# An interesting problem in elementary mechanics. Reply

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. )

An interesting problem in mechanics

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…

# Review of Gravity, the movie, discussions. Reply

A discussion on Space movie Gravity, which I saw recently.

I remember one fact, that concerns, Physics, the roughly 50000 miles an hour (correct?) speed of ISS level debris that was coming, it set me thinking, are they violating the Relativistic Laws? For a while, and then I realize its per hour, not second, (that later would be grossly incorrect, 50 K miles / sec would violate Relativity certainly) that comes out to be 20 km/sec and thats perfectly enough close to what sort of speed, earth, moon, any satellite are typically found with, in our Sun’s Gravity. (in free fall) Even Rocket’s launching requires escape velocity. 11.2 km/sec. So they have clearly done their research on the Physics, as far as I could get in that moment. More…

# How heavy is water molecule? Reply

Saturday, February 19, 2011 at 4:30 am UTC + 05:30

Just a simple calculation, I did, says; the heaviest meson we know, is 35% lighter, than the water molecule, and about 22000 times heavier than electron. I am thinking along side the PDG list of particles; all atoms and molecules can have their properties mentioned …

A quick division by 0.35 gives that water molecule is therefore, 62.86 K heavier than one electron. Thus the water molecule nucleus is 6.29 K times heavier than the total electrons it has revolving around its nucleus. (There are 2 H and 1 O = 10 electrons right? Or is it 18?)