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A Mobius strip club. Why is a physics book always unhappy? Because it always has lots of problems. What would you call a clown in jail? Silicon Silly Con.
Why couldn't the moebius strip enroll at the school? They required an orientation. What animal is made up of calcium, nickel and neon?
A CaNiNe. Without any instrument, how can you determine which is Magnetic? A six feet man and his six year old son are swinging together at a park swing.
They are on a separate, identical swing. The man has four times the mass of the child. Every minute, Gear B makes 15 complete turns.
Physics Puzzles. Car Parts Puzzle - Assemble the parts of the automobile. Interactive car structure. Rocket Parts Puzzle - Assemble the parts of the rocket.
Interactive rocket structure. Train Parts Puzzle - Assemble the parts of the steam locomotive. Interactive train structure.
Bicycle Structure Puzzle - Build yourself a bicycle. Interactive bicycle structure. Energy Types Puzzle - Distribute kinetic and potential energies.
Force Types Puzzle - Sort the properties of different forces. The restraining thread is burned or cut and the system is set in motion, the left side rising and the heavier right side falling.
While the masses are in motion the spring balance reads the same as before. Explain why. When discussing kinetic theory, textbooks often model an ideal gas as a box with infinitely massive walls containing very tiny particles bouncing from the walls.
Part of the argument considers one such particle bouncing from the wall. We are told that the collision is perfectly elastic and the particle rebounds from the wall with the same speed it had before hitting the wall.
That tells us that the ball rebounds with unchanged kinetic energy, which students are all too willing to accept uncritically.
We reasonably conclude that no energy was lost to the wall. But what about momentum? So how can the wall gain momentum without gaining any energy?
Are textbooks deceiving us again? Resolve this with an energy and momentum calculation. Elastic definitions. Textbooks tell us that a perfectly elastic body is one which, when deformed, returns to its original shape without loss of energy.
They also tell us that a perfectly elastic collision is one in which the participating bodies conserve both kinetic energy and momentum.
But consider a bell, made of brass with a brass clapper. Bells and their clappers are made of nearly elastic metals, and both preserve their shape after many collisions.
A perfectlhy elastic collision is one that conserves mechanical energy without loss to dissipative processes. The collision of clapper and bell is not a perfectly elastic collision, for considerable energy is lost as sound, radiated away from the bell.
Also the swinging bell and clapper soon come to rest, so you know their energy was dissipated somehow. So how can elastic bodies undergo inelastic collisions?
Resolve this apparent contradiction. Idle question: Would a bell and clapper made of perfectly elastic materials make any sound?
Textbook treatments of relativity sometimes illustrate the "equivalence principle" with the example of a person in an elevator.
The elevator cable breaks and the hapless occupant falls with the elevator, experiencing a "weightless" condition in which he floats freely in his elevator frame of reference as if there were no external forces acting.
Textbooks often say that the person inside would be unable, by any experiment, to determine that there was a gravitational field in his elevator.
This example is, of course, flawed, for with sensitive instruments a person in the elevator could detect the gravitational field.
Ellipse or Parabola? Physics textbooks spend much space discussing trajectories of projectiles in the earth's gravitational field. But Newton tells us that the path of a cannonball in the absence of air drag is a portion of an ellipse with the center of the earth at one focus.
The famous picture "Newton's mountain" illustrates this. So if you were asked "What is the path of a projectile, an ellipse or a parabola? Newton's third law says: If body A exerts a force on body B, then body B exerts and equal and oppositely directed force on A.
Newton's other laws would be useless without this important law. Newton's laws are said to be universal, applying everywhere and at all times.
But Newton's third law cannot be correct in all cases, even in classical physics. Show why, with a simple example. But a little thought reveals that it cannot be true in all cases.
Give an argument why that is not a serious issue. Floating idea. A beaker of water sits on a scale used to measure its weight. A ball, less dense than water, would normally float on the water.
But it is tied down, completely submerged, by a string fastened to the bottom of the beaker. The ball is surrounded by water and does not touch the beaker walls.
