A full list is found at http://www.phy6.org/StarFAQsA.htm
and links arranged by subject are at http://www.phy6.org/stargaze/StarFSubj.htm.
396B Posssibility of Asteroid Hitting Earth (2)
325. Tapping Atmospheric ElectricityI would like your views on a proposed new Atmospheric Power Generation (APG) technology. A device containing a large numbers of radioactively treated needles in an electron emitting device is elevated into the atmosphere by an airship, and is connected to a ground-based power converter through a conductive tether. Electrons are drawn from the ground, flow through the power converter and tether, and are emitted into the atmosphere by the needles. The voltage field drawing electrons from the needles is the atmospheric voltage gradient, and the current flow is affected by air conductivity at the applicable altitudes.
It has been proposed that the maximum amount of power we would be able to extract from the atmosphere globally will be limited by the total power normally residing in positive ions within the global atmospheric circuit. This number is about (250KV)*(1,000A) = 250MW.
We would be very appreciative if you would share any of your thoughts on any of the questions and possibilities above.
ReplyPlease tell your partnership that this idea is not likely to be useful.
What you have in mind, as I understand it, is an electrical circuit which taps the atmospheric potential at an airship moored at some altitude, sends a current through the mooring cable to the ground (where some electric power can be utilized), and closes the circuit back through the atmosphere, to the region around the airship where, presumably, more electric charge is waiting to be neutralized.
Just apart from the electric aspects, let me state that an airship moored at even 1 kilometer is a technological challenge. The cable and its insulation will be heavy, especially since it has to both moor the airship and carry its own weight, forces which stretch it in opposite directions. The airship--if filled with helium, will be expensive, if with hydrogen, it must be very gas tight, and in any case, airships at that altitude are very vulnerable to storms (think of lightning, too).
But beyond that, the atmospheric electric field contains rather little energy. It is maintained, if I understand, by the global distribution of thunderstorm clouds. Suppose you remove some of it, how soon will it be replenished? You close your circuit through the atmosphere at 1 km below, through the weak conductivity of air (mostly caused by cosmic rays). However, the thunderstorms replenishing the potential may be hundreds if not thousands of kilometers distant, through the same poorly conducting air!
326. Global disaster in 2012?I am asking this question on behalf of my son who is concerned about the information regarding the Mayan Calendar. The Mayan Calendar indicates that on Dec 21, 2012 something drastic may happen to Earth. Some people think a pole shift will happen that day which will cause flood of two mile high water. . Could you please share your thoughts as a scientist about this?
ReplyI have received a substantial number of questions like yours--and this is only 2007! Rest assured, no disaster is foreseen on that date. Rather than answer you specifically, let me direct you to my questions-and-answers section, e.g.
and look up there questions #306, #291b, and #264 (and their replies), also, if you wish, #302.
. . . . . Continuing the questionThanks. It is just that my son has done a lot of searching on this topic and stuff about a black hole, a pole shift, gamma ray bursts, asteroids and many coincidences have come up. Everything leads to 12/21/2012, including a web program predicting the end of the world on that day and the date showing up in I Ching.
Are all these predictions just pseudoscience and authors bending the truth or is there actual scientific evidence about what's going to happen in 2012? Also, is the Earth's magnetic field really weakening and the earth's rotation really slowing?
ReplyAs far as I can see, there is no physics or astronomy involved, just a lot of astrology. It is not a lie, it is just superstition.
The Earth's main north-south field is weakening, as it has been for centuries, by about 5% per century, maybe now speeded up to 7%. Scientists do not regard it as unusually fast. The field may reverse polarity in 1500 years or so--or else, its slow change may rise again. Records in ancient lavas tell that both of these have happened.
The Earth's rotation is slowing down because of the attraction of the Moon and Sun, raising tides on Earth. Now and then the total accumulated slowing down adds up to a second, and master clocks are reset accordingly. This happens at intervals of years (see Wikipedia. after asking Google about "leap seconds") and is also rather slow.
327. What's the difference between speed and velocity?You probably get these kinds of questions all the time, so I'll try to be brief. I am trying to articulate (and really understand) the difference between speed and velocity,
'The question is,' said Alice, 'whether you can make words mean so many different things.'
