Physics!

I'm finally getting to the calculus in physics, too! Yesterday I watched the lecture on pendulums, springs, and simple harmonic oscillation, (the one where Walter Lewin rides a pendulum across the room to show that its period is independent from mass) and today I watched the lecture about work and energy.

The SHO lecture has a little bit of calculus, mostly pretty simple and used to manipulate terms to get equations. The equations I had all seen before, last year in honors physics. However then we had just been given them, with little to no explanation of where they came from. Now that I've seen the math, I can understand the concept and reasoning behind the equations.

With work and energy calculus was deeply involved, using integrals and some manipulations to derive the equations we had again been given without explanation last year. This was then taken further when the calculus was used to understand work, energy, and gravity in three dimensions, something that had not been touched upon last year. 

This is the physics that I really enjoy. 

Calculus!

Last night was the fourth class of the Multivariable Calculus class I am taking at Harvard Extension, and we're finally doing calculus!

Pretty much everything up until now has been vectors, geometry, and parameterization, all necessary to learn pretty well before we actually got to the calculus, but to me it is less interesting and less fun. Last night though we got to partial derivatives, and velocity and acceleration vectors. 

Beauty.

Welding Class 2

Last night was my second welding class. Last class was all safety and a tour of the facilities, but this class we actually got to weld! And it was so much fun!

First we cut ourselves a bunch of pieces of steel. They were shaped like isosceles right triangles without the hypotenuse. Then we watched the instructor demonstrate the welding, and then we ourselves did it. It's not a short process, and a steady hand and patience are a huge help, but it's still a lot of fun! After most people had done their first weld, the instructor proceeded to show us to weld using a filler wire, which is a copper coated steel wire (The copper is used to protect the steel from oxidation. It burns away as soon as you heat it up in the flame. If the steel wire oxidizes it can weaken the weld) that you use to fill in gaps in the weld if the two pieces of steel are too far from each other, which happens since we're not always welding straight edges or perfectly cut steel.

I think that this class will absolutely be worth all the difficulty of getting into Boston every Tuesday after a cross country meet and not getting home until after 10.

Knifemaking

I took a class this weekend at Prospect Hill Forge in Waltham called "Nothing but Knives."

It consisted of three three-hour sessions. The first was a practice knife where we used mild steel (steel with about .16-.29% carbon) and the instructor taught us all the parts to making the knife. This was mostly review for me since I had previously taken the Simple Knives class there which was essentially the same thing.

The second session we made the real knife, using high carbon steel (about .30-1.70%. What we used was probably around .8-.9%) which is much harder than mild steel. It heats differently and fights back more when being smithed. 

The most interesting part, however, was after we had finished hammering the blade, and we annealed it. The instructor had a basic understanding of the metallurgy behind much of this process, and so he told us about it. Some of it I knew already, but some was new. For annealing, we heated the blade up to the point where the whole thing was hot enough to change from a Base Centered Cubic crystal structure to a Face Centered Cubic structure, called austenite. At this point the steel also ceases to be magnetic. I don't know why, though I sure would like to. After we have heated the blade to this temperature we placed it into an ash bed and left it to cool overnight. The slow cooling allows the steel to form large grains, making it very soft.

In the third session we came in and removed our knives from the ashes. We wanted them soft so that we could grind and file them easily. So we proceeded to grind and file for quite a while. This is mostly what makes the blade, since you can't get it sharp enough to cut anything with a hammer. After lots and lots of grinding, when we have a decently sharp blade, we begin the tempering process. This starts with again heating the blade up to an austenite temperature, and then cooling it rapidly in a vat of oil. Not only does this make it very hard and brittle from the rapid cooling, but gives it a nice oil finish.

After this comes the main tempering. A really hard brittle knife isn't so good, since it can be brittle enough that dropping it on the floor might shatter it. Also it would be really really hard to sharpen. So we took large metal clamps, heated them really hot, and then held them against the back part of the blade. 

At this point our instructor explained to us tempering colors. Steel will, starting at about 300 degrees, start showing colors. It starts with a light straw color, goes to bronze, then brown, then purple, then deep blue, then a bright teal color. It's pretty dramatic. His theory as to why this occurs is that a very very small oxide layer forms, small enough to be transparent, but still diffract the light, creating the colors. He's not sure about this, though, so it would be a cool thing to check. This is useful because it can tell us what temperature the blade is at. We hold the hot clamp on until the blade becomes bronze. We then quench it very quickly. The purpose of this is to leave the blade hard enough to hold and edge but soft enough to sharpen well and not break off. After the tempering comes some final sharpening, and then you have a finished knife!

The class was great, and lots of fun, especially since I learned not just how to make a knife, but much of the materials science behind it!

Below is a picture of the knife I made:

Vectors, vectors, vectors.

Had my third calculus class today. Still learning about vectors. Even though they don't excite me as much as calc does, they're really cool, useful, and powerful. I'm amazed at how much simpler they make expressing fuctions in two or more dimensions, or how they can make geometric proofs that took a page in ninth grade simple. 

What I wonder most, though, is why I've had so little exposure to them. In precalc we did a unit on them, but it was really no different than what you might do with lines in analytical geometry. there were no dot products or cross products. Then in physics, we learn a little more about vectors, but when it comes to dot products and cross products we are just told to plug values into some equation that magically works, with no explanation as to why. 

