All Questions
12
questions
3
votes
1
answer
112
views
Confusions on The Gravitational Energy of a Point P in a Cube
I have been working, quite tirelessly, to try and find an answer to a question that has been bothering me for some time now.
I have been working over some proofs, in the Newtonian Mechanics world, to ...
- 152
1
vote
1
answer
56
views
How to calculate the potential energy of a large object as an integral?
Usually when calculating the potential energy of a body it is sufficient to take its center of gravity’s distance from the ground in order to get a result according to the formula $E_p=g*h*M$. But the ...
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
$$
V(\mathbf{a})=\int\int\int\dfrac{1}{\vert\mathbf a -...
- 95
0
votes
2
answers
239
views
Direct calculation of the gravitational potential inside a hollow sphere
I calculated the gravitational potential inside a massive sphere with constant density and got the result:
$$\Phi = -2\pi G\rho R^2 + \frac{2}{3}\pi G\rho R_p^2$$
Where $R$ is the radius of the sphere ...
- 16.7k
0
votes
2
answers
298
views
What is the meaning of Gravitational Potential when multiple point masses are involved?
According to Wikipedia "The gravitational potential $V$ at a distance $x$ from a point mass of mass $M$ can be defined as the work $W$ that needs to be done by an external agent to bring a unit ...
- 379
0
votes
1
answer
182
views
Better understanding of the definition of Gravitational Potential as the improper integral $\frac{1}{m}\int^x _{\infty}G\frac{Mm}{x^2}dx$
According to Wikipedia "The gravitational potential $V$ at a distance $x$ from a point mass of mass $M$ can be defined as the work $W$ that needs to be done by an external agent to bring a unit ...
- 379
3
votes
1
answer
491
views
Better derivation for the gravitational potential energy
I was shown this derivation for the gravitational potential energy, and I'm not very happy about it assuming that $\frac{1}{\infty} = 0$. Is there a better derivation, either using a completely ...
- 73
-1
votes
3
answers
1k
views
Derive gravitational potential energy for this system [closed]
This is on a study guide for my Physics 221 final. I feel like I almost got it but I am off by a sign error. Here is the question:
Here is what I got so far:
Known:
$$F_g = \frac{GMm}{r^2}$$
$$U_g =...
- 101
3
votes
1
answer
204
views
How to calculate the gravitational binding energy of a uniform cube of length $L$ and mass $M$?
The functional form is known already (as attached). But what is the solution for this integral?
- 425
0
votes
1
answer
51
views
Nonlinear GPE of a solid block seems wrong
I am trying to calculate the gravitational potential of a solid block, and I have a nonlinear answer which strikes me as wrong.
A block with horizontal surface area $A [m^{-2}]$ and uniform density $\...
- 5,148
12
votes
2
answers
22k
views
Gravitational potential energy of any spherical distribution
The general formula to get the potential energy of any spherical distribution is this :
\begin{equation}\tag{1}
U = - \int_0^R \frac{GM(r)}{r} \, \rho(r) \, 4 \pi r^2 \, dr,
\end{equation}
where $M(r)$...
- 7,592
4
votes
2
answers
326
views
How do you know which way to choose the limits of an integral?
I am reading http://www.feynmanlectures.caltech.edu/I_13.html#Ch13-S4
In the beginning of equation 13.18, in which Mr. Feynman calculates the potential energy of an object outside a spherical shell, ...
- 527