All Questions
41
questions
1
vote
3
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75
views
How much time does it take for an object to fall from space? [closed]
Let's say there's an object of mass $m$ in space, $h$ meters away from the surface of the Earth. $h$ is large enough that $g$ cannot be assumed to be constant. The acceleration varies according to ...
- 117
-4
votes
2
answers
117
views
Is Newton's gravitational acceleration centripetal instead of attractive?
In 1845 W. R. Hamilton demonstrated [1] by the use of the hodograph representation that the velocity of any Keplerian orbiter is the simple addition of two uniform velocities, one of rotation plus ...
2
votes
1
answer
267
views
How to calculate the period of non-circular orbits?
How to calculate the period of non-circular orbits?
By conservation of mechanical energy:
$$
E = -\frac{GMm}{r} + \frac{1}{2}\mu \left ( \dot{r}^2 + r^2 \dot{\theta}^2 \right )
$$
By the conservation ...
- 1,525
-3
votes
1
answer
41
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Potential energy change is not negative? [closed]
$\Delta U = -(W_{earth} + W_{ball})$
$W_{ball}$ is almost 0, as earth's displacement by the falling ball is super small, so $\Delta y$ of the earth could be negligible and $W_{ball} = 0$. so:
$\Delta ...
- 137
0
votes
1
answer
44
views
How to obtain the equations of motion and trajectory of a particle from the effective potential?
In a certain problem regarding motion of a particle in a gravitational field with axial symmetry, I have an expression of an effective potential $\Phi_{eff}(r,\theta)$. Now, I am interested to study ...
- 2,015
0
votes
0
answers
43
views
Why is it important to release energy as quickly as possible to perform a vertical jump?
Let's assume that we create this mechanism, where we must decide if the actuating cylinders are double-acting hydraulic or pneumatic with a spring inside.
the goal is for the mechanism to suddenly ...
1
vote
1
answer
82
views
Conic Section in Newton's Cannonball Problem
From the Classical Mechanics Lecture Notes by Helmut Haberzettl, we know that in Newtonian Mechanics, the solution to Kepler's problem can be parametrized as a conic section equation
$$r(\varphi)=\...
- 381
0
votes
2
answers
57
views
If the change in potential enegry is equal to the negative of the work done, then this principle isn't consistent here in the case freely falling body
Let us assume that a body of mass $m$ falls from height $h_1$ to $h_2$ :
Here the Work done by gravitational force (Conservative force) is :
$$\mathrm{Force \ ×\ Displacement} = mg \ (h_2-h_1) \tag1$$
...
0
votes
2
answers
114
views
What is the effective potential for photons in Newtonian gravity?
I am confused about the movement of photons and their trajectory, I hope you can help me:
What kind of path does light follow in Newtonian gravity?
What is the effective potential for photons in ...
- 1
0
votes
3
answers
224
views
Equation of motion of a classic inverted pendulum in free fall
I was thinking in this interesting problem:
Suppose we have this inverted pendulum:
But without this control force $F$ and the system would by loose from a height $h_0$, with initial velocity $0$ ...
0
votes
1
answer
648
views
Newton's first law - elevator lift upward and downward force [duplicate]
Why does $F_c$ is equal to $F_g$ and why $F_c$ isn't greater than $F_g$? $F_c$ is moving it upward right, so the force must be greater than gravity to pull it upwards I think.
- 101
1
vote
1
answer
1k
views
When is the effective potential equal to the total energy?
I have a question about the energy of a particle in orbit due to a gravitational attraction. The effective potential given by the gravitational force is defined to be
$$
U_{\text{eff}} = \frac{L^2}{...
- 207
1
vote
1
answer
82
views
Exact distance travelled by an object due to gravity only
I am aware of the fact that for two point masses in space, the time that it will take for them to collide is, T=$\pi \sqrt{\frac{r_i^3}{8GM}}$, where M is the sum of the 2 bodies' masses, $r_i$ is the ...
- 13
4
votes
2
answers
253
views
What is definition of weight of person in elevator moving with acceleration?
I have a question, I need your help with understanding definitions. Let's recall the famous problem:
What is the weight of the person mass m, if the elevator moving up with acceleration a?
of course,...
- 55
9
votes
2
answers
741
views
Can the equivalence principle be safely used in non-relativistic mechanics?
Imagine an ideal pendulum in a train. While the train is in uniform motion, Newton's laws apply within the train, and we can easily write down the equations of motion for the pendulum. Now assume the ...
- 9,304