'The question is,' said Humpty Dumpty, 'which is to be master --that's all.'
328. Effect of Gravity on Electromagnetic Waveshello sir!!
i just want to know what is the effect of gravity on electromagnetic waves
ReplyAn EM wave such as light is distorted very slightly by gravity. It takes a very strong gravitational field to produce a distortion sufficiently strong to be observable. For more, see
329. Why is North the reference, not South?I am the student of earth sciences in Pakistan. My question is why we take north as reference in our maps or drawings, why not south? Why compass needle points always towards north pole?
ReplyOur maps originated around the Mediterranean, well north of the equator. In those countries, the north star or a spot near it in the sky (see http://www.phy6.org/stargaze/Spolaris.htm ) is the pivot around which the stars seem to turn at night, and the sun in the day. North is therefore a direction easy to establish at night. It is also the direction of the shadow of a sundial at noon, when the shadow is shortest.
Naturally, it was taken as reference direction. Interestingly, though, when the ancient Chinese discovered the magnetic compass, they viewed it as pointing south. Since the compass needle points (very nearly) north-south, deciding which of these directions is to serve as reference can be one's own choice.
330. The lowest 700 km of our AtmosphereI have been looking through your website with much interest.
I am an artist based in Notttingham England and for the last year I have been conducting a long-distance collaboration with an artist in Toronto, Canada. Our most recent project is a performance walk through our cities inspired by the idea of climbing enough stairs to see each other over the horizon.
We have been helped with the calculations and are aiming to climb the 699km calculated, using stairs. This of course will take us a long time and so this is an ongoing project that will happen in stages. This weekend we start another stage of our journey. We are taking an audience on our walks this time, and I would like to tell them more about what it would be like at the height we are aiming for. Can you give me any pointers on where I could find information like this, or can you help me
ReplyThe atmosphere at 699 kilometers is at most a trace of what you and I breathe (and is mostly hydrogen). Where we live, of course, the air is compressed by the weight of all the layers above it, and as you rise, that weight decreases (some is now below you), and the pressure decreases in proportion.
Observations suggest that about half the atmosphere is contained in the lowest 5 kilometers, so at that altitude, air density is down to one half. And so with the next 5 kilometers, and the 5 km after that, and so on (temperature affects that distance too but only moderately). At 10 kilometers you therefore have 1/4 of the pressure and density. At that altitude or a little higher is where most weather processes end. Weather is essentially the process by which the atmosphere removes heat from the ground (where sunlight has put it) and transports is upwards--winds, clouds, rain etc. all play a role, and of course air gets steadily colder, because heat only flows from hot to cold.
At 10-15 kilometers (with one small exception) that process ends, the atmosphere becomes transparent to heat radiation (infra-red) which then flows out into space. It also gets very dry, so when you fly on a jet, you see most clouds below you. The exception is the ozone layer at 25-40 kilometers, which absorbs ultra-violet light and causes some local heating.
If you halve the density every 5 kilometers, at 100 kilometers only about a millionth of the air density the ground level is left, and soon after that collisions between molecules become infrequent. Molecules still collide, but they do not mix as well. Near the ground air is about 78% nitrogen, 21% oxygen and 1% argon. Above 100 kilometers or so, heavier particles rise less. Atomic oxygen (split up by sunlight) is lighter than oxygen molecules and rises fairly high, but helium and hydrogen, being even lighter, outlast all others, even though their part in the atmosphere is very small. Earth is thus surrounded by a big "geocorona" of hydrogen, which astronauts have photographed in the ultraviolet color which hydrogen scatters and in which it glows--see
But that is just the "neutral" atmosphere. Sunlight also separates electrons from atoms to form positive "ions", surrounded by free electrons. Below 100 kilometers these collide and recombine--new ones are created in the daytime, but at night the ion layer ("ionosphere") recombines and disappears. Above about 140 kilometers, the collisions of ions are less frequent, which causes them to be bound mostly to magnetic field lines: electric currents flow well along such lines, but have difficulty jumping from one line to another, that is, flowing horizontally.
