Here are more problems for us to have fun doing...
Problem 2:
It has been stated that Archimedes once saved the Greeks from attack by a Roman fleet by equipping a large number of well trained soldiers with large hand-held plane mirrors and getting them to reflect the sun's rays onto some part of a Roman ship at a distance of 100m, thereby setting it on fire. Comment on the feasibility of such a plan.
You may assume that the mirrors are available, that the solar flux is 1 kW per meter squared, and that the angular diameter of the sun is 0.5 degrees. The ships may be assumed to be wooden. Stefan's constant is 5.7 x 10^(- 8) W m^(- 2)K^(- 4)
Problem 3:
A parabolic mirror is made to focus the sun's disc into a circle of radius 1 cm. Estimate the smallest diameter of such a mirror if it can be used to melt iron. Make any assumptions that are plausible and necessary. Stefan's constant has been given with the above problem, the melting point of iron is 1535 degree celcius, the solar constant at the bottom of the atmosphere is 1 kW per meter squared.
Thursday, September 30, 2010
Sunday, September 26, 2010
Weekend discussions 3
I have a backlog of a few weekends which I hope to catch up with very soon. Anyway, this post is concerned with our discussions yesterday and the day before. So here it is:
September 25, 2010
Session 1: Shruthi
We continued our foray to understand the necessity of a quantum theory, and Shruthi pointed out a few interesting things like whether we could determine the terminal velocity of a steel ball dropped into liquid helium. Th results were more interesting. I think Shruthi will do a better job of discussing that. We then went back to a concept we were all fuzzy about. Matter waves. Superposition. Wave packets. What we all thought was a trivial thing and went right ahead after thinking we understood it, is now coming back to haunt us. I'm struggling to make the problem itself clear. Maybe someone should open it up for discussion here.
Session 2: Raunaq
He said he'd write this himself.
September 26, 2010
Session 1: Karthik
He started off by getting us to discuss what exactly a linear, homogeneous differential equation means. We then worked through the problem of the damped harmonic oscillator, which we went on to study in a matrix representation, finally giving (atleast me) a good idea of exponentiating a matrix. This was followed by a phase space analysis of the problem, at which point Karthik urged us to read up on the Sine-Gordon equation and elliptic functions. He actually wanted to continue next week, but I made him give an introduction to the Poisson bracket as it was previously agreed that I would continue from there. So he did.
Session 2: Harshini
Well, I didn't get to do most of what I'd planned on doing. I started off by basically showing how the Commutator bracket is connected to the Poisson bracket and went on to discuss how these become operators in quantum mechanics. Actually, the problem was I couldn't show how they become operators. Staying true to our policy of not taking anything for granted, we spent a while talking about whether we've missed something in making the leap from something being a physical quantity in classical mechanics, to becoming an 'operator' in quantum mechanics. It doesn't sound quite so serious when put this way, but we struggled over the details for a bit.
Then we followed in the steps of Schrodinger to "derive" the Schrodinger equation, all the time questioning the rationale behind it, and whether it could be done in a better way. Nothing might come out of it, but its very important that these questions are asked. That's what makes what we're doing worth doing.
And before we leave, an ego-check is always done, so that we know that we're not doing anything path-breaking or earth-shattering in these discussions. But what we are doing, is something different.
September 25, 2010
Session 1: Shruthi
We continued our foray to understand the necessity of a quantum theory, and Shruthi pointed out a few interesting things like whether we could determine the terminal velocity of a steel ball dropped into liquid helium. Th results were more interesting. I think Shruthi will do a better job of discussing that. We then went back to a concept we were all fuzzy about. Matter waves. Superposition. Wave packets. What we all thought was a trivial thing and went right ahead after thinking we understood it, is now coming back to haunt us. I'm struggling to make the problem itself clear. Maybe someone should open it up for discussion here.
Session 2: Raunaq
He said he'd write this himself.
September 26, 2010
Session 1: Karthik
He started off by getting us to discuss what exactly a linear, homogeneous differential equation means. We then worked through the problem of the damped harmonic oscillator, which we went on to study in a matrix representation, finally giving (atleast me) a good idea of exponentiating a matrix. This was followed by a phase space analysis of the problem, at which point Karthik urged us to read up on the Sine-Gordon equation and elliptic functions. He actually wanted to continue next week, but I made him give an introduction to the Poisson bracket as it was previously agreed that I would continue from there. So he did.
