This post has 40 interesting problems in elementary mechanics from IE Irodov, Problems in general physics that I solved in last couple weeks. Note that another 30 problems which has been solved will be uploaded after they are scanned, shortly. More…
Here is a problem on mechanics.
Problem; Two particles move in a uniform gravitational field with an acceleration g. AT the initial moment the particles were located at one point and moved with velocities v1=3.0 m/s and v2=4.0 m/s horizontally in opposite directions. Find the distance between the particles at the moment when their velocity vectors become mutually perpendicular.
Here is my ans. (Got to fig. it out in a concise way after scribbling through pages unsuccessfully. )
1. Aristotle Fallacy; A notion that objects need force for their movement. It contradicts the idea of inertia. Newton corrected this by introducing the first law, things continue in their state of motion, a quality called as inertia, without requiring force and the motion changes due to application of force.
2. Earth is flat; that there is a boundary where you fall off its edge. [I am not going to explain or tell you how and when we found this was a horrendously hilarious and misleading notion we had. But it might have been used in the past by parents to discipline their teen-age kids. Don't go out, you will fall off earth. That would have kept them in check.]
3. Rotational Dynamics; Earth is accelerating in a near circle in addition to about itself, so additional forces are acting that changes our observation about the world. Newton tried to understand this (not successful) in his last days, by rotating a bucket full of water, his laws could not explain the effects observed. His laws needed to be modified slightly. The same thing makes objects feel weightless by a given amount if they are accelerating towards a gravitational field (eg merry go round, satellites) This is the basis of many works of Einstein. First came Mach’s Principle which says observations made from objects that are accelerating in circular paths are to be corrected by fixing frames of references to stars that are so far away that the rotational motion is neglected. [if you shake your head while looking at stars and shake your head by looking at nearby objects such as a light post, evidently the light post shakes more and the stars less]. This helps in correcting observed phenomena from earth. Earth moves at 30 kms/second wrt sun … More…
Also (without any direct theoretical connection, but correlation through reality of nature)
3. Photons are classical only in the sense that we perceive light only when photons are produced in large numbers. So large that the laws of the small do not incur large errors because they are in large numbers. Statistically the errors are well understood and eliminated. But when they are produced in very small numbers we can not deduce their laws a priori. [which is why Quantum Mechanics was discovered only in 1920s and not in Galileo's time, In his time the macroscopic behavior were understood and microscopic laws can never be produced from the understanding of macro scope just like a particular individuals attribute can't be found from a large number of individual's group attribute] More…
2. The object can be a large object, eg say something whose picture you are taking. But as explained above its not the energy of the object (or momentum) which is directly coming into the problem. That would be an added degree of concern if the object is moving with certain velocity, a reason why pictures are blurred. Because motion of objects introduces additional energy-time-momentum-position variables and their corresponding uncertainties. For the argument of the above problem one can imagine the large sized object, lets say a bird, is standing still on a tree while its picture is being taken. In that case if the wavelength of the light [few 100 nano meters = 1/10th of a micrometer] is used (eg in a digital-camera) the corresponding accuracy of the light will be less than micrometers. You can take a very sharp picture of the bird, which is lets say 6 inch long. But when you zoom in to a large degree, the inaccuracies will show up. [in this case how to see a micrometer level image? Is a computer sufficient to show us the uncertain edges of the pixels?] If the wavelength (here visible light) is so small, evidently by de-Broglie relationship, momentum or energy of such light is very large. But its not as large to disturb the feelings of the bird. The bird doesn’t have a problem with visible light, and such energy does not disturb its position or energy or any thing so to say. So while Quantum Mechanics is valid, we are accustomed to say this is a classical mechanics situation. To say QM is invalid is incorrect. To say QM is understood to be valid is a knowledgeable position. More…
While writing vegetarian I accidentally wrote begeterean which goes towards bigotry. Supremacy. Vegetarian Supremacy.
But I just wanted to write a small episode about Vegetarianism in “Hindu”. ["Hindu" like "Dharma" is one of the most abused word in modern context, in-fact everything we inherited from our forefathers; we have abused, including ourselves.]
When I was in Japan, (which I am always at) the very polite Japanese people (especially ladies, no holds no bar, cool) threw off at times a particular conundrum toward my psyche. I have been non-veggy from quite young times. (Although borne into a Hindu brahmana family, brahmana, etymo; maharajya maanya, “the honorable” from the nation, Japanese; monoyabaraka)
The conundrum was this; why Hindu people drink cow’s milk but not eat its meat, if cow is holy. [such was silently murmured in little shops, as they were utterly deluded as to howto make sense so that they can serve their customers better]
[giyuu niyuu, giyuu niku] = [Cow Milk, Cow Meat]
The totalitarians often would give you “for Hindus cows are holy, like mother, can we cut our own mother? We drink only mother’s milk na.”
So far so good, A logical analyst like me, while finds cutting an(y) animal for food a bit harsh, yes, but nonetheless just milking the cow is also harsh, and we have tried to find a middle path or moderate approach toward having “rest to mind” by agreeing milking is a far less harsh situation.
We do not tie a woman and lactate her and let her live in shit-bed and even supply that milk via OmFed. Okay that’s a bit funny, but that would be quite harsh and in some people’s definitions P-Graphic.
So the whole question of cow-worship as holy-mother is bullish. It only served us to bring a softer version of “harshness” and we are all facing harsh reality of life and must survive hence cow’s milk serves our purpose of being moderate as opposed to “meat eating aggressors”.
But there is a raging controversy about it and a lotta heated argument especially among Hindu Intelligentsia as to shall we or shall we not eat the cow-meat. I have oftentimes as early as 2004-05 maintained a stoic stance “Food is a personal choice and no one shall insinuate another about their food choice especially in veiled religious aggression”.
We can all become vegetarians but it won’t absolve us of our aggression toward “OTHER” religion. Vegetarianism is not a license to insinuate others, whether meat eaters, halal meat eaters or any kind. In-fact it merely comes from a habit of forming an identity of OTHERs and taunt them regarding how their ways are total bullish and ours is better, then aggression is associated to meat and non-aggression and non-violence to non-meat products, better Hindus vs despicable hindus and so on. We have even invented how garlic is “inflammatory and should be rejected” possibly because it gets used in cooking meat. Our chauvinism has no bound.
But the fact is tying a cow is also violence, if its a Holy Animal. [Although not as violent as cutting its flesh and enjoying, the chicken would also cry, I want to be "holy hindu poultry"]
All in All from food habit we can not decide who is a good person or who is not, from drink habits or smoke habits or any kind of habits we can’t. Someone had said “All habits are bad habits”. (Some would say your writing is a bad habit, but then, what can I say, I only try to bring balance to my psyche by writing, volition of thoughts shall we call it?)
I shall end by saying “Hindu jin ha omoshiroi”. That the Hindu people are interesting. But Hindu shall only mean one from India. Hence one can if say, All Islam is Hindu, one can also say all Hindu are Islam. How can that not be? It can be because we are all mixed to the quantum. Which is where we run into another problem, that we invented for ourselves. History as a license to invent and reinvent.
Everything loses its meaning at the torment of the quantum. We shall realize the quantum and be happy. How about that, even Dalai Lama agrees on that.
Happy lunch hour, I just had mine. Stay Cool.