All Questions
17
questions
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1
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40
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Integrating acceleration + escape velocity over distance [closed]
I am not sure how to title this question so apologies if it's inaccurate.
If I throw an object at thrice the escape velocity of earth, what would be its velocity very far away from earth, (at a ...
- 129
-1
votes
5
answers
477
views
(Not a flat-earther) The mathematics of an infinite flat earth using gauss' law for gravity
On the flat earth website, they prove that the gravitational pull of an infinite flat earth is finite. Is their proof correct?. I'm not that good at physics and can't determine if they're correct ...
- 29
1
vote
1
answer
71
views
Question on Gravity (Ring and Sphere) [closed]
Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If $R\sqrt8$ is the ...
- 19
0
votes
1
answer
98
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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$$
Where $R$ is the radius of the sphere ...
- 16.7k
0
votes
1
answer
438
views
Gravitational potential of a disc [closed]
The question says
Find the potential at the center of a disc whose surface area density varies as $$σ = σ_0(1+\cosθ)r $$ where theta is the angle made by the radius with the horizontal and $r$ is the ...
user318937
0
votes
2
answers
166
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Calculating the gravitational field on a point mass at central axis of a uniform ring [closed]
Consider a uniform ring of mass $M$ and radius $r$ and centre $O$. Let $P$ be a point on the central axis of the given ring at a distance $a$ from the centre of the ring (line passing through the ...
user297948
1
vote
1
answer
130
views
Finding velocity $v$ and position $r$, given a time $t$ under the acceleration of a gravitational force [closed]
I was messing with the maths, when I tried to find the velocity as a function of time, $v(t)$, and the position, also, as a function of time, $r(t)$ under the gravity force.
$$ m \ddot{r} = -G \frac{...
- 1,525
0
votes
2
answers
729
views
What is the gravitational potential of a homogeneous sphere? [closed]
I am studying gravitational potentials from the book Galactic Dynamics by James Binney and Scott Tremaine. They provide the equation from where the potential of a spherical system is to be derived as:
...
- 197
0
votes
2
answers
787
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How to calculate center of mass of a hollow hemi-sphere with some thickness?
When we calculate Center of mass (COM) of a hollow sphere, we assume that it's thickness is
infinitesimally small, but in real world, we do not have any object with zero thickness, so how can we ...
-1
votes
3
answers
1k
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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:
$$F_g = \frac{GMm}{r^2}$$
$$U_g =...
- 101
0
votes
2
answers
480
views
Feynman's proof for Newton's shell theorem [closed]
I have two questions concerning this proof:
Firstly, what is the difference between the increments ds and dx? Are they not just the same thickness of the strip?
Secondly, why can the integral ...
- 406
2
votes
3
answers
832
views
What's my $\mathrm dM$? Gravitational Potential inside a circle of mass
I'm trying to find the gravitational potential for an arbitrary point within a ring of uniform mass density. The point is constrained to be in the same plane as the ring.
So we start with:
$$\Phi=\...
- 53
0
votes
1
answer
91
views
How to find an equation for $x$ in terms of $t$ for a particle falling under gravity with resistance given by $mkv^2$? [closed]
Okay so I have determine the velocity $v$ and displacement $x$ as functions of $t$ for a particle falling under gravity with resistance given by $mkv^2$.
I have set up the equation of motion divided ...
- 35
1
vote
1
answer
1k
views
From Paris to ... London [closed]
(Excuse the pun in the title, couldn't resist)
Paris and London are connected by a straight underground tunnel, as shown in the diagram below. A train travels between the two cities powered only by ...
- 3,569