Session 2: Harshini
Well, I didn't get to do most of what I'd planned on doing. I started off by basically showing how the Commutator bracket is connected to the Poisson bracket and went on to discuss how these become operators in quantum mechanics. Actually, the problem was I couldn't show how they become operators. Staying true to our policy of not taking anything for granted, we spent a while talking about whether we've missed something in making the leap from something being a physical quantity in classical mechanics, to becoming an 'operator' in quantum mechanics. It doesn't sound quite so serious when put this way, but we struggled over the details for a bit.
Then we followed in the steps of Schrodinger to "derive" the Schrodinger equation, all the time questioning the rationale behind it, and whether it could be done in a better way. Nothing might come out of it, but its very important that these questions are asked. That's what makes what we're doing worth doing.
And before we leave, an ego-check is always done, so that we know that we're not doing anything path-breaking or earth-shattering in these discussions. But what we are doing, is something different.
Weekend Discussions - 2
Our discussion sessions have been going well. I hope we can dedicate more and more time and effort to what's been going on in these sessions. This has really provided us with a good platform where we have the freedom to think and question without having to take anything for granted. So far its been very unconventional. We are in fact unlearning a lot, and these sessions are the only place where this kind of unlearning, I feel, has been welcome. So far, so good.
I will now be putting down here what I have been doing in a little more detail.
Session 1 : Space, time and Structure
Our high school physics begins with Newton's laws of Motion. By the end of MSc. we would have investigated motion a little further and spoken about it in terms of Lagrangian and Hamiltionian. When Einstein came up with his theory of relativity, he showed that space and time actually had a structure. A structure that evolves dynamically. This should perhaps be enough motivation to question about the very structure of the space and time on which motion actually takes place. Doing this won't be an easy task. We can't observe physical effects of time to model its structure, and yet everything that happens is parametrised using time. One big leaps in our understanding of time came when Einstein said that the faster you move in space, the slower you move in time. And this stitches space and time forever. You can't talk about space or time, you can only talk about space-time. Also, he showed that mass has something to do with space-time. The closer you are to a heavy mass, the slower the time flows for you.
We express time as the amount distance travelled with a certain velocity. And velocity as the amount distance travelled in certain time. If you try to talk about the structure of space and time in terms of distance and velocity, this is as far as you'll get. The only thing that can be further broken down here is distance. A space where we can talk about distance between two points is called a metric space. We seem to live on such a space. To be even able to talk about why our space the way it is, we need to talk about a more general space which does not have the notion of distance on it. This general space is known as a topological space. We go on later to define a metric on it.
I hope in the first session I was successful in motivating the reason behind going into some amount of topology and differential geometry. Though these are some purely mathematical structures, I feel that when used by physicists, they should be powerful tools to gain new insights into any physical concept and to look at physics in a unified sense.
Towards the end of the first session we tried entering into a little bit of set theory. And how sets are looked at in a topology. I ended with a few definitions like open and closed sets.
The assignment (which was successfully completed by all) was to look up a few theorems and lemmas, more importantly 'The Axiom of Choice' , Zorn's lemma. Also, to look up how a vector space and an algebra is technically defined. There was another long term assignment given which was to think if it was possible to arrive at the fact that there had to be a observer independent constant velocity given that space and time both are relative in our universe.
References: (1) Naive Set theory by P. Halmos (2) Differential Geometry and Lie Groups For Physicists by Marian Fecko (3) Wikipedia:)
I have spoken for three other sessions, the summary's for which will soon be put up. Our new aim is to be able to make lecture notes as well and turn them in to soft copies.
Karthik has been doing a wonderful job with classical mechanics. He has motivated us to think of a lot of things that haven't been thought of before. Shruthi has been showing failures of classical mechanics and has been trying to bring in the notion of wave-particle duality and making us think as to why a new theory was needed . And Harshini has been dealing with the mathematics of QM and the how's and why's of it. She did a nice derivation today which she will probably summarise later.
