Thursday, October 23, 2014

Nobel Prize in Physics goes to 2 Japanese and 1 American - Blue LED

It you have an LED TV or computer monitor, you have this year's group of Nobel Prize winners to thank. Having a blue LED along with the other two primary colors, red and green, allows one to have the pixels necessary to make white light and all other colors for pictures. The great thing about LED lighting of any kind is the large drop in electrical energy necessary for the system. While presently some 20% of the world's energy is used for lighting, LEDs may drop this to about 4%! This is the sort of practical application to better the world we need to see more of, and that is celebrated with the Nobel Prizes.

The Nobel for Medicine and Physiology goes to and American and two Norwegians, for their discovery of how the brain figures out our positioning - that is, how we know where we are! Pretty cool stuff! Oh, and one of the three is indeed a woman.

The Nobel for Chemistry goes to two Americans and one German, for developing super-fast fluorescent optical microscopes that can attain high resolution at the nanoscale (i.e. can watch molecules!). Not bad!

Check this out, seniors: Gravity for Sticks and Rings

When it comes to the math, what we are working on in EM as far as electric potential and electric fields for charge distributions should be the same as gravity. Check out the following videos if you want to see some fancier math and strange situations for gravity, as they just follow the analyses we have done for electric charges. It is neat to see what happens with a hollow earth, or digging a tunnel through the earth and jumping in. Then there is Gauss's law for gravity, and the NON-Gauss geometries. Keep in mind you can also check out the main concepts Einstein used to come up with general relativity.

Lessons for October 23

Periods 1-2 and 8-9, check out how to begin circuit analysis. In the Ohm's law lab, from data I've seen in some groups, you should see current, I, is linearly related to voltage. And also, current is related to resistance^(-1), or I proportional to 1/R. Combined we'll get an empirical formula of I = V/R. This is Ohm's law. We already know the rules for series and parallel resistance.

Periods 3-4, check out why momentum is conserved, and then an example of perfectly inelastic collisions with a ballistic pendulum.

Monday, October 20, 2014

Classes for Oct. 20

For periods 1-2 and 8-9, check out this video on finding potentials at various locations of the charged sticks. Focus on how to set up the integrals, and what the proper limits of integration are. You can try the 1980 (back page) and 2002 problems (second to last page) of the packet from Friday.

For periods 3-4, check out this video for air friction and terminal velocity. You can try the 1984 problem, and then try to complete the lab (don't worry about the last analysis question for the time being).

For COMAP teams, have at least one person from each team come to one of the organizational meetings on Tuesday, either before school at 8 am, period 5, or period 6. Note that there are some online resources that can be found here.

Sunday, October 12, 2014

Resources for COMAP 36-Hour Problem Contest

Want to try your hand at developing a viable solution to a real-world, open-ended problem with different approaches that can be taken, and no single 'right' answer!  Complex problems hound us in all fields in real life, so being able to attack such problems and develop reasonable solutions is a skill set that is necessary in the 21st century. You are going to have to collaborate, do research to find reliable resources of large data sets, use technology to assist the process, communicate your work, use more advanced thinking and problem solving skills (such as developing a mathematical model), make predictions that can be tested against a real world sample, develop creative solutions, and so on!

To assist you, here are various resources that will hopefully be helpful for you and your team:

Check out other open-ended, complex problems from the COMAP High School Mathematical Modeling Contest (HiMCM) and the Moody's Mega Math Challenge. The home pages are: HiMCM and Moody's.

Problems from past contests are: HiMCM and Moody's.

Exemplar papers from Moody's.  This includes an ETHS team paper that took 5th place nationally!!!  See what a good paper looks like.  See how teams took a problem and broke it down into simpler pieces, and what assumptions they made.  See how a mathematical model was developed, and what math techniques went into the model's development.  See how they explained their work.  See how they used the model to make predictions that could be tested against real data and other information. See how they determined and explained the weaknesses of the model.  Might as well learn from some others who did a good job with this process!

Judge's perspectives from Moody's can be found on this page, and for COMAP on this page (pages 17-35).  These are especially useful because they point out what makes for an average solution paper compared to an outstanding solution paper!  Are you doing these things for your solution paper?  If not, why not?  How can you re-adjust and make the solution better?  If you had more time, what would you focus on to try and improve your solution proposal?

For optimization problems, check out this file that outlines an example of using Excel Solver. You can find lots of YouTube videos for how to use Solver, including one here. Keep in mind Solver can be used to maximize, minimize or find set values of functions for open-ended problems.

Teams might consider drawing out a flow chart early on in the process that outlines key components and assumptions you want to make.  Get a visual picture of what this all looks like, and think about what is connected to what.  Do you expect direct or inverse relationships?  Linear or non-linear?  What factor or parameter, when changed, will have an effect on other parts of the model/solution?

We hope these all help you in this process.  Good luck, and have fun with it!