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Physics Puzzles

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Physics Puzzles Uranium-238 Riddle Video

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Physics Online Puzzles Collection. There's no record that it was ever built and used. Lenardo's goof 2. Lenardo da Vinci's notebooks have a number of errors.

Here's one showing water streams from holes at various heights in a water tank. What's wrong with this diagram.

How should it look? Leonardo's aerial screw. Codex Atlanticus. Leonardo's goof 3. Leonardo da Vinci proposed several ideas for man-powered flying machines.

One, called the "aerial screw", had a rotating screw-shaped airfoil, powered by two men on the platform below, turning cranks.

Aside from the trivial observation that even two men wouldn't provide enough power, this idea has a serious flaw of physics that would prevent it from staying aloft.

What is it? Obviously this idea didn't fly. Textbooks often say that when an object is at the focal plane of a converging lens, the light from it, passing through the lens, forms a real image "at infinity".

However it can equally well be said that it also forms a virtual image "at minus infinity", easily seen by looking through the lens toward the light source.

So a single lens is producing two images. How can this be? Are we playing fast and loose with the word "infinity" here?

In some mathematics courses teachers used to say "parallel lines meet at infinity". More careless language, it seems.

Resolve this confusion. This raises another question. But is this all? Does a lens produce any other images?

If you are right handed, your mirror image is left handed. If you touch your right ear, your image touches its left ear.

But your image is not standing on its head. At first this seems paradoxical for the mirror is symmetric about its normal.

You can rotate the mirror around its normal axis, and the image does not rotate. So why isn't the image also symmetrical about this normal? Resolve this confusion with a simple argument.

You must be careful and precise in your use of language. Virtual image rotation. A Dove prism has the interesting property that when you look through it and rotate it, the image rotates through an angle twice as large as the prism was rotated.

If you don't have such a prism, use an equilateral prism, looking through it, as shown, so that the light has internal reflection at one side of the prism.

Up periscope. Submarines played an important role in WWII. You have seen those movies where the captain looks for enemy ships through a periscope, a long narrow tube extending upward to just above the water surface.

Those were days before TV and fiber optics, so the periscope used only lenses and reflecting prisms. You know that looking through a long, narrow tube you cannot see more than a very narrow field of view, yet periscopes could see a much larger field.

These periscopes could be 30 feet long and six inches in diameter. Looking through such a tube you'd see a field of only one degree.

How can this be done using only an optical system with glass lenses? The physics of falling. Every introductory physics textbook tells you that in the absence of air drag, two bodies of different mass fall with the same acceleration, that is, they will fall equal distances in equal times.

Galileo is usually mentioned in this context, though others did the experiment before him, and he probably never did the experiment with freely falling bodies certainly not at the leaning tower of Pisa.

But Galileo had a simple logical argument to conclude that the mass of the falling body does not matter. Remember that in Galileo's time algebra had not been invented, and calculus came along even later.

So how did Galileo conclude this important result, using only a simple logical argument? Weighing a moving system. Weight reduction?

We are often told that if we keep moving we'll lose weight. But does a moving object's weight depend on its motion? A classic physics laboratory experiment is an Atwood machine: two unequal masses on the end of a string passing over a pulley.

The system can be made to accelerate slowly enough to easily measure its acceleation, and with a little mahematics, determine value of the acceleration due to gravity.

The Atwood machine shown is suspended from a spring balance. Suppose the heavier side right side hanger is fastened to the hook of the spring balance by an additional thread, preventing the masses from moving.

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. At which point, A, B, C or D will the water flow fastest? There is a car with a flat roof, on a plain level road.

There is a helium balloon in the car, barely scraping the roof — any slight force will move it. You start the car and accelerate forward very fast.

Does the balloon move with respect to the car? If so, how? No any trick and no any air from window. There are two cylindrical rods of iron, identical in size and shape.

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Physics Puzzles
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Physics Puzzles

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