At 200 kilometres and higher, the ionosphere does not recombine, but its density goes down with distance, since most ions are still held by gravity. Around that level collisions become rare and molecules rise and fall like tossed stones. There are up to a million ions and electrons per cubic centimeter at that altitude (the numbers must match), but only about 100,000 at 600 kilometers.
In addition, some electrons and ions acquire much higher energy by processes having to do with the Sun and the solar wind. They are much too fast to be held by gravity, but magnetic forces which originate inside Earth can trap them. Their number is not large--but they can be interesting, since they carry electric currents which modify the magnetic field, and at the highest energies they constitute the Earth's radiation belt. At places the edge of this belt may come down to 699 kilometers or so, but between Nottingham and Toronto you are likely to be just below the radiation belt, and the "radiation" will not reach you.
That is a very quick description of the region you plan to "cover." And by the way, it would be hard to climb as many stairs as you plan without repeating some, even if you do much of the climbing indoors. My parents in New York lived on the 10th floor of a building with 36 floors, and sometimes I climbed up 35 floors and went down by elevator, just for exercise. It was rather boring. And you would need a thousand such climbs just to gain 100 kilometers. Good luck with your project!
331. Doomsday 2012?I'm sure you will probably be laughing by the time you get to the end of this e-mail, but the answer to the question is important to me.
My husband was watching some sort of television show that was promoting the idea that the world might end in 2012. The evidence provided was that this is the year the Mayan calendar ends and that planets will align with a black hole, thus magnetic pole reversal will occur. Hence, life here on earth will end as we know it - catastrophic flooding, radiation, etc.
I don't know much about the earth's magnetism, although I have been reading about it since I stumbled upon your website after I finally went to NASA's website. Most of the information on the internet regarding 2012 presents doomsday predictions relating to the pole reversal.
My question: Is there any evidence that a magnetic pole reversal will occur in 2011 or 2012? Is this something that has been newly discovered?
From what I understand from your website, a pole reversal will probably not occur for at least 1200 or so years and this is only if current trends hold true. In addition, it seems that we always have some magnetism during a pole reversal, it is only that the magnetism is weaker.
ReplyIt constantly amazes me how superstitious some people are. How should the Maya know about magnetic reversals, if they had no way of being aware of magnetism--no iron, even, they were essentially still in the stone age! How should they have known about black holes, a concept requiring information about stars and gravity which even in our civilization (with its telescopes) are less than a century old? Yes, they had a very accurate calendar, but so did the priests of ancient Babylon.
Incidentally, you seem to have understood well what you read on my site about reversals. They are not expected to not change anything important for life on Earth, and as noted, at the present rate one will not happen sooner than in 1000 years. Even that is uncertain: the geomagnetic record of old lavas suggest that the "main field" of Earth fluctuates constantly, and in the past "excursions" have taken place when the field seemed to approach a reversal, but then changed to an opposite trend.
332. Where does a Flying Bird get its Support?My class and I have a physics question. Could you please give a scientific answer?
A large bird cage is attached to a digital scale, and the mass on the scale reads 20 kg. A bird is sitting on a perch in the cage.
The bird then gets off the perch and flies around the cage without touching anything. Will the mass reading on the digital scale change?
Ask yourself: when the bird flies around, what keeps it aloft? By Newton's 3rd law, if it is held up by an upward force of 20 kg (or an appropriate number of Newtons, pick your favorite units), an opposite and equal downward force must be applied SOMEWHERE. My guess is that the wings of the bird cause a downward motion of air, with an equal force.
(Another example; a propeller drags an airplane forward with force F. We know that an equal and opposite force must act on the air, and it does--the well-known "prop wash" blowing air backwards. And if a helicopter hovers above water, you can see the force of that wind on the surface of the water, too.)
So the bird must constantly push air downwards, with a force of 20 Kg. What sort of cage is it in, anyway? If the cage has a solid bottom, I suspect that force is transmitted to it and from it to the scale. There should be little or no change in the registered weight.
If however the bottom of the cage consists of loose wires, air blown down through it passes between the wires to the air below the cage and ultimately, to the air in the rest of the room and to the floor. The registered weight should then be much less.
