pakisagutan.. di ko to lam eh.. hehe!!

Poisson and Gaussian
Throw N balls at random into B boxes. Let a be the average number of balls, N=B,
in a box. Let P(x) be the probability that a given box has exactly x balls in it.
(a) Show that

P(x) ¼ is approximately equal to [(a^x)(e^-a)]/x!

Certain assumptions are needed for this expression to be valid. What are
they?

(b) Show that if a is large, the above Poisson distribution essentially becomes a
Gaussian distribution,

P(x) = [(a^x)(e^-a)]/x! and is approxiamtely equal to {e^[-(x-a)^2]/2a}/sq.rt. of [2a(pi)]

pang theo mech mga parekoy!! sabi sa source "A boring problem daw!"

Consider a rigid, solid Earth with radial symmetry and outside radius R, rotating with constant angular velocity w. Start at the equator and drill a sufficiently large diameter hole straight through the center of the Earth and out the other side. Never mind that the center of the Earth is pretty hot, and probably flows. Don't worry about ground water, or ocean water, filling the hole, etc., etc. Consider that these don't happen, maintaining the integrity of the hole you've drilled.
Now hold an object above the hole and release it to fall down the hole. Will the object hit a wall? If so, which one, the East, West, North, South, or some other wall of the hole?
Solution. Since the force on the falling object is radial at all times there's no torque on it (about the center of the Earth). Therefore, the angular momentum of the falling object is conserved. Then rw = Rwe where w is the angular velocity of the falling object, r is its distance from the center of the Earth, R is the radius of the Earth and we is the angular velocity of the Earth. Since r decreases with time, w must increase with time, therefore w > we all the way down. The falling object gets "ahead" of the walls of the hole. Since the Earth rotates west to east, the falling object must hit the east wall.
The same argument can be used for an object dropped from a high tower at the equator.
This conclusion is not affected by the radial distribution of mass within the Earth, just so long as it is a solid Earth (as given).
Some books give the problem in a different fashion. They specify that the Earth also be at rest. Kleppner and Kolenkow [An Introduction to Mechanics, McGraw-Hill, 1973] ask students to show that in this case the motion is simple harmonic with a period of 84 minutes, and note that this is the same as the period of an Earth satellite in low orbit with r approximately equal to R. That solution is straightforward.
K&K specifically exclude consideration of hitting the wall, by saying: "In deriving this result, you need to treat the Earth as a uniformly dense sphere, and you must neglect all friction and any effects due to the Earth's rotation." I wonder why they didn't just say, "Assume the Earth doesn't rotate."
They fail to address some obvious questions.
Why should this be the same period as the satellite in low Earth orbit? Is there some insightful-conceptual way we might have expected this?
What if the hole were drilled through the center starting at some other latitude?
What if the hole were drilled perpendicular to the Earth's axis and through the Earth's center, starting at any latitude?
What if the hole were drilled in some other way? If it were drilled pole to pole, the rotation of the Earth wouldn't affect the fall. There's a related problem. In Chapter 7 of Lewis Carroll's 1893 book Sylvie and Bruno. The fictional German professor, Mein Herr, proposes a way to run trains by gravity alone. Dig a straight tunnel between any two points on Earth (it need not go through the Earth's center), and run a rail track through it. With frictionless tracks the energy gained by the train in the first half of the journey is equal to that required in the second half. And also, in the absence of air resistance and friction, the time of the journey is about 42 minutes (84 for a round trip) for any such tunnel, no matter what the tunnel's length.
Martin Gardner discussed this in one of his Scientific American "Mathematical Games" columns.
The period in the frictionless hole:
Restating the question: The period for the circular "skimming" orbit (of radius equal to the Earth's radius, R) is

T = 2p (R/g)1/2

Show that this is the same as the period of motion in frictionless straight hole through the center of the stationary Earth.

Partial Answer:

First let's address the question of the force on an object within a homogenous spherical distribution of mass.
The force on a piece of mass at point P a distance r from the center is due to all mass in the sphere of radius less than r.

image for this problem..
http://www.lhup.edu/~dsimanek/scenario/shell.gif

All mass at distances greater than r contributes nothing. This can be seen by subdividing the mass in the outer shell into many shells of infinitesimal thickness. Then take infinitesimal solid angles with vertices at the point P. The two pieces of mass within the solid shell contribute oppositely directed forces at P, of size proportional to the inverse square of their distances from P. But by geometry, their volume is proportional to the square of their distance from P. Therefore, their forces are equal, and being oppositely directed, add to zero.
The mass within r is proportional to r3. Its gravitational force acts as if it were concentrated at the center of the sphere, and therefore the force it exerts at P is proportional to r-2. Therefore the gravitational force at distance r is proportional to r3r-2 = r.
Now consider the straight hole or tunnel through the Earth, but not through the center of the Earth.
The hole has frictionless walls, or tracks. The gravitational force within the Earth is f = -kd where d is the distance from the center. When d = R the force is mg. At the center of the Earth the force is zero.
At any angle ß, the component of gravitational force along the tunnel is f = F(r)sin(ß). At distance x from the center of the hole an object is distance r from the center of the Earth. x = r[sin(ß)], and we already know that F(r) = -kr and

k = mg/R so
f = -kr sin(ß) = -kx
e2 ung image for that question..
http://www.lhup.edu/~dsimanek/scenario/earthole.gif

Therefore the force is proportional to the distance, meeting the requirements for simple harmonic motion with an effective "spring constant" k.

thermody nmn..

