Category: other

How are tessellations used in roofing, tiles, and quilts?

Tessellation is the covering of a surface without gaps or overlaps using one or a small number of basic shapes. It’s a natural activity for roofers, tilers, and quilters, since those activities involve forming complete surfaces with a limited number of shapes. Since there are an infinite number of possible tessellations, people are always trying to create interesting new ones. You can find these in a tile catalog or a quilting guide. Tessellations appear in physics in the context of crystal structure, where surfaces and volumes must be filled completely with a few basic molecular arrangements. Quasicrystalline materials—materials with orientational order but no longer-range order—are a particularly interesting example of tessellation in physics.

How does an electric eel produce an electric charge? I know that it can produce up to 600 volts, but what does 600 volts mean without knowing the amount of current?

The eel produces this voltage by rearranging ions in specialized muscle cells called electroplaques. While I’m not an expert in this, I suppose that they use energy derived from food to pump ions through the cell membranes of these electroplaques in order to create charge imbalances between the two surfaces of those cells. By stacking hundreds or thousands of electroplaques in series, they succeed in separating positive and negative charges to great distances on their bodies and thus produce voltage drops in excess of 600 V.

You’re correct that current is an important issue here, since even household static electricity can separate enough positive charge from negative charge to reach thousands of volts. However, static electricity can reach very high voltages because there is no current flow to deplete the separated charge. In the case of an electric eel in water, the water conducts current well enough that the eel must continue to separate charge to maintain the 600-volt potential difference between its ends. I’m not sure how much current flows through the fresh water in this situation, but I would guess that it’s at least 1 ampere and possibly more. That means that the eel is moving a considerable amount of charge each second and using in excess of 600 watts of power. If the eel were a salt-water fish, it wouldn’t be able to reach a 600-volt potential difference at all because salt water conducts current far to well and an enormous current would flow in that case.

When you make a telephone call, you send an analog signal from your phone to a central station. Is this direct current or alternating current? How do you and your neighbors share the line?

When you are talking to a friend over the telephone, the telephone company uses a special power supply to send a constant (direct current) through your telephones. Your telephone and your friend’s telephone share this current so that if your telephone draws more, your friend’s telephone receives less. When you talk into the microphone of your telephone, the current your telephone draws fluctuates up and down with the air pressure fluctuations at the microphone. As a result, the current through your friend’s telephone fluctuates down and up, the reverse of the current fluctuations in your telephone. A speaker in your friend’s telephone uses these current fluctuations to recreate the sound of your voice. When there are other extensions active in your home, they are all sharing this current so that talking into one telephone causes sound to be reproduced in all of the other telephones, both in your home and in your friend’s home. While modern electronics have changed the telephone system extensively, so that this direct current sharing isn’t quite the reality it was 30 years ago, all of the complicated electronic circuitry works to simulate this same relationship.

What is the difference between a fruit and a vegetable?

A fruit is the ripened ovary of a flowering plant, often with a woody stem, while a vegetable is the edible product of a herbaceous plant (a plant with a soft stem).

In high school, we said that an object on the ground has zero gravitational energy, while an object above the ground has some. But if a hole opened up in the floor, the object on the ground would fall – so it must have SOME potential energy, right? At the center of the earth, would you have no gravitational potential energy? If not, why – doesn’t the sun still pull on you?

You’ve brought up an interesting subject. Many quantities in physics are only well defined relative to some reference point. For example, your velocity is only defined relative to some reference frame; typically the earth’s rest frame. Viewed from a different reference frame, your velocity will be different. The same holds for gravitational potential energy. When you choose to define the object’s gravitational potential energy on the floor as zero, you are setting the scale with which to work. For altitudes above the floor, the object’s gravitational potential energy is positive, but for altitudes below the floor, that energy is negative. As the ball falls into the hole, its gravitational energy becomes more and more negative and its kinetic energy increases. To avoid working with these annoying negative potential energies, you should choose to set the gravitational potential energy to zero at the lowest point you’ll ever have to deal with; for example, the center of the earth. But the center of the earth isn’t really the limit of gravitational potential energy. The object could release even more gravitational potential energy by falling into the center of the sun. It could release still more by falling into the center of a giant star. Fortunately, there is a genuine limit. If you were to lower the object slowly into a black hole, the object would release absolutely all of its gravitational potential energy. In fact, it would release energy equal to its mass times the speed of light squared (the famous E=mc² equation of Einstein). The object would actually cease to exist, having been converted entirely into energy (the work done on you as you lower the object, presumably at the end of a very sturdy rope). This effect sets a real value of zero for the gravitational potential energy of an object: the point at which the object ceases to exist altogether. Final note: if you drop something into a black hole, it doesn’t vanish the same way, because its gravitational potential energy becomes kinetic energy as it enters the black hole. The black hole retains that energy and grows slightly larger as a result. When you lower the object on a rope, you retain its energy and it doesn’t remain with the black hole. The black hole doesn’t change as it “consumes” the object.

