2
answers
239
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Direct calculation of the gravitational potential inside a hollow sphere
I calculated the gravitational potential inside a massive sphere with constant density and got the result:
$$\Phi = -2\pi G\rho R^2 + \frac{2}{3}\pi G\rho R_p^2$$
Where $R$ is the radius of the sphere ...
- 16.6k
-1
votes
1
answer
827
views
Find Potential energy of a hanging chain
A chain of Length L is fixed at one end to a point and the rest of the chain is hanging such that the other end of the chain just touches the ground. Find the potential energy of the chain given its ...
0
votes
1
answer
128
views
Why have we assume that the there should be no acceleration in deriving the Electrostatic potential energy
In the NCERT textbook grade 12, it is mentioned before deriving the work done in moving a charge $q$ from point $R$ to $P$ in presence of an electric field at Origin, $O$ by charge $Q$
Two remarks ...
- 753
0
votes
1
answer
96
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How do I integrate this function? [closed]
I have an exercise where I have to calculate the potential energy function $U(x)$ of this force $F$. I know the function is given by integrating $-F$, but how do I do this? $c$ is a constant, and a ...
-1
votes
3
answers
1k
views
Derive gravitational potential energy for this system [closed]
This is on a study guide for my Physics 221 final. I feel like I almost got it but I am off by a sign error. Here is the question:
Here is what I got so far:
Known:
$$F_g = \frac{GMm}{r^2}$$
$$U_g =...
- 101
3
votes
3
answers
133
views
Evaluating Potential Energy Integral in Quantum Chemical Calculations
My question is what are the steps for taking an integral of the following form?
$$\int e^{-\alpha|\mathbf r- \mathbf R_a|^2} {1\over|\mathbf r- \mathbf R_b|} e^{-\beta|\mathbf r- \mathbf R_b|^2} dV$$
...
- 68
1
vote
1
answer
452
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Buckling of a slender column - total energy
I'm following Goldbart's Mathematics for Physics book, and I ran into a problem with exercise 1.4 (page 43). We have a formula for the energy stored in a slightly bent rod aligned on the $z$ axis:
$ ...
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
1
vote
1
answer
1k
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Derivation of the self gravitational potential energy of a sphere
I have been searching on the Internet but have not found a derivation of the formula for the self gravitational potential energy of a sphere. Can someone show how to do this? I assume it involved 6 ...
- 175