Strange wall-ball problem

Okay I get it - the title is not that imaginitive.
Hi there! The organic post that was to be never came up because I left my copy back in school but its some pretty interesting isomerism nuts that I was shown by my teacher. For now its some physics- collision style!
In fiitjee and other study mats there is always this obscure thing that concerns a ball with a wall. (Wall=infinite mass, ball=m)When the ball collides with the wall having an initial velocity u it returns back with the same velocity provided that the collision is elastic. Now fix the ball, let the wall strike the ball with a velocity u.Whatt happens now?

Contrary to all common sense the ball lurches forward with a velocity 2u.why??
A friend of mine kaustav sengupta (never mind the too erudite tone of the sentence) made sense when he said that consider the first case as in figure1, the frame instead of being stationary with respect to the ground is having a velocity u to its right. then?/Â…..we get the second case, fig2, minus the comment about not making sense.
Comment if u knew it
Comment if u did not
Comment if u think itÂ’s wrong
Comment anyway!

the return of sith :-)

hi there! i came back from skool yesterday and went through the whole blog. the idea was great i think.to start a blog that lays importance to the subtle nuances of physics and maths(not much of a chemistry there).and i m rlly happy that the posts have not dried up.as per catching up - it was good to hear that ftse was actually a mess. u know wat? a friend of a friend of mine,mutual friend that is, reads in fiitjee delhi classroom courses and he told us that they were taught in advance in the discussion classes abt 80% of the sums - a leak if there ever was one.assuming of course that he wasnt, u know, throwing off.anyway i was down in confidence for weeks.sort of brings things into perspective, doesnt it?
anyway i will be posting one on organic pretty soon - its been neglected for long.
pss:i will be staying here till 27th.then i wont come back to home till march.

Whatz prooved & Whats not :: A DEAD END SUPPLIMENT !

Hey all !

Hmm ...
Another Dead End ? Nope I'm saturated of those now. But this one's interesting enough to be brought to notice of the blog.

A seemingly remarkable proof indeed for prooving that all numbers are interesting !
But Can a subjectivity of the problem be discussed mathematically ? The answer seems to be yes !?!

Now lemme introduce you 2 a couple of DEAD ENDS :

(1)

To Proove : Every natural number N can be described within 15 words.
Assumption : Let there be a set S of number which cannot be expressed within 15 words.
Ordering the set S & pickig out the first element, say P we get P as :
P is the "the smallest natural number that cannot be unambiguously described in fifteen words or less".

:. P can be described within 15 words.
By Reductio Ad Absurdum ;
We herey proove the Statement that :
EVERY NUMBER CAN BE REPRESENTED WITHIN 15 WORDS.

(2)

I begin this one, relating to the THEOREM OF MATHEMATICAL INDUCTION as quoted by Arun in a comment to the previous post.

"

The principle of mathematical induction basically is a logical proof of extention. If you can show that:
1) The statement is true for the base case, i.e. 0 generally,
2) That if it is true for n, n-1, n-2, it IMPLIES truth for n+1.

"


Okay. Let there be a statement S(n) depending on n which can be either TRUE or FALSE.

I DEFINE S(n) as :
S(n): "In ANY group of 'n' blog-members, all have equal ages."
OR
"In a set of blog-members-ages from ANY particular blog, all values are equal."

Now proceeding on the lines of the above discussed theorem, lets discuss S(1).
: " In ANY group with 1 blog-member, All blog-members have equal ages ( Takin one member at a time since n = 1 )."
Clearly S(1) is TRUE.

Assume that S(k) is TRUE which implies that :
: " In ANY group of 'k' blog-members, all have equal ages."

Now to proove S(n) for all N belongs to (1,infinity), We must proove S(k+1).

So now we have a set of (k+1) blog-members. Of those, we can choose different combinations of 'k' blog members. In each of these combinations, all blog-members would have equal ages. Therefore, All blog-members in the (k+1) blog-member set are equal in age.
:. S(k+1) is TRUE if S(k) is TRUE.


S(1) is true. S(k+1) is TRUE When S(k) is TRUE.

:. by the THEOREM OF MATHEMATICAL INDUCTION ...

S(n) is TRUE.

Implying this for the blog KVPY2005 : Fused Bulbs... I hereby proove that all memebers in this blog are equal in age, which is conincidentally true within the limits of error. lol.



Ill leave the implications to be discussed by the blog members.

WAITING FOR COMMENTS

(desperately hehehe)

Twish

Boring Numbers?

Hey. It's been a long time since I've posted anything, so I'll make a candid proof I saw on the net somewhere.

This deals with a really fundamental theory:

There is no such thing as a uninteresting number.

As we deal with the earth-shaking proposition, one must have a deep fundamental knowledge of sets. Let us limit our theory to the infinite set of natural numbers.

On with the proof:
Let N be the set of all natural numbers, of which X represents the set of uninteresting number. First let us order this set X in numerical order. Let us now analyse the first number of this set. Our understanding of what makes a number interesting is so fragile that to produce such an example is a great step forward. Thus this number being the FIRST uninteresting number is of vital importance, bringing our interest to it. Thus it can not belong to the set, and isn't the first element. Let X' be the revised set omitting this fraud. Thus the second term of set X is the first of set X'. We can apply the same reasoning here, and easily omit this element, and continue to do so for all other numbers of the set, making it a null set. Thus it is easily proved that there is no uninteresting number.