I urge everyone to post the summaries of their talks. It really has been a wonderful time discussing and opening our eyes to the fact that we really don't know anything.
ciao
I will now be putting down here what I have been doing in a little more detail.
Session 1 : Space, time and Structure
Our high school physics begins with Newton's laws of Motion. By the end of MSc. we would have investigated motion a little further and spoken about it in terms of Lagrangian and Hamiltionian. When Einstein came up with his theory of relativity, he showed that space and time actually had a structure. A structure that evolves dynamically. This should perhaps be enough motivation to question about the very structure of the space and time on which motion actually takes place. Doing this won't be an easy task. We can't observe physical effects of time to model its structure, and yet everything that happens is parametrised using time. One big leaps in our understanding of time came when Einstein said that the faster you move in space, the slower you move in time. And this stitches space and time forever. You can't talk about space or time, you can only talk about space-time. Also, he showed that mass has something to do with space-time. The closer you are to a heavy mass, the slower the time flows for you.
We express time as the amount distance travelled with a certain velocity. And velocity as the amount distance travelled in certain time. If you try to talk about the structure of space and time in terms of distance and velocity, this is as far as you'll get. The only thing that can be further broken down here is distance. A space where we can talk about distance between two points is called a metric space. We seem to live on such a space. To be even able to talk about why our space the way it is, we need to talk about a more general space which does not have the notion of distance on it. This general space is known as a topological space. We go on later to define a metric on it.
I hope in the first session I was successful in motivating the reason behind going into some amount of topology and differential geometry. Though these are some purely mathematical structures, I feel that when used by physicists, they should be powerful tools to gain new insights into any physical concept and to look at physics in a unified sense.
Towards the end of the first session we tried entering into a little bit of set theory. And how sets are looked at in a topology. I ended with a few definitions like open and closed sets.
The assignment (which was successfully completed by all) was to look up a few theorems and lemmas, more importantly 'The Axiom of Choice' , Zorn's lemma. Also, to look up how a vector space and an algebra is technically defined. There was another long term assignment given which was to think if it was possible to arrive at the fact that there had to be a observer independent constant velocity given that space and time both are relative in our universe.
References: (1) Naive Set theory by P. Halmos (2) Differential Geometry and Lie Groups For Physicists by Marian Fecko (3) Wikipedia:)
I have spoken for three other sessions, the summary's for which will soon be put up. Our new aim is to be able to make lecture notes as well and turn them in to soft copies.
Karthik has been doing a wonderful job with classical mechanics. He has motivated us to think of a lot of things that haven't been thought of before. Shruthi has been showing failures of classical mechanics and has been trying to bring in the notion of wave-particle duality and making us think as to why a new theory was needed . And Harshini has been dealing with the mathematics of QM and the how's and why's of it. She did a nice derivation today which she will probably summarise later.
I urge everyone to post the summaries of their talks. It really has been a wonderful time discussing and opening our eyes to the fact that we really don't know anything.
ciao
Saturday, September 18, 2010
Summary
I haven't checked my mail in over a week, so couldn't respond sooner. Sorry. Anyway, lets get down to business. After much ado, this structure has been finalised for our discussions.
Karthik will be dealing with Classical Mechanics, and following that, Electrodynamics.
Raunaq's is a course in Theoretical Physics. More on that by him.
Shruthi and I will be handling Quantum Mechanics(non-relativistic). between us, as it was decided that all of us will give one lecture per week.
The following is a summary of what has been happening for the past few weeks in our sessions:
September 2, 2010
Session 1: Raunaq
He started by getting us to question the basic notions of space, time and velocity, and it was left to us to prove that if the definitions of the above depend on each other, i.e. they are interrelated, then there must exist a constant velocity, and this velocity turns out to be the maximum velocity anything can have, i.e., the speed of light. We then tested new waters by being introduced to elementary set theory. A lot of mind-bending for us non-mathematicians!
Session 2: Karthik
Another session of questioning and unlearning. We spent the hour talking about our 'definitions' of force, momentum, acceleration and our understanding(or in my case, not!) of Newton's laws. This discussion took up the whole sessions as we analysed these so-called 'basics' and discovered new ways of looking at it.
