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LaTeX equation test

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I use equations quite a bit. What I have been doing is writing the equations in LaTeX and then taking a screen capture of the output. I think this makes nice looking equations, but it sure takes a while. Here I am testing [LaTeX for WordPress plugin](http://wordpress.org/extend/plugins/latex/). The following *should* be some equations:

$$\vec{F}_\text{net}=\frac{d\vec{p}}{dt}$$

$$a^2+b^2=c^2$$

End of test. This was only a test. Had this been a real post, it *might* have had something useful.

**update** not sure if I like the way the equations look.

Basics: Making graphs with kinematics stuff

rhettallain 4 Comments

**pre reqs:** [kinematics](http://blog.dotphys.net/2008/09/basics-kinematics/)

Suppose there is some experiment in which you throw a ball up and collect position and time data (with video analysis). What do you do with this data? Your instructor told you to make a graph, but how do you do that?

Here is the fictional data you (or I) collected:

![data2](http://blog.dotphys.net/wp-content/uploads/2008/09/data2.jpg)

Here is the text file with the data if you want to reproduce the graphs I make here [kinematics data](http://blog.dotphys.net/kinematics_data.txt)

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Mr. Miyagi and learning

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So here I was in thermal physics class. The students were talking about the assigned homework and then asked: “can’t we get some homework credit for this? Why are we even doing this?” Immediately in my head popped “wax on, wax off”. This was the same situation Mr. Miyagi (from [The Karate Kid](http://en.wikipedia.org/wiki/The_Karate_Kid)) was in with Daniel-san. Homework should not be done just for the points. Homework should help the students become more proficient at blocking blows from the test.

I really like the movie karate kid. Mr. Miyagi brings up some good points. How does Daniel-san learn about karate? Is it by sitting and listening to Miyagi? No, he learns by doing some stuff. At first Daniel-san does not see the point of the exercises, but in the end, he wins.

![200px Karate kid](http://blog.dotphys.net/wp-content/uploads/2008/09/200px-karate-kid.jpg)

Computational Physics and a group of 1000 8th graders

rhettallain 1 Comment

I like computers, really I do. Computational physics is a good thing. However, there is a small problem. The problem is that there seems to be a large number of people out there that treat numerical methods and simulations as something different than theoretical calculations. You can tell who these people are because they refer to simulations as “experiments”. But what do these simulations really do in science? What is science really all about?

**Science**

To me, science is all about models. Making models, testing models, upgrading models. Models. Some examples are the model of gravity. One such model is that there is a gravitational force between any two objects with mass. This force is inversely proportional the square of the distance between them. (This is Newton’s model). Is this model perfect? No. Is this model the truth? No. How did this model come about? Experimental evidence.

**Models**

Well, how do you make models and what form can they take? To make a model, you collect some observations. The model should agree with these observations. This model could be a physical model (like the globe). It could be a mathematical model (like V=IR). It could be a numerical model – like a [vpython](http://vpython.org) program of a baseball trajectory with air resistance. These are all models.

**8th graders**

What does any of this have to do with 8th graders? I claim that any numerical calculation or simulation could be done with a group of 1000 8th graders rather than a computer. What does a computer do? (a computer program really) A program takes a problem and breaks it into a bunch a really small steps. It then does each of these steps and combines them together in some way. Just like a group of 8th graders with TI-89 calculators. Clearly, they are just computing something – they are not a separate type of science (other than theory and experiment).

Energy issues are like the reverse Y2K problem

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There was this commercial on the radio about Trane heating and cooling units. The ad claimed that the units could use up to 50% less energy than your existing unit. This started me thinking (because before that I was in a complete state of non-thinking). Do you remember the Y2K problem? Basically, when people started writing programs back before Star Wars they had to be very conservative. The hardware of the time did not afford the programmers to have frivolous code. To conserve, they only used the last two digits to represent the year (1970 was represented as 70). Obviously this became a problem in 2000. So, for computers and programs, people started very conservative and the hardware became less conservative.

Now look at appliances. When people first started getting electricity in their house, it was a completely new thing. But how much electricity would a household use? At one point (I read somewhere) that it was projected that electricity could be so cheap it would be free. In this case, why make an efficient AC unit? Look at many of our energy uses today (including cars). They seem to have the legacy of being extremely inefficient.