The string obviously exerts and upward force on the bottom of the beaker. The string breaks, and the ball rises to the surface, floating there.
The string no longer exerts that upward force on the beaker. Does the scale now read more, less or the same as before? Support your reasoning with a free body diagram.
Holey physics. Physics problems are often framed with highly idealized situations. Here's a classic problem of that kind.
If a straight hole were drilled all the way through the earth right through the earth's center, and a stone dropped down the hole, how long would it take to return?
To keep this simple, ignore the fact that the hole could not be drilled through the hot material in the earth, and if it were, it would fill immediately with magma.
Then there's the pesky complication of the earth's rotation, so we must halt that, for the stone would collide with the wall of the hole.
Which wall, by the way? Drilling the hole along the N-S rotation axis of the earth would be one way to avoid this issue. To complete the idealization, assume the earth's density is homogenous.
And to extend the problem, after you have found the previous answer, suppose that a straight tunnel were drilled from New York to San Francisco.
Now install a railway track through the tunnel. How long would the trip take in an unpowered railroad car, without being given any push, neglecting friction, etc.?
As usual we seek the simplest solution, preferably not even requiring calculus. Forever is a long time.
On an infinite frictionless plane could a perfect cylinder, given an initial push, roll forever? Friction is a drag.
Students sometimes suppose that friction always opposes a body's motion, tending to reduce its speed. But there are many everyday examples showing that friction can be necessary to initiate and sustain motion.
Give some examples. State the definition of friction so that it cannot be misinterpreted. Racing photons. Consider light passing through a converging lens from a point source to a point image.
The light rays passing through the lens near its edge must travel a greater distance from source to image than do the rays passing through the center of the lens.
Wouldn't this make the rays arrive at different times and possibly cause destructive interference at the image?
Unweaving a spectrum. Sir Isaac Newton is famous for his experiments with light and prisms. He showed that the light passing through a prism separates disperses into a colored fan spectrum.
He also showed that if that colored light is then passed through another prism, properly arranged, it can be recombined into white light.
Thus, he argued, the colors are actually in the white light, not created by the prism. Here's a gallery of examples from the web, supposed to illustrate this experiment.
Textbooks and web pages frequently illustrate this experiment with such pretty pictures—and get it terribly wrong! Google prism recombine white light and view the images.
Most of the images will be wrong in one or more serious ways. This is a telling example of why the web is called "the misinformation highway", for it is dangerously compromised by potholes.
If you tried to duplicate this experiment in the lab, following these examples, you would surely fail.
Identify the errors in each of these. What is a correct way to decompose white light into colors and then recombine it into white light?
There are several ways. I once had a student who wanted a project for extra credit to raise his unimpressive average.
I suggested he go into the lab and duplicate this experiment. He copied textbook illustrations and failed every time. He was frustrated.
Finally I suggested he might find out where the college library was, then locate Newton's "Optiks".
There he found out one way to do it successfully. The Soda Can. Here's a puzzle from Martin Gardner's collection. It is an old problem, but the method is still instructive.
Assume that a full cylindrical can of soda has its center of gravity at its geometric center, half way up and right in the middle of the can.
As soda is consumed, the center of gravity is initially lowered. When the can is empty, however, the center of gravity is back at the center of the can.
There must therefore be a point at which the center of gravity is lowest. Knowing the weight of an empty can and its weight when filled, how can one determine what level of soda in an upright can will move the center of gravity to its lowest possible point?
To devise a precise problem assume that the empty can weighs 1. It is a perfect cylinder and any asymmetry introduced by punching holes in the top is disregarded.
The can holds 12 ounces 42 gram of soda, therefore its total weight, when filled, is Reverse Osmosis. A correspondent from New Zealand sends us this ingenious idea that he saw in the Dec.
We'll let him describe it: Osmosis is a process where water flows through a semi-permeable membrane from a less concentrated to more concentrated solution.
Reverse osmosis is where water flows through the membrane from a strong solution to a weak one. Of course you must have pressure behind the membrane to make it flow the "wrong" way.