Confronted with such a question, always ask yourself--what IS going on?
333. Why does Sun seem to move?I am Cameron. I am 8 years old. I have read several books about space and know some of the planets. My teacher has asked me to find out why the sun seems like it moves in the sky? I have tried to find out the answer on several different websites but have found them very confusing for me. Please can you answer this question in a simple way so i will be able to understand.
I do not know what books your teacher recommended, but YOU have my web sites, and all answers are there. Just read them! (And tell your teacher. There also exist lesson plans)
Briefly, there exist two motions of the Sun across the sky ("apparent" motions, because we are the ones who really move). The daily motion--rising in the east, setting in the west--happens because the Earth rotates around its axis. The Moon, and the stars seen at night, all have similar motions. If the Sun were above the Earth's equator, it would trace the same path day after day.
In addition, over the year the Sun's position among the stars traces a big circuit, around a circle which makes an angle 23 1/2 degrees with the equator. That is why we have seasons. In summer the Sun is in the north part of the sky, days are longer and we have summer (in the USA and Europe). In winter it is south of the equator--long nights, short days, cold weather.
The line among the stars which it follows is known as the ecliptic. We cannot see where the Sun is among the stars, but we can guess its position by comparing it to the stars seen at night, which change over the year (on any day, the Sun is among those stars we cannot see). That motion is caused by the orbit of the Earth around the Sun.
As for the rest, read!
334. Why don't waves disturb each other?I am YS from Malaysia, a physics degree student. I came across your website at phy6.org while I was searching for an answer to my question.
I've been learning about waves and superposition and I am very familiar with the effects when two waves meet. However, just recently, I realized that I don't know what happens after the two waves meet (waves traveling in opposite direction, heading towards each other).
I am surprised to learn that after two waves (traveling towards one another) meet, they will continue their paths as if nothing happened after the superposition incident. Do you know why does this happen?
I manage to find many websites that explain the events before and during the superposition. But I haven't manage to find any website with a detailed explanation (with theoretical explanation, mathematical calculation, etc) to the events after the superposition.
I do hope you can help me out or at least direct me to a website. And I really appreciate all the effort and knowledge you have shared in your website.
Thank you and have a wonderful day. Warmest Regards from Malaysia,
ReplySuperposition is a mathematical property derived from linearity. If you have a linear equation
2x + 3y + 4z = 0
and you have some (x,y,z) that solves it (for instance, [1, 2, –2]), , and you also have a completely different solution (X,Y,Z) (for instance, [–2, 4, –2]) which also solves it, the sum of the solutions, and indeed any linear combination (3 times the first minus 5 times the second, say) is also a solution.
If your equation has powers or multiplication of unknown numbers, for instance
x2 + 2y3 – 6 zx = 0
that property does not exist, because the equation is nonlinear.
Waves satisfy a linear "wave equation." That equation involves calculus rather than being algebraic like the ones above, but many similarities still hold. In particular, if you add two waves in any fixed proportion, the result also satisfies the equation (you can even subtract), and creates the sum of the effects. You sit in a room and the radio is playing while you talk to a friend, and the sounds propagate independently. You shout to a friend across a ballfield while the friend shouts at you--you hear your own voice first and then the friend's, and with the friend it is in opposite order. The two sounds cross each other unchanged.
Not all phenomena are linear. Waves on the surface of water are. So are electromagnetic waves--which is why many radio and TV stations can share the same space. Shocks are not linear. If you want to examine the mathematics, start with the wave dimension in one dimension, which has relatively simple solutions.
335. Does the Moon's motion Change?Looked at your website and thought you would be able to help. Does the moon change with the seasons? This would be in regard to perception, brightness, position, relative to the Earth??? Thanks, if you have any thoughts.
ReplyThe Moon's motion is not far from the ecliptic, which rises high in the sky in summer and is lowest in winter: its motion therefore changes with the seasons somewhat like the Sun's.
The ellipticity of the Moon's orbit cause some changes in its apparent size, but not by much--I do not think people notice.
