## Wednesday, November 18, 2015

### Python Activity - Double Pendulum (Chaotic system)

This activity builds off of the last one, where we begin to see and use an actual Python program to simulate the motion of real objects. Last time we looked at a tossed ball that bounces. Not only did we begin to see how to insert equations that the simulation runs over and over to calculate the points where the ball goes from time step to time step, but also had animations of the bouncing ball. That program is now a template for us to use - we can change the equations we put into the program in order to simulate other objects besides a bouncing ball.

This time, we will use a simulation for a more complicated type of motion, the double pendulum. This is a pendulum hanging from a pendulum. If we tried to calculate and plot points for this system, we could not do so by hand since it is too complicated (and also a chaotic system). So this is a case where we really do need a computer to solve the motion numerically so we can find out what it does. The activity for today is here. Some years ago, a former student wrote his own simulation for this, where he simulated two double pendula hanging from a rod, so they affected each other via vibrations through the rod (called coupled double pendula). His paper is is here if you are curious.

## Thursday, November 12, 2015

### Classes for November 16

Happy Monday, everyone!

4 Chem-Phys:

Take a couple minutes to compare work and answers on the multi-loop circuit problems. When you are OK with those, watch three short videos, and take good notes on both:

i. How do Kirchhoff's rules lead to the resistor rules for series and parallel? Hopefully this will make sense and you'll see where the weird reciprocal rule comes from for parallel.
ii. How do Kirchhoff's rules change for capacitors, and what are the rules for adding capacitance in a circuit? Turns out we have the same two rules as for resistors, but they are swapped.
iii. What are capacitor (only) circuits and how do we solve them? Keep in mind the main thing we will be looking for with capacitors is how much charge is stored by each capacitor in the circuit. The approach is basically identical to finding currents in resistor circuits: Find total capacitance, find total charge with Q = CV (this is like Ohm's law for capacitors), then redraw the circuit as a series circuit - each capacitor in series has the same total charge on it, and then you can find the voltage for the parallel branches using V = Q/C.

Keep in mind that there is a new unit for capacitance, called the farad (F; named after Michael Faraday). One farad is defined as a device that can store 1 coulomb of charge by using a 1 volt battery to hold that charge on the capacitor. A 1 F capacitor is actually quite large...you will see units of microfarads, and even as small as picofarads, in real devices.

After watching these, break into groups and you can try the following. There are no hard copies of the problems, but you can pull up an online version of the book on the screen. To do this, do the following:
Go to the Mastering Physics site.
Click on Sign In.
Username = ethsphysics; PW = ethsphysics1
Click on Launch Your eText
You can type in 812 in the page box at the top to get to the problems below.

HW Set for Tuesday: Chapter 24, Exercises #15, 16, 17, 21 on page 812, and 63 on page 815.

AP Physics C:

Take a few minutes and talk through the homework problems together. Are these torque problems making any sense to you?

Watch a video on equilibrium with rotations involved. Take good notes, and realize there is one new condition to equilibrium: not only do we balance forces in each dimension, but now we need to balance torques if there is an axis of rotation.

HW Set for Tuesday: Ch 11 #13, 19 (page 7 of packet)
Ch. 11 Either #46 or #70 (page 8)
Torque brain teasers (page 9 of packet); reach class consensus
If you have any time left over, definitely feel free to work on your lab. We are looking for the lab report on Wednesday.

I will see all of you Tuesday!

## Wednesday, November 11, 2015

### Classes for November 12

4 Chem-Phys:

Welcome back! I hope Chemistry went well this past unit; hopefully you had the correct solutions to your test.

We are going to get into circuit analysis, where we will be most interested in learning the basic rules of resistor circuits (we were introduced to some of these last time). We now have 'discovered' Ohm's law, V = IR. We also were given the rules for series and parallel resistors: R_s = R1 + R2 + R3 + ... and R_p = (1/R1 + 1/R2 + 1/R3 +...)^-1.

There are two other even more important and fundamental rules for circuits of all kinds (at least the types we will study this year), called Kirchhoff's 2 rules.
1. In series, all voltage losses will add to the total voltage put into the circuit (i.e. the battery voltage), or V_total = V1 + V2 + V3 + ...
2. In parallel, the currents in the branches add up to the total current that went into the parallel set, or I_total = I1 + I2 + I3 + ...