September 5, 2010
Session 1: Harshini
It was initailly decided that Shruthi and I would handle electrodynamics, before we settled on QM. But we had one session, where we didn't get past Coulomb's law, due to our tendency to analyse every little thing without taking anything for granted. Its not a bad thing at all, for it helps in gaining a better understanding of the subject, and reveals flaws in our understanding. But due to time-constraints, we've decided to cut down on our long-winded discussions.
And oh, this discussion went on for so long, Shruthi didn't even get a chance to talk that day. Sorry S.
September 11, 2010
Session 1: Karthik
Now we dug our teeth into the concept of inertia and this lead to another round of discussion. We managed to proceed to the concept of phase diagrams and their usefulness and importance in Classical Mechanics. Then he introduced the concept of the Lagrangean which started off another round of discussions. Time-management was really becoming a problem now! Again, this was the only session we could have on this day.
September 12, 2010
Session 1: Shruthi
Hers was an introductory lecture to show the need for a new theory at a micro-level. She discussed the problem of black body radiation, the anomalous behaviour of liquid helium under certain conditions, the phenomenon of superconductivity etc. She sent us links to videos of experiments to demonstrate some of these phenomena. This session brought to light many interesting experimental phenomena.
Session 2: Raunaq
We dove right into set-theory, having dutifully completed the assignments we had been given. In this session, we dealt with what actually makes up vector spaces(one of our assignments, actually)and we were then led to an introduction to Lie algebra, followed by some problem-solving. And oh, abstract mathematics caused a lot of brouhaha again.
Karthik will be dealing with Classical Mechanics, and following that, Electrodynamics.
Raunaq's is a course in Theoretical Physics. More on that by him.
Shruthi and I will be handling Quantum Mechanics(non-relativistic). between us, as it was decided that all of us will give one lecture per week.
The following is a summary of what has been happening for the past few weeks in our sessions:
September 2, 2010
Session 1: Raunaq
He started by getting us to question the basic notions of space, time and velocity, and it was left to us to prove that if the definitions of the above depend on each other, i.e. they are interrelated, then there must exist a constant velocity, and this velocity turns out to be the maximum velocity anything can have, i.e., the speed of light. We then tested new waters by being introduced to elementary set theory. A lot of mind-bending for us non-mathematicians!
Session 2: Karthik
Another session of questioning and unlearning. We spent the hour talking about our 'definitions' of force, momentum, acceleration and our understanding(or in my case, not!) of Newton's laws. This discussion took up the whole sessions as we analysed these so-called 'basics' and discovered new ways of looking at it.
September 5, 2010
Session 1: Harshini
It was initailly decided that Shruthi and I would handle electrodynamics, before we settled on QM. But we had one session, where we didn't get past Coulomb's law, due to our tendency to analyse every little thing without taking anything for granted. Its not a bad thing at all, for it helps in gaining a better understanding of the subject, and reveals flaws in our understanding. But due to time-constraints, we've decided to cut down on our long-winded discussions.
And oh, this discussion went on for so long, Shruthi didn't even get a chance to talk that day. Sorry S.
September 11, 2010
Session 1: Karthik
Now we dug our teeth into the concept of inertia and this lead to another round of discussion. We managed to proceed to the concept of phase diagrams and their usefulness and importance in Classical Mechanics. Then he introduced the concept of the Lagrangean which started off another round of discussions. Time-management was really becoming a problem now! Again, this was the only session we could have on this day.
September 12, 2010
Session 1: Shruthi
Hers was an introductory lecture to show the need for a new theory at a micro-level. She discussed the problem of black body radiation, the anomalous behaviour of liquid helium under certain conditions, the phenomenon of superconductivity etc. She sent us links to videos of experiments to demonstrate some of these phenomena. This session brought to light many interesting experimental phenomena.
Session 2: Raunaq
We dove right into set-theory, having dutifully completed the assignments we had been given. In this session, we dealt with what actually makes up vector spaces(one of our assignments, actually)and we were then led to an introduction to Lie algebra, followed by some problem-solving. And oh, abstract mathematics caused a lot of brouhaha again.
Monday, September 13, 2010
Weekend Discussions
In one of my previous posts ( A good weekend), I mentioned bumping into Karthik and how we discussed a lot of random things. One of the things we discussed has led to what I feel is a very wonderful thing.