And the appearance of the Moon changes with position. We see a "Man in the Moon", but in Argentina the appearance is different--not because the position of the Moon differs, but because the "up" direction does.
For some interesting observations, see http://www.phy6.org/stargaze/StarFAQ12.htm#q197
336. Big Dipper and WeatherHello from Newfoundland, Canada
I was just wondering if there was any truth about the handle of the Big Dipper ......they say that when the handle is up it means nice weather and when the handle is down it means really bad weather. Please email me and let me know what you find out. Thank you very much.
ReplyI have not heard that story before and cannot think of a reason why it would hold true. The Big Dipper of course goes around the pole of the sky every 24 hours--I think right now its tail points east-west, and then towards morning it points up, while a few hours ago it slanted down.
You might think of that tail as the pointer of a 24 hour clock. If you know whether one position of that clock should give different weather than another (in particular, noting that any kind of weather usually persists longer than 12 hours), you might have an argument...
337. What IS the Ecliptic?I was looking at your site. Would you possibly mind helping understand something? I don't understand the definition of the ecliptic. Is it the daily motion across the sky or is it the path of gradual shift in position over the course of the year?
ReplyIt is neither. It is the flat plane of the orbit of the Earth around the Sun.
Draw in your mind a line from Earth to the Sun. As the Earth orbits the Sun (in one year), Earth and Sun are always at opposite ends of that line. So seen from Earth, the Sun moves in the plane of the ecliptic, too, and its path among the stars is also in the ecliptic.
The line traced by that path among the stars is ALSO called the ecliptic, and is so labeled on star charts. The 12 constellations along this path are the famous "zodiac" and each corresponds to a month.
But there is more! The ENTIRE SOLAR SYSTEM is flat, and the planes of the orbits of all major planets (and of our Moon, too) are all near the ecliptic, usually just a few degrees off. So to the casual eye, the Sun, Moon and planets ALL seem to move (more or less) in the ecliptic. If you step out on a clear evening, the Sun has just set at some spot on the horizon, the Moon is some distance away, and there are some bright stars right on the line between the two--these are probably planets, because all these objects move in (almost) the same flat plane, and we on Earth view this plane edge-on.
338. Precession, Greenhouse and more...I'm really enjoying your web page, you seem to have a lot of info at hand. Maybe you will find some of my questions of interest, and stop them from waking me up in the middle of the night.
I tried to explain the precession of the earth's axis to some friends of mine. Which of the following is correct?
A) In 13000 years summer in the northern hemisphere will be in December instead of June, as supported by the picture on your web page http://www.phy6.org/stargaze/Sprecess.htm
B) The calendar is adjusted so summer will always be in June, although the background of space in summer will be the same in 13000 years as it is now in winter (as supported by your answer to http://www.phy6.org/stargaze/StarFAQ11.htm#q174)
A couple more questions:
1) The southern hemisphere is slightly warmer (can't remember how much) than the northern because when it's summer in the southern hemisphere the earth is closer to the sun because of the elliptical orbit. In 13000 years, the north should be slightly warmer than the south - but again, the question is how much?
2) How much energy does the sun deposit on the earth in a year, and how much energy do humans dump on the earth in a year (through all power generation sources and fuel burning activities). What percentage of heat on the planet comes from the sun and what percentage is from humans?
3) I'm also fascinated by the whole global warming / clean energy arguments - my view is that if you really believe CO2 is the root of all evil, you should simply replace all power plants with nuclear plants, and then build more nuclear plants to drive electric cars, heating, etc to replace burned fuels. Somehow I don't believe that will cool off the planet, but it may help if I knew the answer to my question # 2 above.
Here's another one - If I grow sugar cane (which pulls carbon out of the air), harvest it, make ethanol, burn that for energy in cars (and in the sugar cane / ethanol processing plant), do I have a net zero carbon contribution to the environment even though I am burning fuels? I probably end up putting a lot more water vapor into the air though.