To summarize: Computer programs start out being efficient and then go to not needing to be efficient (because computer processing is relatively cheap). Appliances start out being inefficient and are moving towards being more efficient. Really, that is all I wanted to say.

Basics: Vectors and Vector Addition

rhettallain 7 Comments

**pre-reqs:** trig

Think of the following two things. Temperature and wind speed. These are two different things that you could measure, but there is one big difference. Wind speed has two parts to it – how fast and which direction. Temperature is just one thing (no direction). Temperature is an example of a scalar quantity (just one piece of information). Wind speed is an example of a vector quantity – multiple pieces of information. Here are some other examples:

**Scalar:** mass, money, density, volume, resistance
**Vector:** velocity (most physicist reserve the word “speed” to mean just the magnitude), acceleration, force, momentum, displacement, electric field

Ok, I get it – but who cares? Well, if you are taking an introductory physics course, you should care. Here is a question I like to ask to start the discussion of vectors:

If I move 3 feet and then 2 feet, how far am I from where I started?

The answer is that there is no answer. I commonly get the quick answer of 5 feet, although this is only one possible answer. Let me illustrate this question with some pictures.

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Amazing Blob Jump Launch Video Analysis

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Can you believe it? Have you seen this video?

Are you thinking what I am thinking? WOW. How could these people not follow my rules for cool internet video. Once again, here they are:
1 Keep the camera stationary. This way I don’t have to keep moving the origin in the movie.
2 Don’t Zoom. Same reason, this video followed that rule.
3 Include a clear and obvious calibration object. A meter stick would work, or even a Kobe Bryant (I can look up his height). Maybe it could be a Ford F-150 that has a known length. Something!
4 Include the mass and height of all people involved.
5 Use high quality video.
6 Don’t talk about fight club – oh wait, wrong list.

Despite failure to follow all these rules, I have managed to analyze this video. Really when I saw it, I said “wow” – was that real? It looked real, but who would get shot up that high? (it is on break.com, so fake is a possibility).

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Physics of Linerider IV: Friction?

rhettallain 1 Comment

Friction in Line Rider

Is there friction in Line Rider? Does it function as physics would expect? To test this, I set up a simple track:

![Page 6 1](http://blog.dotphys.net/wp-content/uploads/2008/09/page-6-1.jpg)

Basically, a slope with a flat part to start with and to end with. Let me show you something simple before further analysis:

![Page 6 2](http://blog.dotphys.net/wp-content/uploads/2008/09/page-6-2.jpg)

This is the x-position vs. time for the line rider on the first horizontal portion of the track (before he or she goes down the incline). This shows the rider traveling at a constant speed of 0.71 m/s. If friction were present, the rider would slow down. If you do not believe me (and why should you?) try creating your own line rider track with a long horizontal section. The rider will not stop, but continue on at a constant speed.

Ok, so no friction on the horizontal line. This makes a little bit of gaming sense. Who would want a rider to stop in the middle of the track and be stuck? That wouldn’t be fun. But, is there friction on non-horizontal portions? To test this, I will use the work-energy principle.

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Physics of Linerider III: Air Resistance

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There is no air resistance in line rider. Sorry to spoil the suspense.

To test for the presence of an air resistance force, a track was created that let the rider fall.

![linerider air 1](http://blog.dotphys.net/wp-content/uploads/2008/09/linerider-air-1.jpg)

(note the markers on the side. These are used to keep track of how the origin is moving).

Below is the y position of the rider as a function of time:

![linerider falling](http://blog.dotphys.net/wp-content/uploads/2008/09/linerider-falling.jpg)

In this situation, the rider falls about 100 meters. A quadratic line is fit to the data and an acceleration is obtained that is very similar to the previous case (where air resistance was assumed to be negligible). If there had been air resistance, this graph would have become more linear as the rider fell. Perhaps 100 meters is not far enough to fall, but in real life this should be far enough to detect the presence of an air resistance force. Or does it? Lets make a simple check.

Continue reading “Physics of Linerider III: Air Resistance” →