Comment by Kotlopou on Modelling an inelastic, rough, constrained collision
I will add links to resources I used for these contact mechanics into the question.
View ArticleComment by Kotlopou on Helium balloon energy gain
This makes sense (and I will accept unless something better appears); I just hoped that there would be a way to conceptualise the potential energy as some displacement of air.
View ArticleComment by Kotlopou on Modelling an inelastic, rough, constrained collision
Thanks, this at least provides something. I hoped there would be an analytic solution, though. Is it possible that the stiffness loss ends up being zero through some symmetry? Once I get back to a...
View ArticleComment by Kotlopou on Angular momentum of linear motion of sphere without a...
But is this valid if r is not constant for all matter? You just gave me the particle approximation again. If it is exact, then I am missing the reason.
View ArticleComment by Kotlopou on Angular momentum of linear motion of sphere without a...
@Bernhard Oops, corrected.
View ArticleComment by Kotlopou on Angular momentum of linear motion of sphere without a...
You seem to have ignored the sphere-not-particle part, which is the entire point of this question. I edited the title to make the focus clearer.
View ArticleComment by Kotlopou on Why does an object in circular motion stay in a circle?
-1 because this doesn't answer the question, just says "the object is in circular motion because of the centripetal force".
View ArticleComment by Kotlopou on Is fuel cell efficiency limited by thermodynamics?
This is true, and yet we often calculate the efficiency of engines with thermodynamics, because it's implied that they should work with arbitrary amounts of fuel while remaining the same size. That is...
View ArticleAnswer by Kotlopou for Feynman's proof for Newton's shell theorem
1) If you study the image more closely, you see that ds is length along the sphere, while dx is the horizontal thickness. Because the incremental piece is inclined, ds and dx are different distances.
View ArticleConstantly damped pendulum
The drag force in a damped pendulum is often assumed to be either linear (viscous drag) or quadratic (air drag). However, there is another case where I have failed to find any analysis.If we have a...
View ArticleAnswer by Kotlopou for Torque and inverted pendulum
I assume that by "extra weight", you mean the mass $m$. If we assume the displacement $\theta$ is small, $M$ will exert a torque of $Mgl \cos(\theta) \sim Mgl$ (with $g$ being either the original $g$...
View ArticleAnswer by Kotlopou for What lies between "perfectly smooth" and "perfectly...
There is no answer that conserves energy. First, from elasticity, we know that the normal component of the velocity stays constant. We then have two unknowns: the new tangent velocity and the new...
View ArticleWhat lies between "perfectly smooth" and "perfectly rough"?
In elastic collisions of spheres, there are two approximations that can be made: Either they are perfectly smooth, and you ignore the rotation component, or they are perfectly rough and the rotation is...
View ArticleAnswer by Kotlopou for Changing length of Pendulum
The first question is: Does your pendulum have a string or a rod? If you were to, say, suddenly introduce 20 meters of string without moving the mass at the end, it will fall straight down, and then...
View ArticleAnswer by Kotlopou for What happens in Newtonian mechanics when a particle...
The situation at the origin is a singularity, but it can be worked around if you leverage symmetry (and assume no collision takes place). Simply make a special case that acceleration for $x = 0$ is...
View ArticleAnswer by Kotlopou for Why is the period of a pendulum on the Moon $\sqrt{6}$...
You can modify the second formula:$$T_m = 2 \pi \sqrt{\frac{l}{\frac{g}{6}}} = 2 \pi \sqrt{\frac{6l}{g}} = 2 \pi \sqrt{6\frac{l}{g}} = \sqrt{6} \left(2 \pi \sqrt{\frac{l}{g}}\right) = \sqrt{6} T_e$$
View ArticleAnswer by Kotlopou for Small oscillations of a bar pendulum in a free moving box
The term is negligible because three small values are multiplied - $\dot{\theta}$, $\dot{\theta}$ and $\theta$, whereas in the other terms, only one such term appears - $\theta$ or $\ddot{\theta}$....
View ArticleAnswer by Kotlopou for Were alchemists right?
They were wrong in the same way the people who made human-sized wings to fly were wrong. The goal of flight/metal transmutation is not impossible, but the methodology is naive and hopeless.
View ArticleAnswer by Kotlopou for If you were to have an empty balloon, would it float?
1: Assuming the frame is lighter than air of the same volume as the vacuum inside, yes. It would not have a balloon shape, though.2: By experience with helium baloons, no way. This source (paywalled)...
View ArticleHelium balloon energy gain
I answered a question about a "vacuum balloon" and came up with a problem I feel should be simple, but I cannot find the answer. Imagine a zero-drag balloon of a density $a$. It floats up to a height...
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