How about this - solar cells are about 10% efficient (varying widely depending on type). Does that mean they absorb 90% of the energy that hits them as heat which gets radiated off in all directions? If I paint my roof highly reflective white and keep as much of the heat from the sun as possible away from it, and my neighbor covers his roof with solar cells and converts 10% of the energy to electricity and then runs his air conditioner with that to cool the house (which has 90% of the energy radiating all around it), who ends up with the net lower energy footprint? Are solar cells really environmentally friendly if they create a big black footprint that converts 90% of the energy that hits them to heat near the ground that gets radiated vs a more reflective surface or maybe an agricultural area growing sugar cane for example?
ReplyIt is sure easier to think up new questions than answering them! But I will try
Of you two interpretations of the effect of precession of the equinoxes on the seasons, (B) is the correct one. This is also discussed in http://www.phy6.org/stargaze/StarFAQ14.htm#q226
Now to other questions:
339. Latest Sunrise, Earliest SunsetAfter reading the "Stargazers" sites on Kepler and ellipses, etc., I was wondering about one thing that I haven't been able answer.
I understand why, as you point out, the winter season in the north is shorter than the summer season (equinox to equinox) (Kepler's second), and that the solstices and equinoxes do occur on approximately the same dates every year.
But then I found out that the day of the year with the earliest sunset (in the afternoon/evening) occurs in early December, and the latest sunrise occurs in early January. The corresponding thing happens around the summer solstice. Why doen't these dates coincide with each other, and with the solstice itself??
ReplyThis may be related to an extra correction to solar time known as "equation of time", reaching a maximum around +16 minutes in November and a minimum around –14 minutes in February. A similar effect (but smaller) occurs in summer
The matter is also discussed at "Variation in time of Sunrise" http://www.physics.rutgers.edu/~twatts/sunrise/sunrise.html
ResponseThanks for the information. It finally resolves my questions about this phenomenon. Now I can finally stop recording the morning sunrises and evening sunsets throughout the year.
340. Falling off the Earth's Bottom?My 2nd Grade grandson is full of science questions, and now one for some reason I absolutely cannot answer: If the world is round, why don't people on the "bottom" side of the world feel as if they are upside down?
I assume it has something to do with gravity, but I also wonder if it has something to do with the structure of brains and how they perceive. The problem is that even if I get a really large sphere, and put a powerful gravitational pull in the middle of it and station little metal figures all over it, from the six year old POV, the little figures on the bottom ought to feel like they are upside down, because in fact they are.
I looked through all the earth and gravity questions on your site, but couldn't find this. It may be hopelessly elementary, but I didn't know how to explain it. cheers, and thanks
ReplyIf your grandson is in grade 2 at age 6, then he is doing very well indeed!
There really exist two questions here:
But even before that, people living by the seashore realized that ships disappeared over the horizon as if they went around a hill. First the hull could no longer be seen, then the high sails. And even after that, you could climb a hill and see it again. It only makes sense if you went "behind a hill."
Also, the stars in the sky always form the same constellations. But they are not all visible from one place. Far north, little more than half the constellations are seen. Then as you get closer to the equator, more and more appear. They still rise and set like the sun, but they are always close to the southern edge of the sky. Demonstrate to your son with a ball why this only makes sense if Earth is a ball, too.
But then, why don't we fall off? Everything suggests that the earth pulls us down towards its middle. About 350 years ago an English scientist, Isaac Newton, noted (it is said) how apples fell from the tree and wondered if the same force that pulled the apple down also held the moon close to Earth, in an orbit around it. By a calculation he showed made sense. And why doesn't the Earth run away from the sun? Same force, towards the middle of the sun. So he named that force "Universal gravitation"--universal meaning it is everywhere.
The force exists in the laboratory, too, but there, even with big balls of lead it is so weak that it can just barely be measured. Henry Cavendish first did so, some 200 years ago.
You may also ask your grandson where exactly "down" is. If the Earth is ball-shaped, there is really just one preferred direction--towards its middle!
Let your grandson keep asking good questions, and he will go far!
341. Rolling down a SlopeMy daughter is a 10th grader working on her science project. I am trying to help explain why two spheres of identical size but different weights will accelerate down an inclined plane at different rates. I long ago lost my physics books and I am having a hard time putting to words (much less equations) what I think I remember about moment of inertia and angular momentum. We did a project over the weekend cutting a tennis ball and pasting lead weights to the inside to double the weight and timing their progress down an inclined plane. It was even fun to watch the numbers differ slightly when we made one ball with all of the weights at the very center (filled the ball with foam insulation first, then cored out a center hole).
