Brain Teasers from Richard Feynman
There are many interesting brain teasers associated with the great physicist Richard Feynman. I like them because they are easy to state and understand, but they can be hard to solve. Here are four of them. The first one is easy, the second one is a little harder (but you should be able to get it with a hint), the third one is pretty hard, and I haven't been able to solve the fourth one yet, and I suspect it is hard.
Mirror
Train
Sprinkler
E&M Paradox
I found this problem in No Ordinary Genius by Christopher Sykes. It's pretty easy.
You look in a mirror, and let's say you part your hair on the right side. You look in the mirror, and your image has its hair parted on the left side, so the image is left-to-right mixed up. But it's not top-to-bottom mixed up, because the top of the head of the image is there at the top, and the feet are down at the bottom. The question is: how does the mirror know to get the left and right mixed up, but not the up and down?
I this problem is also from No Ordinary Genius by Christopher Sykes. It's a little harder than the previous one. Try to solve it on your own first, then read the hint...you'll get it after the hint.
What keeps a railroad train on the tracks?
Hint: No...it isn't the flanges.
Hint: There is a axle connecting the adjacent wheels on a train car.
Hint: The axle does not have a differential. So the wheels on both sides of the train always spin at the same speed.
This problem is from Surely You're Joking, Mr. Feynman! by Richard Feynman.
You have an S-shaped lawn sprinkler-an S-shaped pipe on a pivot-and the water squirts out at right angles to the axis and makes it spin in a certain direction. Everybody knows which way it goes around; it backs away from the outgoing water. Now the question is this: If you had a lake, or swimming pool-a big supply of water-and you put the sprinkler completely under water, and sucked water in, instead of squirting it out, which way would it turn? Would it turn the same way as it does when you squirt water out into the air, or would it turn the other way?
(from The Feynman Lectures on Physics, Vol. II sec. 17-4)
Imagine that we construct a device like that shown in the figure. There
is a thin, circular plastic disc supported on a concentric shaft with
excellent bearings, so that it is quite free to rotate. On the disc is
a coil of wire in the form of a short solenoid concentric with the
axis of rotation. This solenoid carries a steady current I
provided by a small battery, also mounted on the disc. Near the edge
of the disc and spaced uniformly around its circumference are a number
of small metal spheres insulated from each other and from the solenoid by the
plastic material of the disc. Each of these small conducting spheres
is charged with the same electrostatic charge Q. Everything is
quite stationary, and the disc is at rest. Suppose now that by some
accident-or by prearrangement-the current in the solenoid is
interrupted, without, however, any intervention from the outside. So
long as the current continued, there was a magnetic flux through the
solenoid more or less parallel to the axis of the disc. When the
current is interrupted, this flux must go to zero. There will,
therefore, be an electric field induced which will circulate around in
circles centered at the axis. The charged spheres on the perimeter of
the disc will all experience an electric field tangential to the
perimeter of the disc. This electric force is in the same sense for
all the charges and so will result in a net torque on the disc. From
these arguments we would expect that as the current in the solenoid
disappears, the disc would begin to rotate. If we knew the moment of
inertia of the disc, the current in the solenoid, and the charges on
the small spheres. we could compute the resulting angular velocity.
But we could also make a different argument. Using the principle of the conservation of angular momentum, we could say that the angular momentum of the disc with all its equipment is initially zero, and so the angular momentum of the assembly should remain zero. There should be no rotation when the current is stopped. Which argument is correct? Will the disc rotate or will it not? We will leave this question for you to think about.
We should warn you that the correct answer does not depend on any nonessential feature, such as the asymmetric position of a battery, for example. In fact, you can imagine an ideal situation such as the following: The solenoid is made of superconducting wire through which there is a current. After the disc has been carefully placed at rest, the temperature of the solenoid is allowed to rise slowly. When the temperature of the wire reaches the transition temperature between superconductivity and normal conductivity, the current in the solenoid will be brought to zero by the resistance of the wire. The flux will, as before, fall to zero, and there will be an electric field around the axis. We should also warn you that the solution is not easy, nor is it a trick. When you figure it out, you will have discovered an important principle of electromagnetism.