We decided that it was essential for us to channelize our efforts and make the best of what time we have. Spend a little time learning from each other. To give each other what the education system couldn't give us. This was just an idea, but it is yet to materialize completely. It is easy said than done. But here is the story of what has been done so far.
We decided to tell Shruhi, Harshini, and Raghu about what we had thought about and wanted to see if anything could be done. Shruthi and Harshini were available after GR's class on sunday and as expected they were really enthusiastic about it.
We had to figure out when and where we could meet. Shruthi immediately said that she could make available a place where nobody will disturb us and which is easily accessible to everyone of us. Thank you Shruthi. This is one of the main constraints we would otherwise have had to deal with. Now that the spatial co-ordinates had been decided, we had to zero in on the time co-ordinates. It was again rather quickly decided that we would be meeting on thursdays and Saturdays, between 6 and 8 in the evening. It went as planned for a week, and due to some other practicalities we have decided to meet on saturdays and sundays instead.
Raghu has joined us and we are now a group of five. It is a nice group of people with different mentalities and unique areas of creativity. Some of us are inclined towards theoretical physics, while the others have a more experimentally oriented mind. Each of us will be giving one course. Harshini will probably be summarizing what all has been done so far, and who is doing what etc. And when she does, I urge everyone in the group to comment and add what they learnt from the particular lectures. It will give us all a perspective from the other's point of view. Harshini has also been recording the lectures for future reference.
All the speakers gave assignments and have been taken up seriously by all present. We have deliberately restricted the discussion to the five of us in order to avoid dilution.
Ego clashes are bound to happen as well. We however hope to minimize this and focus on learning as much as we can and make the most of the time we spend together.
We have had 4 sessions so far, which sums up to a total of 8 hours of lecture. Hope to have many more of such fruitful hours.
PS : Thanks to Michael, a very good friend of mine, we now have a bigger white board. Thank you Michael.
We decided that it was essential for us to channelize our efforts and make the best of what time we have. Spend a little time learning from each other. To give each other what the education system couldn't give us. This was just an idea, but it is yet to materialize completely. It is easy said than done. But here is the story of what has been done so far.
We decided to tell Shruhi, Harshini, and Raghu about what we had thought about and wanted to see if anything could be done. Shruthi and Harshini were available after GR's class on sunday and as expected they were really enthusiastic about it.
We had to figure out when and where we could meet. Shruthi immediately said that she could make available a place where nobody will disturb us and which is easily accessible to everyone of us. Thank you Shruthi. This is one of the main constraints we would otherwise have had to deal with. Now that the spatial co-ordinates had been decided, we had to zero in on the time co-ordinates. It was again rather quickly decided that we would be meeting on thursdays and Saturdays, between 6 and 8 in the evening. It went as planned for a week, and due to some other practicalities we have decided to meet on saturdays and sundays instead.
Raghu has joined us and we are now a group of five. It is a nice group of people with different mentalities and unique areas of creativity. Some of us are inclined towards theoretical physics, while the others have a more experimentally oriented mind. Each of us will be giving one course. Harshini will probably be summarizing what all has been done so far, and who is doing what etc. And when she does, I urge everyone in the group to comment and add what they learnt from the particular lectures. It will give us all a perspective from the other's point of view. Harshini has also been recording the lectures for future reference.
All the speakers gave assignments and have been taken up seriously by all present. We have deliberately restricted the discussion to the five of us in order to avoid dilution.
Ego clashes are bound to happen as well. We however hope to minimize this and focus on learning as much as we can and make the most of the time we spend together.
We have had 4 sessions so far, which sums up to a total of 8 hours of lecture. Hope to have many more of such fruitful hours.
PS : Thanks to Michael, a very good friend of mine, we now have a bigger white board. Thank you Michael.
Friday, September 3, 2010
Problem 1
Harshini's post has brought back a few things from when I was a kid. One of the first things that brought to my mind the thought of becoming a scientist was the cartoon Dexter's laboratory. My interests did change but it did invariably come back to physics. I actually even wanted to be a wildlife photographer in 9th standard, but then I realized photography(and for that matter anything else) wasn't really my cup of coffee.