Your help would be greatly appreciated. Might even help me to be the good guy
ReplyWhen a weight slides or rolls down a slope, all the energy comes from gravity.
Ignoring now friction, which is small in the case of a rolling object, all that energy ends up as kinetic energy. A smoothly sliding object descends with a single accelerating velocity v and its kinetic energy gain is (1/2)mv, easily calculated from the loss of height.
In a rolling object the situation is more complicated: part of the energy goes into the bulk motion of the mean velocity down the slope, but part also goes into energy of rotation. (It follows that where friction can be neglected, a rolling object loses height more slowly than a sliding one!) The problem is that the kinetic energy of rotation is hard to evaluate without using integral calculus.
Consider a rotating CYLINDER. The part near the axis has very small rotation velocity and therefore negligible kinetic energy of rotation. As we increase the radius r, the velocity increases in proportion to r, until we reach the outer radius R, which moves with some velocity v and that--if the cylinder is rolling down the slope without slipping--also equals the velocity of descent (which is smaller than in the case of sliding!).
You can imagine the cylinder as being divided into narrow cylindrical layers of thickness "dr", each filling the space between distance r and r+dr, and rotating with a velocity appropriate to that distance, namely (r/R)v. That gives the layer a rotational energy proportional to [(r/R)v]2, and the energy is also proportional to the mass of the layer, which again is proportional to r. If we make the layers very narrow (and very numerous), the energy goes to some limit, proportional to the 4th power of R, and that is what calculus gives you.
With a rolling sphere, it is harder, because the layers have different width--widest on the axis of rotation. But this can be handled, too.
The final velocity (and time of descent) depend on the amount of energy going into rotation, and that can vary, depending how the mass is distributed. If most of it is near the axis of rotation, it rotates relatively slowly and absorbs less energy. If most of it is on the periphery (as in many flywheels) it takes a lot of the energy. That explains your experiment.
342. Pelton Wheel Efficiency(question asked verbally by a rancher from Costa Rica)
I have a Pelton wheel turbine, receiving high-pressure water from a reservoir up on a hill. It is connected to an electric generator, which supplies power to my ranch.
When I open the casing, I see that water still rushes past the wheel with great speed, which means that the turbine is not getting all the water's energy. How can I make sure that it extracts energy most efficiently?
ReplyAs described in the section on the Pelton Wheel Turbine, this turbine is most efficient when the speed u of its rotating "buckets" is half the speed v of the water jet. The velocity v depends only on the height of the reservoir and therefore (assuming the pipes are big enough) should be constant. However the velocity u depends on the electric load on the generator, which is drawn from the energy supplied by the turbine. If you overload the generator (too many lights, motors etc), u drops below optimum. If the load is light, the turbine spins easily and u is faster than the optimum.
Essentially, the efficiency of the turbine depends on the speed u of the turbine buckets. If the load is too large, u drops, and in the limit, u=0, the wheel stops and the jet is just turned around to shoot backwards, delivering zero energy. In the opposite case, if the load is essentially zero, negligible energy is produced and the jet tends to move the buckets at its own speed v. In the limit u=v, the jet hardly hits the buckets, and the stream continues forward at the same speed. In between, at u=v/2, the maximum energy is extracted and the water dribbles down, its kinetic energy all removed.
The simplest remedy seems to be an automatic valve at the intake of the pipe high on the mountain, controlled electrically by the response of the turbine. If the water still shoots forward from the wheel, let less water in, if it is reflected backwards, let in more, and if it dribbles, the volume is right for the load. The control loop should be relatively insensitive and have a delay of a minute or two, to allow the water enough time to change its flow in the pipe and to prevent the control from reacting to any small loads switched on or off. You should be able to figure out the rest.
