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Jan
18
comment How does the height reached by a projectile of given flight time depend on air resistance?
Very nice writeup, thank you, Floris.
Jan
18
comment How does the height reached by a projectile of given flight time depend on air resistance?
I was curious whether 1) someone might find an heuristic argument that works in not only the limiting case of very thick air 2) whether it's possible that the answer depends on the parameters, e.g. overestimates for some initial conditions and underestimates for others 3) whether the result is only true for v^2 drag, or whether other models of air drag (drag coefficient depends on v, ball is spinning) have different results.
Nov
15
comment Why doesn't the entropy increase when two similar gases mix with each other?
You need to be more specific about what you mean. What is the "work lost"? What exact process are you referring to? What do you mean by "available work"? What do you think the enthalpy of mixing is? The logic in my answer is extremely simple. What do you think the problem with it is?
Nov
15
comment Why doesn't the entropy increase when two similar gases mix with each other?
I'm afraid your comments do not make much sense to me. The fundamental principle is that spontaneous processes have positive entropy change for the universe. That is the principle behind this answer.
Nov
15
comment Why doesn't the entropy increase when two similar gases mix with each other?
Entropy is not "unavailable energy". Entropy and energy don't have the same units. The statement in my answer says that if you are increasing the entropy by a certain amount, you should be able to decrease the entropy of the environment by just slightly less than that and still have the process be spontaneous.
Nov
5
comment Perturbation Method in Mechanics: Average velocity of a small mass on a vibrating inclined plane
@Samuel Thanks for getting me to think about it a bit more!
Nov
5
comment Perturbation Method in Mechanics: Average velocity of a small mass on a vibrating inclined plane
Samuel, maybe it will help to note that if you reduce $g$, you'll make the transient period longer. The condition on the final velocity is basically kinematic. The friction force is fixed and larger than the force required to hold the block up. Therefore, the block zig-zags such that it isn't falling straight down the slope. The final velocity is derived from how much zig-zag there is in the steady state. In the steady state, reducing $g$ reduces the force from friction and the force required to stop acceleration down the gradient by the same factor, leaving the kinematic condition unchanged.
Nov
5
comment Perturbation Method in Mechanics: Average velocity of a small mass on a vibrating inclined plane
Aritra, the answer describes the steady-state solution. There is a transient period during which this analysis does not hold. The block begins sliding because initially, before the shaking begins, the block does not move. Once the slope starts shaking, the block moves horizontally because frictions pushes it. But the friction force is then exactly horizontal, so the gravitational force is unopposed and pulls the block down the plane. It accelerates down the gradient until it gets to $w$.
Nov
5
comment Perturbation Method in Mechanics: Average velocity of a small mass on a vibrating inclined plane
@Samuel, please just do the algebra. There are two expressions containing $F_x$. It can be eliminated.
Nov
5
comment Perturbation Method in Mechanics: Average velocity of a small mass on a vibrating inclined plane
The answer already shows that explicitly by providing a complete solution.
Nov
5
comment Perturbation Method in Mechanics: Average velocity of a small mass on a vibrating inclined plane
Because that's the component from the normal force pointing down the plane. I changed the notation as $F_y$ was not the force in the $y$ direction.
Nov
5
comment Perturbation Method in Mechanics: Average velocity of a small mass on a vibrating inclined plane
@AritraDas Yes, I see I made a mistake before, and have updated the answer. I still don't see a need for perturbation theory.
Nov
2
comment Is Conservation of Energy maintained when the orbit of a rotating mass increases in diameter?
Why do you claim, "It's certainly not being lost to vibration or heat."?
Oct
30
comment Effect of enlarging one of the slits in Young's Double Slit experiment
just use algebra
Oct
28
comment How is one process reversible and its reverse non-reversible?
Yes. That's right.
Oct
26
comment Why are basic physics problems neglecting to include atmospheric pressure?
Because the air underneath the block is exerting approximately equal pressure upwards. If you truly made a seal with the table so that no air could get it, it would be extremely difficult to lift the block. This is how a suction cup works.
Oct
23
comment How do I use the kinetic energy formula using mass as lbs and velocity as mph?
that's the idea, but I don't think you converted to kg correctly
Oct
23
comment How do I use the kinetic energy formula using mass as lbs and velocity as mph?
en.wikipedia.org/wiki/Pound_(mass)
Oct
23
comment Why don't we include the adhesive and cohesive force while calculating rise in a capillary tube?
The derivation I gave used $\gamma$ for the energy per unit area of the water-tube interface. You can put whatever name on that you want. I did not reference the water-air interface.
Oct
23
comment Why don't we include the adhesive and cohesive force while calculating rise in a capillary tube?
I can't fathom why you think they're being omitted; I explicitly included them as $\gamma$.