You find dexter( and some times tom and jerry) mixing up these random chemicals and colourful liquids and surely enough there would eventually be a big bang.I told my mom to get me one of those and she told that they are just cartoons. And then at school in 8th std. , I first heard of an actual explosive chemical reaction. When you put sodium in water it is supposed to react violently and can also be explosive, and our chem teacher said she is going to show it to us in lab. She ended up putting a tiny bit of sodium in water and all you could see was a tiny bubble of fire. And then I thought may be this was as 'explosive' as it gets in real life. I was a bit disappointed.
A few years later I was helping these people build up a lab( for school kids ) and I told them to buy a few things including sodium. I used to get a lot of time alone there to come up with experiments that would excite kids and once my school mate Sneha was around to help and everyone else had gone to have lunch. I slowly slipped in the idea of trying out the experiment with sodium. I was actually scared of doing it alone and also I wanted a partner in crime if something went wrong.
We filled a small glass beaker with water and I just took up a chunk (as big as a match box!) of sodium and put it in the beaker. Before we could see what was happening , small glass pieces were flying everywhere and the water just vaporized with a huge bang. This is a very memorable event, because a) this was the first time I saw an explosive reaction I had read so much about all through my chemistry classes and b) Not a single glass piece touched us. That actually left us shocked for quite a while. There was not a single place in the room where the glass pieces didn't go, and I had almost no time to move away after putting the sodium. It was pretty unbelievable. For once I wished my lab teacher was around shouting at me as usual to put on the safety glasses which I conveniently forget to carry to college. But I guess we just got lucky and lord murphy was on a holiday I suppose.
After that we used plastic buckets filled with water and put larger chunks of sodium and we showed every kid who walked through the door what " Smoke on the water and fire in the sky" actually looked like.
After experiencing a completely institutionalized learning at college and school, it is really refreshing and revitalizing when things are experienced and learnt in any unconventional ways.
All through school and college we are made to solve problems so that we can get more marks, or get through an entrance exam and have an amazing life ahead. But that's not why take up problems to solve, now is it? So lets try to solve some nice problems just to have fun. I will be posting up a problem as regularly as I can, and Harshini said she will be too. Please do try to spend a few minutes thinking about them, I'm sure it will be worth it. Solutions will be put up eventually. Here is the first one, enjoy :-)
When told that the world record for the pole vault was about 18 feet, the fast-rising athlete Rod told the press, 'Give me a pole long enough, and I will raise the record to 30 feet'. Could he manage it? How high might he get if tried hard?
You find dexter( and some times tom and jerry) mixing up these random chemicals and colourful liquids and surely enough there would eventually be a big bang.I told my mom to get me one of those and she told that they are just cartoons. And then at school in 8th std. , I first heard of an actual explosive chemical reaction. When you put sodium in water it is supposed to react violently and can also be explosive, and our chem teacher said she is going to show it to us in lab. She ended up putting a tiny bit of sodium in water and all you could see was a tiny bubble of fire. And then I thought may be this was as 'explosive' as it gets in real life. I was a bit disappointed.
A few years later I was helping these people build up a lab( for school kids ) and I told them to buy a few things including sodium. I used to get a lot of time alone there to come up with experiments that would excite kids and once my school mate Sneha was around to help and everyone else had gone to have lunch. I slowly slipped in the idea of trying out the experiment with sodium. I was actually scared of doing it alone and also I wanted a partner in crime if something went wrong.
We filled a small glass beaker with water and I just took up a chunk (as big as a match box!) of sodium and put it in the beaker. Before we could see what was happening , small glass pieces were flying everywhere and the water just vaporized with a huge bang. This is a very memorable event, because a) this was the first time I saw an explosive reaction I had read so much about all through my chemistry classes and b) Not a single glass piece touched us. That actually left us shocked for quite a while. There was not a single place in the room where the glass pieces didn't go, and I had almost no time to move away after putting the sodium. It was pretty unbelievable. For once I wished my lab teacher was around shouting at me as usual to put on the safety glasses which I conveniently forget to carry to college. But I guess we just got lucky and lord murphy was on a holiday I suppose.