Keep in mind that in series, there is ONE CURRENT going through everything on that path.

In parallel, EACH BRANCH HAS SAME VOLTAGE DIFFERENCE across it, and each branch can have different currents.

A few have suggested checking out a video on Band Theory, just to (hopefully) have a clearer sense of where energy bands come from. This may help with understanding conductors from insulators and semiconductors a little better.
More importantly for now, check out the video on how to analyze a combination circuit; the main goal is to figure out how many amps of current flow through every part of a circuit.

Take good notes, since these introductions to the rules will be used over and over again, not only with resistor circuits but also circuits with capacitors and inductors. In fact, the Kirchhoff rule for series (about voltage losses adding up to the input voltage) is, for us, the most important rule of all, and will allow us to write equations down for every circuit we work with.

For HW, try the circuit problems on page 5-6 of the packet; start error analysis of the last quizzam (solutions are online, in Gauss folder).

Thank you for all your support and understanding, as my family has gone through this episode with my mother! You will never know how much it means to me. I will be out Friday, which should be the last day. See you soon!  :-)

## Sunday, November 8, 2015

### Classes, Nov. 9 and 10

3 Chem-Phys:
To get ready for the quizzam on Tuesday, there are practice problems on Doc V's 3 Ch-Ph school website. In the Newton's laws folder, there is the file Review set, which has questions/problems and solutions. There are general F = ma problems, and a couple circular problems, including a banked road. In the Gravity folder, there is a file Review set - PR Gravity with some practice questions. There is also a problem (don't worry about the elliptical orbit problem). There is a separate file with solutions. Also, don't forget there are numerous worked examples in your book, additional odd problems you can try and check yourself, and so on. There are videos on: binary orbits; circular motion problems; gravitational potential energy (with escape velocity and Schwartzshild radius of black holes); tension problems.

AP Physics C:
To get ready for the quizzam on Tuesday, there are practice problems on Doc V's AP Physics C mechanics website. In the momentum folder is a file Review Set - PR momentum. There is a separate file with the solutions. Work on these, any of the problem sets or AP problems (don't forget the AP Exam folder and the solution folder). In your book, there are numerous worked examples and other odd problems to try and check yourself. There are videos: momentum conservation; inelastic collisions.

For everyone: If you want to look at other AP exam examples for any type of problem, check out the file in the AP Exam folder called AP_Review_Mechanics_Problems_by_Topic_and_Year, where you can hopefully identify some problems in a hurry. This is the last file in the folder - scroll to the bottom.

Good luck on the quizzams. I should see you on Thursday.

## Wednesday, November 4, 2015

### Python Simulation Activity II: Double Pendulum

This activity builds off of the last one, where we begin to see and use an actual Python program to simulate the motion of real objects. Last time we looked at a tossed ball that bounces. Not only did we begin to see how to insert equations that the simulation runs over and over to calculate the points where the ball goes from time step to time step, but also had animations of the bouncing ball. That program is now a template for us to use - we can change the equations we put into the program in order to simulate other objects besides a bouncing ball.

This time, we will use a simulation for a more complicated type of motion, the double pendulum. This is a pendulum hanging from a pendulum. If we tried to calculate and plot points for this system, we could not do so by hand since it is too complicated (and also a chaotic system). So this is a case where we really do need a computer to solve the motion numerically so we can find out what it does. The activity for today is here. Some years ago, a former student wrote his own simulation for this, where he simulated two double pendula hanging from a rod, so they affected each other via vibrations through the rod (called coupled double pendula). His paper is is here if you are curious.

## Tuesday, November 3, 2015

### Links for class

For 3 Chem-Phys, watch the video on binary orbits. Take detailed notes on this, and feel free to go through any portions of it again if necessary. The homework problems will revolve around the video. After the video, you can work on those problems, and also you can get into your lab groups and work on the lab report. Remember that the report depends on the best-fit functions you get for the four graphs of data.

For AP Physics C, you can work in smaller groups of 3-4 and get data from the ballistic pendulum device. While you can get the data together and work together to ensure you are understanding the principles behind it, you should each write it up separately. As you rotate through getting data, you can work on the homework set, as well as the lab report for the air track data. The ballistic pendulum mini-lab is due Wednesday, the air track lab on Thursday. If anyone needs a review, there is a ballistic pendulum video going through the principles.