To get fresh water to flow from seawater through a membrane takes a pressure of about 20 atmospheres.
This is the basis of desalinating devices used on large ships. Now, at this depth the head of salt water in the ocean around the end of the pipe is more than 20 atmospheres, say 21 atmospheres, so fresh water flows out of the ocean salt water into the fresh water pipe.
You may have to adjust the depths a bit depending on the density of the sea water but the principle seems plausible.
Not only will this device give an endless stream of fresh water but can be used to run a small generator. The figure shows the tube in the ocean, its top end curved to direct water to the little water wheel, W.
You've gotta love perpetual motion proposals that are so simple, with no moving parts, and hold promise of solving our world energy problems and our fresh water resource problems as well.
That is, if only we can get enough of these machines running at once. Pressure in the ocean varies linearly with depth, increasing by about 1 atmosphere for each 10 meters of depth.
So the pressure in the ocean at a depth of about meters feet is 20 atmospheres above atmospheric pressure. This fact may or may not be helpful.
This seems to be a great idea. But it won't work. Why not? An answer is given in the April. See also the June issue.
Which egg is boiled? This is a very old problem. Two eggs are on the table, one is fresh and one has been hard boiled.
How can you determine which is boiled without breaking their shells? Which is hollow? Two spheres have the same diameter, weigh the same, and are painted the same color.
One is solid, of lightweight material. The other is a hollow shell made of denser material. Without damaging them, how can you tell which is hollow?
An attractive puzzle. This puzzle is often criticized for perceived ambiguity. Here's a version with most of the ambiguity removed. You are given two iron bars, identical except for the fact that one bar has been magnetized, the other is not magnetized.
Using nothing other than the two bars and your hands, how can you determine which is the magnet? We will allow gravity to operate as usual on you and the bars.
Heat one of the bars very hot and let it cool. If the bars no longer attract as strongly, then the one you heated was the magnet.
Drop one repeatedly on the floor. If the attraction between the bars is reduced, then the one you dropped was the magnet.
But we ruled these out by specifically requiring that you must use only the bars and your hands. No string or wire can be used, no other metal, and nothing to heat a bar.
You can't even use the magnetic field of the earth. So what is the simplest way to identify the magnetized bar?
One answer, well known, is the "T" test. Place the bars touching in a T configuration, with the end of one at the center of the other. If they attract, then the one which is the upright of the T is the magnet, for the other has its poles at either end and no pole at its center.
But magnets of high permeability materials can be made with many poles, for example one with a [N SS N] arrangement. Such a magnet would not tend to point north when suspended and might fail the "T" test.
What's the simplest way to identify the magnet, no matter how that magnet's poles are arranged? Which is longer?
Prepare two metal tubes. Mine are cut from 1 inch diameter aluminum tubing from the hardware store. One tube is 11 inches long.
Try to ensure that the tubes have no scratches or imperfections that could distinguish one from the other. Hold them up, one in each hand, and ask if anyone can visually see that one is shorter than the other.
Of course no one can. Hold them side by side, touching, and the difference is obvious. Ask someone to take them, then turn around to hide them from your sight, choose one, and then hand it back to you.
You pretend to judge its length between your hands, touching the tube at its ends, only with your fingertips. What is your secret? Rolling paradox.
Physics textbooks define the force due to friction as a force tangent to two surfaces at their point of contact. Consider a ball or cylinder rolling without slipping on a perfectly flat and level surface.
We expect it to slow down. We naively assume that friction is the reason it slows down, eventually stopping. Certainly the friction is opposite to the ball's velocity, and would therefore decelerate the ball's motion by Newton's second law.
But that force due to friction has a torque, and this vector torque around the center of mass of the ball is in the same direction as the ball's angular velocity vector.
This would increase the ball's angular velocity, making it roll faster and faster. When inventors first proposed railway transportation, using steel wheels on steel rails, some skeptics said "The wheels will just spin in place, and the contraption won't go anywhere.
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