Lovely proof isn't it? But there does exist a very important logical consideration. If one considers ONLY the negative numbers, our present ordering is befuddled, but do not panic. Suppose we order them in REVERSE order, letting greatest come first. Thus we can proceed by the same steps as above.

Now, we come to a very important juncture. If we combine these two sets, and look at ALL integers, we're stuck. For sure the negativity is an important difference between '+' and '-' numbers, and we can't ignore it. A set of Z has no beginning or end, so we CAN'T order it, and use this lovely proof for it. So it seems that the interesting-ness of certain '+' or '-' numbers makes other numbers loose there interesting-ness. But I thought interesting-ness was an intrisic property of a number. I.E. that a number can be called interesting because of a property that it exhibits, i.e. primality (it being prime) or it's square-ness/cube-ness/n-power-ness, or a pattern exhibited by its digits (like 12321).
Appealing to this logic, we could either conclude two things: That there exist no uninteresting numbers, or that the interesting-ness of a number does infact depend extrisicly as well as intrisicaly, and that it depends on a negative counterpart (whether that is the negative of the same number or not can not be concluded though).
As much as I'd like to take the latter, for it's more complicated, and that it IS earth-shaking in its statement, I'll abuse Occam's Razor and say that the former is obviously true.
Occam's Razor is: All explanations are simple, and the more complex one is more probably wrong. Note the keyword: Probably. It's generally quoted with overexagerrations like:
When you see a reflection:
1) Light is getting reflected
2) There is an alternate reality, which can be entered through the window, and which is inhabited by people who look EXACTLY like you, and happen to do EXACTLY what you are in front of the mirror.
Sometimes I think that life would be a lot more fun if it weren't so obviously 1.
That's all for now. I hope to be back this weekend with a post on the brain.
Signing off and Id Mubarak,
Arun

BEFORE THE BEGINNING AND BEYOND THE END (PART 2)

Hello again all of you. I am back, with a spicy second part of my article. The contents of this article as well as the one it follows is a collection of well laid facts cemented with the author's own ideas. Thanx 4 reading guys, enjoy. Please refer to the previous section wjenever in doubt.


Let us now extend our view of the symmetry about the big bang, we can go forth to say that the previous universe too must have originated from another big bang. Therefore, this brings us back to the concept of oscillating universe theory. However, the problem with oscillating universe is Entropic considerations. The problem is the following:

The oscillating universe theory says the entropy of all the singularity states of the universe have same entropy. Now let us assume the whole of the universe as one system. Suppose right here right now, I drop an egg and break it. I have thus increased the entropy of the universe. However, when our universe reaches its next big crunch, the entropy has to be same as that of the last singularity. There is the problem, entropy remaining constant although the system is experiencing an irreversible process. I will try to provide an explanation for it.

All of us know about supernovae explosions. Some parts of a dying star blows off as a huge explosion into the realms of the vast universe, and the remaining collapse into a tiny dwarf star. Let’s apply this logic to the entire universe.

Let S1 and S2 be two singularity states. A big bang at S1, expansion, and then contraction and finally a big crunch at S2 are the sequence of events. The change in Entropy is ΔE. According to Boltzmann postulate or the definition of Entropy,
ΔE = kb (ln Ω1 - ln Ω2) where, the sigma are the no of ways in which the same microscopic arrangements can be restored from a starting state.
So what we do now is very simple. We ‘transfer’ all the disorder in the whole of the universe to say a few moles of gas molecules. We outcast there molecules and allow the rest of the universe to move into singularity 2.

Let me make this more lucid. While playing billiards (or pool or snookers ... whatever), on a perfectly friction less table, we first break the triangular arrangement in the middle by a slow strike, the balls go a little haywire and keep moving and colliding with each other. As these collusions continue, the entropy is constantly increasing with time. But there is a remote possibility that say seven of these balls will again come back and form a tight arrangement. The remaining two will remain in a state of even increased randomness. Thus we can say that the entropy got localized to the two balls or got transferred from the other seven balls to the two.

This is one way in which we can satisfy both the oscillating universe theory and the second law of thermodynamics. But this too has a lot of problems of its own. First and the most important is that it is unable to explain the birth of the universe (I am talking about the real birth – the first big bang) and it too says that there has to be some thing beyond our universe.

It says our universe is constantly losing its mass into darkness (dark energy?). It predicts a very gruesome death to our lovely universe. A heat death scenario – a situation when there will be no energy gradients and hence there will be no process. (All processes require flow of energy.) But certainly it has done one good thing for sure, it has increased the life span of our universe to much beyond of what Big bang theory had proposed. It never says that the Big bang theory is wrong but it says that the big bang was not the beginning but only a phase change in the history of our universe.

I will not end this article with a conclusion as conclusions are for the readers to devise. It is a philosophical question and until we find a proof we can only speculate. We are like a child who presses its nose on a mirror, accepting it to be window. He knows it is not the reality. It is only the preconception in his mind. Reality lies beyond the glass- break it open. But he is afraid that in the process of breaking open the mirror and discovering the reality, he will destroy his well constructed sand castle.

Saurya Time Mishra

PS: Sorry if u couldn't c the comments before. Dunno y, but still, u can add them now!

~Gr81~