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.

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!

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!  :-) 

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.

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.

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.

Python Programming Activity I: Bouncing Ball

Today we will actually try to modify a Python script written by Mr. Dempsey. The full exercise is on his website, and can be found here. Give it a try, help each other out, and do not hesitate to ask him questions. Also, pay attention to the techniques being used to actually do a simulation - these are built upon the concept of a time step. This is all outlined in this activity. Good luck!

Electric potential for shells

There are worked examples for finding the electric potential when you have shells of charge, as well as materials that are charged.  Check it out on the web page, it is entitled "Potential - Shells and Integration."

There is also a video on this with thin shells.

For Classes Thursday and Friday, Oct. 15, 16

For 4 Chem-Phys classes (1-2, 8-9):
On Thursday, begin with volunteers to be at the board and, as a class, reach consensus on the homework problems. In particular, you can pull up the solutions for the 2002 AP problem with the partial ring of charge. Go through these with small groups if there are questions, and talk them through.
Once done with the problems, you can begin the lab on equipotential lines and gradients. Before starting, Lucy (in period 1-2) and Danny (in period 8-9) will demonstrate how to get your data. You will ultimately make maps of equipotential lines on the white grid paper...do not draw on the black conductive paper. You should have time to get your data today, and any extra time can be spent working on the analysis.

On Friday, start off by doing the two collaborative problems, and turn them in before leaving. The rest of the time you have to work on the lab - keep in mind that you should individually do and turn in the AP problem, and do the ActivPhysics simulations on equipotential lines. Use Internet Explorer on the school computers, which seems to work better than Chrome or Firefox. If you are unable to complete the simulations here, finish it up over the weekend.

Over the weekend:
Take a look at the video, and take notes, about finding electric potential with multiple shells of charge. We will bring in voltage with the Gauss's law next week.
If interested, there is a video on band theory, which may help understand where the 'bands' come from.


For AP Physics C (3-4):
On Thursday, begin with volunteers to be at the board and, as a class, reach consensus on the homework problems. After that, watch and take notes, and discuss if necessary, a video on potential wells. This refers to graphs of potential energy as a function of position, and also makes use of the gradient concept F = -dU/dr.  When this is done, you have time to work on the homework set for potential wells (last page of packet), and also to try and complete the lab. Whatever is left, take as homework.

On Friday, reach consensus on the AP problems on potential wells. Pull up the 1995 'Nike' problem solutions if you all wish.
When this is done, watch the DVD on string theory. This is part 2 of The Elegant Universe. Take notes on it, since we will get into modern examples next week. Finish up any lose ends of the lab before leaving.

Over the weekend:
Watch and take notes on the video about gravitational potential energy.

Scholarship possibility for the Ladies

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