Mark Eichenlaub
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 Apr 20 comment Is perfectly diffuse reflection entropy maximizing? Hi Carl, is it possible to be more precise? We do not spread the light out evenly among all solid angles; instead the intensity per unit solid angle obeys Lambert's law. Apr 1 comment Why does the atmosphere rotate along with the earth? Sorry, I don't understand what the pronoun "it" is referring to in your question. Mar 21 comment Why can't a rope be pulled completely straight? When the rope is straight, you can pull the middle down without the side weights going up to first order. When the rope is not straight, the side weights will have a first-order rise when you pull the middle down further. The bottom of the hill is where steps do not change your height to first order. I don't know what statistical terms you want defined. Mar 8 comment Which direction will the yoyo move? That assumption is fine where it is. The yoyo moves because there is nothing to stop it from rolling and lowering its potential energy. 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.