All Questions
15
questions
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1
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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
3
votes
1
answer
112
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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
51
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Problem with Deriving work done by gravitational force and gravitational potential energy from the first principles
Suppose we have a system with Two point masses of mass $M$ and mass $m$. And we want to derive Work done. Lets say M is fixed or $M>>m$. Initially assume mass m is at rest at a distance of $a$ ...
- 45
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
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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.
$$ m \ddot{r} = -G \frac{...
- 1,525
0
votes
3
answers
147
views
The force of gravity between a shperical shell and a particle
I am trying to understand the proof of why the force acting on a spherical shell and a particle is
$$\frac{GMm}{r^2}$$
Where M is the mass of the sphere and m is the mass of the particle.
I am looking ...
- 5
0
votes
2
answers
787
views
How to calculate center of mass of a hollow hemi-sphere with some thickness?
When we calculate Center of mass (COM) of a hollow sphere, we assume that it's thickness is
infinitesimally small, but in real world, we do not have any object with zero thickness, so how can we ...
0
votes
1
answer
51
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Nonlinear GPE of a solid block seems wrong
I am trying to calculate the gravitational potential of a solid block, and I have a nonlinear answer which strikes me as wrong.
A block with horizontal surface area $A [m^{-2}]$ and uniform density $\...
- 5,148
1
vote
2
answers
416
views
Gravitational force of point mass on a rigid body - Integral proof
Assume a point mass $m$ located at $\vec{x}$. Assume also a solid body whose coordinates $\vec{x}'$ belong to a connected subdomain $\vec{x}' \in \Omega$. The solid body has a non-uniform mass density ...
- 201
12
votes
2
answers
22k
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Gravitational potential energy of any spherical distribution
The general formula to get the potential energy of any spherical distribution is this :
\begin{equation}\tag{1}
U = - \int_0^R \frac{GM(r)}{r} \, \rho(r) \, 4 \pi r^2 \, dr,
\end{equation}
where $M(r)$...
- 7,592
0
votes
1
answer
899
views
Period of a pendulum [closed]
In the book 'Calculus the Early Transcendetals' at page 776 (7th edition) they give that the period of a pendulum with length $\text{L}$ that makes a maximum angle $\theta_0$ with the vertical is:
$$\...
- 291
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
2
votes
0
answers
123
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What is the correct way of integrating in astronomy simulations? [closed]
I'm creating a simple astronomy simulator that should use Newtonian physics to simulate movement of plants in a system (or any objects, for that matter). All the bodies are circles in an Euclidean ...
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