Is there a relationship between the black hole and the point of origin of the universe?

Yes and no. Both involve lots of mass in a very small space. A black hole is a very strange region of space-time, where time runs slowly and the gravity is extraordinarily intense. Around the black hole, everything is swept inward through the hole’s surface. But (as best I understand it) the early universe didn’t necessarily have strong gravity. With mass uniformly distributed in the tiny, compact universe, an object felt gravity pulling it equally in all directions. There was as much mass to the left of the object as to its right. Thus the object would have been roughly weightless. With no gravity to make things lump together into galaxies, stars, and planets, there was no reason for those celestial objects to form. Why they did form is one of the great questions of modern cosmology. As for the universe’s character at the very moment of creation, I don’t think that anyone has a clear picture of what was happening. The very nature of space-time was probably all messed up and the theories needed to understand it don’t yet exist.

What information is now available about magnetic fields and free radicals in our bodies?

Free radicals are molecular fragments with unpaired electrons. The organic molecules in our bodies are normally held together by covalent bonds, an arrangement in which a pair of electrons orbits between and around two atoms in a manner that reduces the total energy of the atoms and thus binds the two atoms together. When only one electron is orbiting an atom by itself, it is chemically aggressive and tends to attack other molecules. That electron is also magnetic and is influenced a tiny bit by surrounding magnetic fields. My guess is that the magnetic fields you normally encounter, whether they are due to the earth’s magnetic field, or to nearby power lines, or even to strong magnets such as those used in magnetic resonance imaging, have very little influence over the chemistry of free radicals in your body. Free radicals are themselves a health issue, but I don’t think that magnetic fields make free radicals any more or less hazardous. If I learn more about this issue, I’ll add it here.

What is DTMF and how can I measure the pulses on a rotary phone?

DTMF is short for “Dual Tone MultiFrequency” and refers to the pair of tones that a telephone uses to send dialing information to the telephone switching system. Each time you press one of the buttons on the telephone, it emits two tones simultaneously. A decoder at the other end recognizes these two tones and determines what button you pushed. One tone is associated with the button’s row and one tone with the button’s column. Since there are four rows of buttons, there are 4 possible row tones and since there are three columns of buttons, there are 3 possible column tones. A fourth column of buttons, A through D, and a fourth column tone are part of the specifications for DTMF but do not appear in normal telephones. Naturally, all 8 tones are different and the web has countless pages that discuss these tones (touch here for an example)

As for measuring the pulses on a rotary phone, you can do this if you can study the telephone’s electric impedance (or resistance). As the dial switch turns, it briefly hangs up the telephone repeatedly. The number of hangups is equal to the number you are dialing (although dialing “0” causes it to hang up 10 times). You can actually dial by hanging up the telephone rhythmically and rapidly several times. If you click the hang-up button 5 times rapidly, you will dial a “5”. To detect that this hanging up is happening electronically, measure the telephone’s impedance—the impedance rises dramatically during each hang-up. If there is a constant current passing through the telephone, the voltage across its two wires will rise. If there is a constant voltage reaching the telephone, the current passing through it will drop. The telephone company detects this repeated change in impedance and determines what number you dialed.

When astronomers study sunspots they occasionally notice that there only seems to be one magnetic pole. But I thought that monopoles didn’t exist that we know of. What’s going on?

While a sunspot may have only one magnetic pole associated with it, there is sure to be an equal but opposite pole somewhere else in the sun. Probably it’s located deep inside the sun or somewhere else on the sun’s surface. Like one end of a long bar magnet, the sunspot looks like a single pole, but it’s really connected to an equal but opposite pole.

How do black holes work?

As you assemble more and more mass together in a small volume, the gravity there becomes stronger and stronger. At first, it becomes more and more difficult to throw a ball upward hard enough to make it sail away from the mass into space. Eventually, you need a cannon to get the ball to leave. And by the time you get enough mass together, the gravity becomes so strong that light itself begins to have trouble escaping. Light falls in gravity, just like anything else. But it travels so fast that you barely notice it falling. However when the gravity becomes strong enough, light falls enough to cause some weird effects. A black hole forms when the gravity is so strong the even light is unable to escape from the mass.