Helium (ç=1.67) is adiabaticly expanded (very slowly) in a well insulated container to a volume four times its original volume. It started at room temerature (22 degrees Celsius) and at a pressure of one atmosphere.

a. What is the final pressure?
b. What is the final temperature?

Consider Helium to act as an ideal gas.

eto mga answers and solution..

a. http://zebu.uoregon.edu/~probs/therm/adiabatic/node2.html
b. http://zebu.uoregon.edu/~probs/therm/adiabatic/node3.html

it's better to do some practices para handa agad sa pasukan di ba friends!!

electromag problem.. para maiba naman.. haha..

Two point charges a and b of both +20nC are placed 10m apart from one another.

http://zebu.uoregon.edu/~probs/eandm/efield/efield.a.gif

a.Find the electric field at point 1
b.Find the electric field at point 2
c. Find the electric field at point 3

this is the hint..
http://zebu.uoregon.edu/~probs/eandm/efield/node1.html

eto po mga answers with complete solution..
a. http://zebu.uoregon.edu/~probs/eandm/efield/node2.html
b. http://zebu.uoregon.edu/~probs/eandm/efield/node3.html
c. http://zebu.uoregon.edu/~probs/eandm/efield/node4.html

pls be concerned.. let's do our part to save mother earth..

Global warming is the most serious threat the world faces today. The warning signs are present , even here in the Philippines . Drought is felt during the rainy season and typhoons strike in the summer months. Sea water level is on the rise and more areas experience flooding . These are only some of the symptoms of a serious and growing global phenomenon: climate change. This environmental crisis puts the lives of millions at risk, hitting the poor countries hardest.

In response to the call for environmental awareness, GMA Public Affairs presents Signos (Fatal Signs), Philippine television’s first full-length documentary on what is considered the most pressing environmental issue today – the world’s changing climate as a result of decades of unchecked human activity. Following in the tradition of Al Gore’s “An Inconvenient Truth", Signos aims to bring the concept closer to home through a nation-wide investigation of the manifestations of climate change.Award-winning journalists, Howie Severino, Maki Pulido and Raffy Tima travel to different parts of the country to prove that the impact of climate change reaches far beyond the glaciers of the Polar Regions. Severino visits Bicol, where a 150-meter fault line and intensifying typhoons threaten to bury towns with landslides. Pulido discovers a town in La Union that has dwindled to more than half of its original size. In El Nido, Palawan, Tima ventures underwater to investigate a phenomenon called coral bleaching.

To provide the most in-depth report, Signos brings together scientists from local and international institutions, including Filipino NASA Senior Research Scientist and Nobel Prize winner, Dr. Josefino Comiso, and experts from the International Rice Research Institute (IRRI), Marine Science Institute, Greenpeace, and World Wildlife Fund for Nature (WWF), and other climate change experts. Signos brings Filipino viewers a comprehensive look on climate change, its causes, effects, and the measures that must be taken to prevent its disastrous consequences.

the "ME" i have become..

i hate the ME i have become,

for crippling anger corrupts my mind,

in this world of struggling men,

where i don't differ to anyone.

i hate the ME i have become,

for awful shatters i have done,

shatter to a preciously owned,

shatter to trash-considered keep.

i hate the ME i have become,

for this heart of mine is deeply scratched,

scratch reflected by a scar,

scar made by my idle hands.

i hate the ME i have become,

for this naive man has falsely grown,

raised by a single parent's touch,

but never lacked a Godly hand.

i hate the ME i have become,

for thousand reasons i articulate,

hat, doubt, and fatal anger,

words capsulized single by "ME."

i hate the ME i have become,

for i want to cry but tears won't flow,

the reason is that my eyes are doomed,

and that my heart's a freezing field.

i hate the ME i have become,

for thoughts like hell run in my brain;

demonic words i often say,

that pawned my soul to horned-tailed ones...

CAT and MOUSE

Softly we tremble tonight,
picture perfect fading smiles are all that's left in site,
I said I'd never leave you'll never change
I'm not satisfied with where I'm at in life.
Am I supposed to be happy?
With all I ever wanted,
it comes with a price.
Am I supposed to be happy?
With all I ever wanted,
it comes with a price.
You said,
you said that you would die for me...
We made plans to grow old,
believe me there was truth in all those stories that I told.
Lost in a simple game cat and mouse
are we the same people as before this came to light?
Am I supposed to be happy?
with all I ever wanted,
it comes with a price.
Am I supposed to be happy?
with all I ever wanted,
it comes with a price.
You said,
you said that you would die for me...
You must live for me too'...
For me too...
yeah, yeah...
You said that you would die for me...
Am I supposed to be happy?
with all I ever wanted,
it comes with a price.
Am I supposed to be happy?
with all I ever wanted,
it comes with a price
You said,
you said that you would die for me...