343. Energy loss rate of our SunA quick question for your website: Is the sun losing mass or gaining mass over time?
ReplyNote: This calculation was also incorporated in the lesson plan on the Sun's energy source
The Sun gains a little mass from comets which happens to hit it, but that is a tiny amount compared to two large sources of energy loss: mass lost by the constant stream of solar wind, and mass lost by the conversion of hydrogen to helium, as part of the nuclear fusion process producing the Sun's heat. Surprisingly, the two rates are not that far apart.
If the density of the solar wind near Earth is about 10 protons per cubic cm (a bit high for an estimate, but we ignore alpha particles), moving at 400 km/sec, then a square cm at the Earth's orbit intercepts about 4 108 protons per sec and a square meter intercepts 4 1012. Assuming each proton has an energy equivalent of 109 ev (actually. 0.938 109) that is 4 1021 ev (the kinetic energy of those protons is negligible by comparison). Using E=mc2 and noting that one ev is 1.6 10–19 joule, the energy-equivalent of the solar wind crossing 1 square meter per second at the Earth's orbit is 640 joule.
The solar constant, the energy of sunlight crossing 1 square meter per second, is about 1300 watt or 1300 joule per second. That energy originates in nuclear reactions in the core of the sun, converting hydrogen to helium, with the mass of the products being slightly less than those of the input ingredients. Since mass-energy is conserved, the energy-equivalent of the mass loss equals the solar constant multiplied by the area of a sphere of radius 1 AU. Per square meter of that sphere, the mass loss is equivalent to 1300 joule/sec.
Thus the sun loses twice as much mass to nuclear processes than it does to the solar wind. It seems remarkable, though, how close those numbers are
344. The Sun's DistanceI don't have any college background but am an Aviation Electronics Tech in the Navy.
However, I've alway wondered about how we know the distance of the Sun. We were told (while I was in high school science) that the earth is roughly 93 million miles from the sun. I asked my science teacher about this, and he jut gave me a dirty look.... anyways, let me ask now, how did we come to that conclusion? Do we know that for sure, or is it still a hypotheses?
ReplyYou asked a somewhat difficult question, but of the kind which lies at the heart of any scientific result--asking not "what is the value" (namely, 93 million miles, as many students are told to memorize) but "how do we know?" Good for you!
"From Stargazers to Starships" traces the answer, but it isn't a simple one. First, of course, people had to realize Earth was one of the planets orbiting the Sun (section 9c) and from observations, deduce the laws which governed the motion of those planets (section 10). The orbits are all close to circles, and assume for a moment they are exactly circular and obey Kepler's 3rd law, which connects distance with the period of the orbit (one year for Earth!).
If at any time we know the actual distance to any planet, and the relative position of Earth and that planet in their orbits at that time (i.e. the angles between the lines from each to the Sun), we can deduce the distance between those circles. From that and from Kepler's law, the radii of the circles themselves. Jean Richer in 1672 apparently was the first to try doing so (section 10a, where the problem you ask about is discussed further). I think (not sure) he derived the slight shift of the position of Mars among the stars during a night, a shift produced because the rotation of Earth carries the observer from one side of the Earth to the other.
More accurate values need take into account the ellipticity of the orbit, making the calculation more complicated, but the principle remains the same.
You may also look up discussion of the first attempt to measure the distance, by Aristarchus around 200 BC--first estimating the distance to the Moon (sect. 8c) and then to the Sun (sect. 9a).
345. Why does sunlight have a continuous spectrum?This follows up question a question asked in #53 about the makeup of sunlight. Why is the solar emission spectra nearly continuous, when the sun itself is mostly made up of hydrogen and helium which themselves have very discrete spectra? Is it due to the cycle of emission absorption as the photon leaves the sun, as you wrote, or is there more to it than that?
ReplyThis is a bit outside my field of magnetospheric physics, but I believe the reply to #53 pretty much sums up the answer. Some other sites on this problem are
The overall conclusion is that a dense hot gas in which photons are continually absorbed and re-emitted, by atoms and ions in fast motion, or scattered by electrons, will give out a spectrum like a black body.
(If you are math oriented, it might remind you of the central limit theorem: the sum of many random variables, no matter what their characteristic distribution, tends to a bell-shaped Gaussian curve).
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