New answers tagged newtonian-gravity
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Gravitation satellite orbiting earth
Your statements are consistent because they are answering two different questions.
The first case, where you keep the angular momentum fixed, $v \propto r^{-1}$. Consider a planet orbiting in circular ...
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What is the maximum displacement at which a series of blocks can be displaced vertically?
I remember such a problem, the displacement of cubes placed one on another was only in one direction. The total displacement could be arbitrarily large, and maximum displacements formed the harmonic ...
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Apple falling from boat mast
However it seems to me that those 2 examples are not the same. On a train, the compartment is closed, so the air is trapped and also moves with the train. With the boat case, there is no close ...
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Apple falling from boat mast
Assuming a 20m mast, I think it takes roughly 2s for the apple to reach the boat, and I'd say that in 2s, the air has ample time to slow the apple enough so that it doesn't fall on the bottom of the ...
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Accepted
What is the base of defining eccentricity like this?
The equation you are considering represents a conic in polar coordinates, and in that form, the coefficient of $\cos \theta$ is the eccentricity. Of course, such an identification is consistent with ...
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Apple falling from boat mast
You are not wrong of course. The examples are supposed to be idealized examples where we ignore air friction.
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Variation of $g(t)$
I think you are struggling with the differences between implicit and explicit time dependence, which was well explained here.
It is true that, since $r=r(t)$ and generally $g=g(r)$, we think about $g$ ...
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Is there a curve such that a ball rolling down it has constant velocity?
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A freebody diagram of the ball will have three forces, ideally in a vacuum. Weight, normal and friction forces. The difference in direction of the normal force and weight add to a resultant force. ...
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Why does not the Moon get faster?
I have not studied about orbit formulas of orbital velocity yet, but you can rely on the following before going to orbit related formulae.
A simple way to understand is that if the moon was closer ...
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Why does not the Moon get faster?
... the moon is also an example of parabolic motion, right?
Not quite. The Moon's orbit relative to the Earth is (approximately) an ellipse. Like a parabola, an ellipse is a conic section. Unlike a ...
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Is there a curve such that a ball rolling down it has constant velocity?
If gravitational potential energy is not allowed to be dissipated and energy conservation must be obeyed,- then answer is NO, such constant speed curve does not exist. But, if potential energy ...
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Is there a curve such that a ball rolling down it has constant velocity?
Without friction, the curve is a horizontal line.
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Is there a curve such that a ball rolling down it has constant velocity?
Lorenz'z answer is the correct one if the only force operating on the ball is gravity. If you add friction then there will instead be a 'curve' consisting a path of constant slope.
The only way to get ...
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Is there a curve such that a ball rolling down it has constant velocity?
This depends on the amount of friction you have.
you need to adjust the slope such that the friction forces $F_\text{fric}$ force cancels the slope downforce $F_\text{slope}$ at the desired velocity.
...
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Accepted
Is there a curve such that a ball rolling down it has constant velocity?
There is only the constant curve. This is because energy is conserved
$$E = E_{\text{kinetic}} + E_{\text{potential}} = \text{const}.$$
so any curve that a ball rolls down (i.e. not a constant curve) ...
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How do you derive the compound pendulum formula?
Here is a rough proof:
Manipulating $\omega=\sqrt{\frac{g}{l}}$ gives
$\begin{align}\frac{2\pi}{T}=\sqrt{\frac{g}{l}}\\T=2\pi\sqrt{\frac{l}{g}}\\=2\pi\sqrt{\frac{ml^2}{mgl}}=2\pi\sqrt{\frac{I}{mgl}}\\\...
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Finding the complete Keplerian orbit from position and velocity
Since you are working in the orbital plane, once you have $a$ and $e$ you can just choose any $\theta$ to get the $r$ value (your equation for $a$).
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Why is the total energy of a bound system w.r.t to its COM less than zero?
The potential energy of the interaction of two particles depends only on
the distance between them, i.e. on the magnitude of the difference in their
radius vectors. The Energy of such a system is ...
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Why is the total energy of a bound system w.r.t to its COM less than zero?
First, I am going to name the frame (which you could have done). $S$ is the initial frame in which the masses are held in "free space". $S'$ is the COM frame.
A bound system is one that won'...
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Why is the total energy of a bound system w.r.t to its COM less than zero?
It is a consequence of how $0$ energy is defined.
In general, energy differences are important. A rock rolls downhill because it loses potential energy. Current flows in a circuit because of the ...
- 45.7k
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"Pressure" due to gravitational compression in a uniform sphere
First, I will do a quick derivation of your pressure equation to demonstrate that it depends on the assumption of constant density. The significance of this assumption to the question will be ...
- 10.1k
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Why is the derivation of gravitational potential energy incorrect if we consider bringing a mass from infinity to a distance $r$ from another mass?
It comes down to the definition of potential energy. Remember that potential energy is thought of as energy that is "available" to do work: if you have already expended that energy (...
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Relationship between height and mass?
Since potential energy is proportional to the product of mass and height, for a constant relationship to be maintained, any factors of increase of mass must have the same factor of decrease in height. ...
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Relationship between height and mass?
mgh=E
E is given us to be constant
let k be some constant
m=k/h
m is inversly proportional to h and gives a graph like this:-
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Accepted
Energy exchange between particle species in gravitational systems
Yes, energy exchange is possible through the collective gravity of the particles.
A trivial example would be to start with a gravitationally bound "subcloud" of one species that is moving ...
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