Kinematics

A dirt-biker rode the first half distance of the race with the speed of 200 miles per hour. For the remaining part he was a bit distracted and covered half the time with the velocity 150 miles per hour and rest of the time, speed up to 250 miles per hour.

If he came second and was beaten by 20 seconds. What was the average velocity of the guy, who came first ?

Einstein's Sphere

An Incredible Sphere was found in the laboratory of Einstein. A cylindrical hole, 6 inches long has been drilled through the center of the solid sphere. Remaining volume of the sphere was needed to solve the puzzling equation, written on the black board.

Can you help?

Hot

Is boiling water always hot ? If not, why not ?

Are we there yet???

Less riddle, more paradox:

To go from point "A" to point "B," one must first go half way. When at the half-way mark, there is now a new point "A." To travel to point "B" takes another trip first to the half-way mark. Since this is and will forever be a renewing course of events, how can point "B" ever be reached?

In the same area of thought; If you break a rock in half, what is left? A half-rock? No, of course not. There is no such thing. You have two rocks. Break one of them in half, and yet another smaller rock. Half again, and again, and again......Is this infinity? Physics will wind you up at molocules and atoms. Religion; God. Others will say you will find things called "Super Strings." Steven King and others say galaxies within galaxies.

I think........well, who cares what I think.

What do YOU think?

Notorious Tank Problem

The notorious Tank Problem that one finds in every single collection of arithmetical and algebraic problems. No doubt, you all remember those classic scholastically dry problems of this order:

"The tank has two pipes -- one leading to fill the tank to the brim and the other out. the first needs five hours to fill the tank and the second ten hours to drain it dry. How long will it take the tank to fill up when the stop cocks are out of both pipes ?"




This problem has a venerable history, dating right back some twenty centuries to Heron of Alexandria. Here is one from his collection for your free time in the weekend.

Four Fountains are there and a reservoir vast.
In but one day the first doth fill it to the brim.
The second two days and nights must play to do the same.

The third takes thrice the time as did the first.
The fourth comes last with four days and nights.
Now tell me when the reservoir will fill,
when all four play at once.



It is two thousand years now that the tank problem has posed and -- such is the force of habit ! -- has been solved wrongly in all this time.

Magnetic "Perpetual" Motion

In attempts to invent a "perpetual motion" machine the magnet and its power have played a role of no mean magnitude. Ill-starred "perpetual motion" machine inventors have tried might and main to apply the magnet to this end. Here is one such project described back in 17th century by Englishmen John Wilkins, the Bishop of Chester.

A Powerful magnet A is placed on the top of the pillar leaned against which is two inclined grooves M and N, one above the other. The upper groove M has a small hole C at the top, while the lower groove N is curved.



The inventor claimed that the arrangement would operate as follows. A small iron ball B was to be placed on the upper groove. Attracted by the magnet A, it ought to roll upwards. On reaching the hole, it should roll down, be carried up by inertial along the curve D, and find itself again on the upper groove M, from whence, again attracted by the magnet, it should again roll up and drop through the hole, roll down and on to the upper groove, ad infinitum.

This the inventor conjectured, would produce "perpetual motion".

What do you think ? Will it ?

Why does Rocket Go Up ?

Professor Feynman was teaching the class.
"Even from students of physics one may often hear a totally wrong explanation of a rocket's flight. They claim that it goes up by thrusting itself away from the air with the help of gases formed from gunpowder combustion. That incidentally is what ancients thought-rockets are invented long, long ago."

He added "But if we were to fire a rocket in an airless void it would fly, and even better than in the air."

What's the right explanation ?

Fantasy & Science Fiction

Isaac Asimov had a 30 years correspondence with Nobel Prize winner Linus Pauling. Pauling read Isaac's science articles in Fantasy & Science Fiction magazine regularly and wrote Isaac whenever he found an error. Here is an interesting excerpt.
From Pauling to Isaac:

I am writing now about your article in the September 1978 issue. On page 123, you say that Amontons and Guy-Lusac observed that if a gas at the freezing point of water, 0 degree Celcius, is decreased in temperature to -1 degree Celcius, then both the volume and the pressure of the gas will decline by 1/274 of the temperature. This is wrong. What you should have said is that _ _ _ I hope you are keeping busy as ever.

What was the explaination?

A Motorless Underground Railway

If you have read the free travel, you will find this more intriguing. A booklet with the odd title A Motor less Underground, Leningrad-Moscow Railway was once put out. Its author A.A. Rodnykh, suggested a very interesting project .

His idea was to "dig a 600-km-long tunnel, linking up two cities Leningrad and Moscow by an absolutely straight underground line. this could give us for the first time the opportunity to travel along the straight instead of following a curved path as now." He wishes to say that all our roads describes arcs, as they follow the curve of the earth surface, while the suggested tunnel will follow a straight line along a chord (assume earth as a circle).

This project - if ever realized - would possess a unique characteristic. In this tunnel a train move by itself. At each point, since the train is going in the downward direction due to gravity, it will not require a motor. The big tunnel will actually be inclined to some angle with the horizontal ground at both the points.

In such a slanting tunnel every object should swing, due to gravity, to and fro like a pendulum, hugging to the bottom. Inside it a train would move by itself along the rails, its weight doing the work of locomotive. At first the train will move very slowly but with every new second its speed would increase, to reach soon a figure so incredible,that the air in the tunnel would offer a noticeable resistance.

Do you see any flaw in this design, A motorless vehicle can help realize the dream of free travel. Why this is not done yet?

Fatal Attraction !

In the autumn of 1912, the ocean linear Olympic, one of the world's biggest ships at the time, was steaming ahead out in the high seas, when another much smaller ship, the cruiser Hawk, rapidly approached it on a parallel course a hundred meters away.

As soon as the two ships took up a position where one pointed the other, a surprising thing happened. the Hawk sharply veered off its course, as if obeying some invisible force, turned the big liner and heedless of the helm rammed into it.The impact was so great that it made a big gash in the Olympic's hull.

A tribunal examined this queer case and found the Olympic's Skipper guilty, as, according to its ruling, he had failed to issue orders to yield the right of passage to Hawk. Consequently, the tribunal, as you can gather, saw nothing extra ordinary about it at all, attributing the the accident to the skipper's negligence.

Actually this was the result of a totally unforeseen cicumstance, a case of mutual attractions of ships at sea and the answer lies in basic physics.

Why do ships attract one another ?