Yet, they are so simple. You can begin learning them in middle school, and all it takes to really fully grasp them is a deeper understanding of trigonometry, something students get their sophomore year. It's like not teaching concepts like radians or limits until 10th or 11th grade, when kids would internalize them and understand them much better having been taught them from childhood.

On Playing With Data

Recently at work I was put in the position of having some data, not much but enough to try to make some graphs, and needing to use it to understand what was going on.

More specifically, I had some dates and the mass of a thing from which we were trying to etch graphite. I wanted to find a way to express the rate of this etch both visually and comparably.

In the end, I didn't exactly reach these goals, but I did learn plenty about Playing With Data, and playing is really what it is!

In all my labs in highschool, you'd do some experiment, take some data, and then they'd have some lab questions or analysis where you'd be gently guided into seeing empirically the equations that you learned the day before. This is nice and all if you tend not to believe the teacher or textbook and you need concrete proof, or if you had a hard time internalizing and understanding the applicability of what you learned, or if you were just really interested (an interest that often went away after doing these labs."

This was quite different. I hadn't been taught the day before what was supposed to be going on (no one really knows), I hadn't learned the equations that the data should fit, and I didn't have some nice numbered questions that brought me gently to the main conclusion or point of the lab.

So I played. I fiddled around with and manipulated the data. I made tons of different graphs, and tons of different best fit lines or functions. 

The most important thing I learned, is that data without visual representation is largely meaningless and is not understandable. When you have just a list of x and y coordinates, it is very very rare that you can glance at them and go, "oh yeah, that clearly indicates this!" However, in a graphical representation of a data, one that's well done and clear, this can be done easily.

The creation of these graphs and the manipulation of this data also let me know another good lesson: more data is better. I was working with a very small amount of data, almost the minimum I could draw any reasonable conclusion from, and while I did have enough to draw such conclusions for my own purposes, it made it much harder and much less reliable. The more data you have, the easier it is to see trends and patterns, and the more exact your mathematical understanding of these will be.

Speaking of mathematics, I learned that it's very helpful to approach data from an analytical and mathematical way so as to gain and understanding of what you should do with the data. In this case we thought that the masses should change exponentially, that is Mass  = Ae^(kt), which would make sense since we assume that the longer it goes, the less graphite there is to etch, and so the rate slows.  This would indicate that if you took the natural log of the masses and graphed it against time, the relation should be linear. This we saw seemed to be true. With further data and investigation into this, we may be able to figure out a way to compare or standardize the etching rate, however I suspect that to do this we would need to look into the role of surface area on the rate.

And finally, documentation is key! in our digital world, no information need be delete (thanks, google) and everything is easily recorded and saved. So record and save it! I kept most of the graphs I made, even if they didn't make any sense, and I keep many of the pictures, even though they don't give any information towards figuring out the rate. All of it could be useful later on.

Work - Graphite etches and diamond-like hydrocarbons

Work today was good.

First off, things are working. I'm currently doing an electrochemical etch of a big thing covered in graphite, and I'm using weighing and pictures to attempt to determine the rate of the etch. So far, it has been pretty successful. Once I get more data points, I'll figure out some way to make the data useful so that it can be compared to further tests, with some variables. My boss suggested normalizing the data by getting percents of weight lost, which is probably what I'll end up doing. This is the first time I've really gotten to work interestingly with data, and to try to figure out on my own what to do with it and how to interpret it. In all the labs in high school, they make you take data and then tell you exactly what to do with it, and you've probably already learned what it means anyways. In this case, I don't really know what it means or how it relates to the variables. Very exciting. I think it would make a great science fair project, if that was what I was going to use it for.

Next interesting event was that I spent a bunch of time talking with my boss about the mechanism for the etch. This is something that no one knows, and that has mystified us from the beginning. If we knew the mechanism, we would know better how to improve the rate of the etch! Our current theories are as follows:

1: Some sort of reactive element or ion (OH-? H+?) is being created in the water and reacts with the graphite in some way, possibly to create CO or carbon dioxide. The problem with this is that most of the etched graphite seems to end up floating as macro-sized particles in the water, indicating that they've fallen off for some reason, which seems against the reaction to form gas unless this reaction likes to occur in crevasses underneath the graphite, taking away a layer and knocking everything above it off. 

2: The conductive graphite in the water creates a short that leads to a potential buildup on either end of the graphite, which causes the breakdown of water and possibly some sort of reaction to occur? This on is fuzzy, but it makes sense that this sort of potential buildup would occur.

3: This idea is weird, and seemed to be suggested in one of the papers I read. They seemed to think that the passage of current through the graphite may through random interactions (kind of like london dispersion, I guess) cause carbon atoms to momentarily become polar enough to be dissolved into the water. Again, if this were to happen, no visible graphite would be floating around in the water, unless it either ate below them or the graphite, after dissolving off the main structure, would fall out of solution and create visible particles.

With each of these potential mechanisms come potential ways to increase the rate:

1: Figure out how to create more of this ion, possibly with more current. Also, try to allow more of this to reach the surface of the graphite and avoid buildup of a layer around the graphite, either through ultrasonic agitation of the water or mixing. 

2: Use the purest least conductive water possible to make the potential difference across the graphite greater. Again possibly agitate the water to prevent the buildup of a layer.

3: More current. Possibly adding a surfactant (which the paper says they did, and that is slightly improved some of their performance)

Apart from this, my boss now wants me to find information about Diamond-like hydrocarbons, and the atomic hydrogen density of various types. So far, I've had little success in this, but I've not spent enough time.

As always, more to do!