Mark Eichenlaub
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 Jan 28 awarded Nice Answer Jan 20 awarded Stellar Question 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. Jan 18 asked How does the height reached by a projectile of given flight time depend on air resistance? Jan 14 awarded Guru Dec 9 revised Why is ice less dense than water? edited title Nov 30 answered Infinite pulley system Nov 15 revised Why doesn't the entropy increase when two similar gases mix with each other? grammar 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 14 answered Why doesn't the entropy increase when two similar gases mix with each other? Nov 6 revised Elementary graphical error analysis added 153 characters in body Nov 6 revised Elementary graphical error analysis added 109 characters in body Nov 6 answered Elementary graphical error analysis 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.