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).

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.

How do compasses work?

A compass contains a magnetized needle, with a north pole at one end and a south pole at the other. Since opposite magnetic poles attract one another, the north pole of the compass is attracted toward any south poles it can find and the south pole of the compass is attracted toward any north poles it can find. The earth happens to have a strong south magnetic pole near its north geographical pole and a north magnetic pole near its south pole. As a result, compass needles turn (the experience torques) until their north magnetic pole ends are pointed northward (toward the south magnetic pole located there).

How do electronic water softeners, where a coil of wire is wrapped around the incoming water pipe, work?

I’ve never heard of such a water softener, but I can voice some skepticism about it anyway. Hard water is water that contains substantial amounts of dissolved calcium, magnesium, and iron. These elements form multiply charged ions in solution and these multiply charged ions tend to bind with soap and detergent molecules to form an insoluble scum. To soften the water, you must remove those ions. A conventional water softener does this by replacing them with sodium ions. The active part of a conventional water softener is an ion exchange resin that releases sodium ions as it binds up the calcium, magnesium, and iron ions. Eventually the resin runs out of sodium and it must be regenerated by flushing it with strong salt water. This regenerating process flushes the calcium, magnesium, and iron ions out of the resin and puts the sodium ions back into it. As for the electronic water softener, where does it put the calcium, magnesium, and iron ions and what does it replace them with? It can’t make those ions disappear and, if it were to extract them without replacing them, it would leave the water electrically charged. So I’m skeptical that any device that doesn’t chemically treat the water directly can soften the water.

I read in an article about batteries about a Reverse Coulomb Counter. What is it?

Although I’ve never heard of such a device myself, I can guess what it means. A coulomb is a standard unit of electric charge. Since a battery is a pump for electric charge, measuring the number of coulombs that have flowed through a battery is a way to determine what fraction of that battery’s storage capacity has been used. (It’s analogous to measuring how many grams of sand have flowed through the neck of an egg timer or how many liters of water have flowed out of a water tower.) When a battery is being recharged, measuring the number of coulombs that have flowed in the reverse direction through the battery is a way to determine how much recharging has occurred. Thus, I suspect that a “reverse coulomb counter” is a device that monitors the flow of charge backward through a battery as it is being recharged. This backward flow of charge should be almost exactly proportional to the extent of recharging.

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.