8
votes
Accepted
Pressure of a gas on the inside walls of a cylinder canonical ensemble
That's a good question. Which is similar to the (more common) question: "What's the pressure of a gas in a gravitational field" (for which you will be able to find more information). The ...
- 1,508
4
votes
Identify the hollow sphere without making a sound!
If you put them at the top of a ramp and release them from rest, the solid sphere will accelerate down the ramp faster than the hollow sphere.
Also, I don't think your logic is correct about fluid ...
- 797
3
votes
Accepted
Integrating Newton's $2^{nd}$ law along path displacement in polar coordinates, handling separation of variables for second order differential terms
You have $$g \sin\theta = R \theta''.$$
Integrating both sides along the circular arc,
$$gR \int_0^{\theta_f} \sin\theta d\theta=
R^2 \int_0^{\theta_f} \theta'' d\theta,$$
where we recall that ' ...
- 1,846
3
votes
Does Newton's 3rd law hold true everytime?
No, the third law is alway valid, and it implies momentum conservation when there are no external forces. If you enlarge your system to include the objects that apply those external forces, then the ...
- 1,220
3
votes
Why the normal vector addition does not seem to work in centripetal acceleration?
Its important to note that the velocity is infact not constant,as it is changing its direction.
But,I'm going to show you why the speed is constant if we have the fact that the angle between the force ...
- 412
2
votes
Identify the hollow sphere without making a sound!
Both float and sink the same way. ( same mass, volume)
But in pendulum oscillations ( not possible without some hand manipulation)
$$ mL^2 \ddot \theta + mgL \sin \theta=0 $$
the hollow sphere has ...
- 1,100
2
votes
Accepted
Identify the hollow sphere without making a sound!
Since both spheres have the same mass and volume their average density will be the same even though the mass of the hollow sphere is concentrated away from the center. Since the degree to which they ...
- 75.7k
2
votes
Understanding geosynchronous orbits in an otherwise empty universe
This is an interesting little question, in that it puts blinders on our observers and asks whether or not we would deduce the same laws as we have found presently.
First off, I would point out that ...
- 50.7k
2
votes
Why does $W_1$ cancel out when $W_1$ perpendicular to the surface and Normal Force cancel out?
There is nothing dropping out. You are misunderstanding the physics that is being told to you.
$$
\begin{align}
\tag1\vec{\mathcal W}&=+\vec{\mathcal W_\perp}+\vec{\mathcal W_\parallel}\\
\tag2\...
- 10.1k
2
votes
Accepted
Does Newton's 3rd law hold true everytime?
Does Newton's 3rd law hold true everytime?
The answer to the title of your post is no. While it holds for most forces, it does not in all cases. An example is magnetic forces. But it does hold for ...
- 75.7k
1
vote
Accepted
Monkey pulley problem doubt: why is tension less that weight of body without string break?
The string will break once the tension in the rope exceeds some maximum amount.
If the tension force acting upward on the monkey is less than the weight of the monkey, then that just means the monkey ...
- 58.2k
1
vote
Accepted
How to Calculate the Stopping Distance of Train on a Complex Track
I think you can solve this working backwards in time; assume that the train has stopped at the correct location, and then integrate backwards in time (or alternatively, model the braking force as an ...
- 1,846
1
vote
Work done by a spring on objects of different masses
A simple thought experiment would say NO, but it depends on some clarification. Work done on one of the masses is equal to the integral of spring force over displacement. In the limit of one of the ...
- 797
1
vote
What is $P$ in axial deformation formula in these cases?
This is an example of a statically indeterminate problem where you can't just get the answer by drawing free body diagrams. It's possible to intuit that you need to consider the stiffness in the ...
- 797
1
vote
Accepted
Goldstein Chapter 6 Question
starting with matrix notation
with
\begin{align*}
&\mathbf{V}=\begin{bmatrix}
V_{11} & V_{1,2} \\
V_{21} & V_{2,2} \\
\end{bmatrix}\quad,
\...
- 12.7k
1
vote
Why the normal vector addition does not seem to work in centripetal acceleration?
The concern raised in this question, as I understand it, is that we start with a tangential velocity:
But then, the acceleration, being perpendicular to the velocity, causes the increment $\mathbf{a} ...
- 505
1
vote
Does Newton's 3rd law hold true everytime?
Newton's third law is just conservation of momentum in disguise.
In the case where action-reaction pairs are net forces between bodies, we can say that conservation of momentum implies Newton's third ...
- 16.8k
1
vote
Would a paddle wheel on a ratchet slowly spin in a pressurised room?
As mentioned by another poster, the Feynman lectures contains an analysis of this exact scenario.
Feynman considers the mechanism of the ratchet itself. Containing a jagged wheel and a pawl which ...
- 621
1
vote
How to find the impact force needed to break an object?
On a microscopic level: when we break something into, say, two pieces, we create brand new fresh surface area where those two pieces were once joined. Because it takes a certain specific amount of ...
- 96.6k
1
vote
How to find the impact force needed to break an object?
This is best done experimentally. By breaking the object by an impact and measuring the required force.
- 4,029
1
vote
How to find the impact force needed to break an object?
I’m aware of tests in safety standards that require a minimum level of impact resistance. But these tests usually don’t involve testing to failure. Individual manufacturers, on the other hand, often ...
- 75.7k
1
vote
Behavior of an ideal spring
Let's pull on an ideal spring from both sides with force $F$.
According to Hooke's law, the extension of the spring is $x=F/k$. But
why would the spring extend at all? I mean, the net force on the
...
- 7,481
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