After that we used plastic buckets filled with water and put larger chunks of sodium and we showed every kid who walked through the door what " Smoke on the water and fire in the sky" actually looked like.
After experiencing a completely institutionalized learning at college and school, it is really refreshing and revitalizing when things are experienced and learnt in any unconventional ways.
All through school and college we are made to solve problems so that we can get more marks, or get through an entrance exam and have an amazing life ahead. But that's not why take up problems to solve, now is it? So lets try to solve some nice problems just to have fun. I will be posting up a problem as regularly as I can, and Harshini said she will be too. Please do try to spend a few minutes thinking about them, I'm sure it will be worth it. Solutions will be put up eventually. Here is the first one, enjoy :-)
When told that the world record for the pole vault was about 18 feet, the fast-rising athlete Rod told the press, 'Give me a pole long enough, and I will raise the record to 30 feet'. Could he manage it? How high might he get if tried hard?
Thursday, September 2, 2010
More things to ponder over a cup of coffee
I was sitting around yesterday without knowing what to do. At this point I usually look towards by book shelf for inspiration. I found it yesterday when I opened the pages of Jearl Walker's "The Flying Circus of Physics". A wonderful book full of problems which the author says himself, "are for fun... What I mainly want to show here is that physics is not something that has to be done in a physics building. Physics and physics problems are in the real, everyday world that we live, work, love and die in."
Here I've stated, word for word, a very curious and interesting problem(like all the others in the book). I don't have an answer, and I haven't looked it up. Thought I'd leave it as an open question for now. And, oh, I've noticed this myself too! But never payed too much attention as I'm too sleepy in the mornings while drinking coffee, and too preoccupied in the evenings. Anyway, it goes like this-
Coffee laced with polygons
If you examine a hot cup of coffee under a strong light that is incident nearly parallel to the surface of the coffee, you will find the surface laced with polygonal cells. They disappear, however, as the coffee cools. You can also destroy the cellular appearance by putting a charged rubber comb (charge it by running it through your hair) near the coffee.
Other liquids show surface designs too. James Thomson, a famous 19th century physicist, noticed the rapidly varying surface designs in a pail of hot soapy water and in strong wines. Later, the Frenchman Bernard was able to make regular patterns in oil surfaces when the oil was heated from below. His regular polygons would slowly evolve into a beautiful hexagonal, honeycomb structure. Still other fluids gave a roll-like appearance. Recently, cellular surface designs were attempted on board spacecraft while under zero gravity.
In these examples, why do rolls and polygons (especially honeycombs) form on the fluid surface? Is the same physics actually responsible for all of the examples? Why do the coffee cells disappear when there is a charged body nearby? Finally, do these several types of surface designs depend on gravity?
The above is listed under the topics- convection, surface tension, nonlinear fluid flow, stability, condensation.
Here I've stated, word for word, a very curious and interesting problem(like all the others in the book). I don't have an answer, and I haven't looked it up. Thought I'd leave it as an open question for now. And, oh, I've noticed this myself too! But never payed too much attention as I'm too sleepy in the mornings while drinking coffee, and too preoccupied in the evenings. Anyway, it goes like this-
Coffee laced with polygons
If you examine a hot cup of coffee under a strong light that is incident nearly parallel to the surface of the coffee, you will find the surface laced with polygonal cells. They disappear, however, as the coffee cools. You can also destroy the cellular appearance by putting a charged rubber comb (charge it by running it through your hair) near the coffee.
Other liquids show surface designs too. James Thomson, a famous 19th century physicist, noticed the rapidly varying surface designs in a pail of hot soapy water and in strong wines. Later, the Frenchman Bernard was able to make regular patterns in oil surfaces when the oil was heated from below. His regular polygons would slowly evolve into a beautiful hexagonal, honeycomb structure. Still other fluids gave a roll-like appearance. Recently, cellular surface designs were attempted on board spacecraft while under zero gravity.
In these examples, why do rolls and polygons (especially honeycombs) form on the fluid surface? Is the same physics actually responsible for all of the examples? Why do the coffee cells disappear when there is a charged body nearby? Finally, do these several types of surface designs depend on gravity?
The above is listed under the topics- convection, surface tension, nonlinear fluid flow, stability, condensation.
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