The following is a handout I give to participants in a short workshop on numerical calculations using python.  This workshop is aimed at introductory college students or high school physics teachers or college faculty.

The following is a mostly up-to-date presentation that goes along with the questions. https://docs.google.com/presentation/d/1erNmpf_5ZUB9Vmc6uro49f220qcismnbkMzj4og7FtI/edit?usp=sharing

If you want a different form - here is a an online textbook with embedded python programs. https://trinket.io/rhettallain_gmail_com/courses/introductory-physics-with-python#/introduction/physics-and-python

Note this online version is incomplete.

Now for the supplements to the presentation.

Numerical Calculations Starter Programs

Here are the programs (along with the questions) that we will work through.  If you prefer to use Glowscript, you can find all the programs here.

Constant Velocity

Object moving with a constant velocity (in 1-D).  Starter program https://trinket.io/glowscript/3c5632203c?toggleCode=true

• Where will the cart be at 2.2 seconds?
• What if the cart has a velocity of 0.62 m/s?
• What if the cart starts at -0.5 m?

Constant Acceleration

An object moving with constant acceleration (in 1-D).  Starter program: https://trinket.io/glowscript/54ff55930d?toggleCode=true

• Why don’t you get exactly 0.9 meters for the final position?
• What if you change the time step to 0.2 seconds?
• What if the acceleration is -0.01 m/s^2
• If the acceleration is -0.02 m/s^2, how long would it take to stop?  Where would it stop? (hint: you can print out the final velocity - print(v).  Also, you might want to think about changing the while loop)

Graphs

Use the constant acceleration program above.

• To create a graph you need two lines:

• f1=series(color=color.red)
• In the loop, f1.plot(t,x)

• Make a graph (just one graph) for position vs. time for the accelerating cart.
• Make a plot of velocity vs. time for the accelerating cart
• Two cars - when do they meet?  Starter program (incomplete) https://trinket.io/glowscript/c3aa7865e1?toggleCode=true 

Mass on a Spring

Model the motion of a mass oscillating vertically on a spring.  Starter program (incomplete) https://trinket.io/glowscript/b4e03c1284?toggleCode=true

• Add expressions for the force, update the position, update the momentum and run the program.
• What happens if you change the time step to 0.1 seconds? What about 0.001 seconds?
• Does the period of oscillation depend on the amplitude?  Try changing the amplitude (the starting y-value)
• What happens if the mass starts with an initial velocity?
• What if the mass is 0.4 kg?

Vectors

Here is a sample program that demonstrates some vector operations. https://trinket.io/glowscript/d6faf70ad3?toggleCode=true

3D Objects

Here are three common objects you can draw in 3D.  Really, you just need the sphere. https://trinket.io/glowscript/b89ad98139?toggleCode=true

Moving in 3D

A simple program that has a sphere moving at a constant velocity. https://trinket.io/glowscript/740fed0059?toggleCode=true

Projectile Motion

This starter program has a ball that is launched straight up. I put a couple of hints in the program.  Remember that a line starting with # is a comment. https://trinket.io/glowscript/5611775c5c?toggleCode=true

• Launch the ball with the same starting speed but at a 30 degree angle.
• Make a plot of position vs time (ball.pos.x is the x-coordinate).  Do y also.
• Make a plot of the y-velocity vs. time.
• Print the final x-position.
• Change the launch angle.
• Change the starting height.
• Does a launch angle of 45 degrees always give the greatest range?

Air Resistance

Here is a sample program.  It’s just like the projectile motion, but it has an extra force. https://trinket.io/glowscript/53d2efb4db?toggleCode=true

• Change the mass of the object
• What is the angle for the greatest range?
• Create another ball with the same initial velocity but without air resistance.

Orbits

Here is an incomplete program showing an object interacting with the Earth. https://trinket.io/glowscript/9266bff0c5?toggleCode=true

• Enter an expression for r - the vector from the Earth to the object.
• Enter an expression for F - the gravitational force.
• Change the initial velocity of the object.  Can you get an orbit?

Three-Body Problem

This is just like the orbit problem above except there are three objects interacting.  https://trinket.io/glowscript/eac36d51f1?toggleCode=true

• Try changing the initial velocity of the planet.  Is it still a stable orbit?

Useful Links

• Glowscript - http://www.glowscript.org
• Trinket - http://trinket.io
• VPython - http://vpython.org
• The presentation from the workshop - feel free to use this.
• Glowscript Tutorial - more in depth series on using VPython https://phys221.wordpress.com/2015/02/26/glowscript-tutorial-1-introduction-and-vectors/
• Incomplete online course teaching physics by using VPython https://trinket.io/rhettallain_gmail_com/courses/introductory-physics-with-python#/introduction/physics-and-python
• Google group - https://groups.google.com/forum/?hl=en#!forum/glowscript-users
• Velociraptor problem http://www.wired.com/2015/10/heres-solve-xkcd-velociraptor-problem-code/
• You should be coding in physics http://www.wired.com/2015/08/coding-physics-course/
• Finding max range http://www.wired.com/2015/03/determining-maximum-projectile-range-numerical-model/
• Electric field due to a charge distribution http://www.wired.com/2014/09/numerical-calculation-electric-field-due-charge-distribution/
• Gauss’ Law http://www.wired.com/wiredscience/2013/11/numerical-calculations-with-guasss-law/
• Finding Pi - http://www.wired.com/2010/03/on-the-8th-day-god-made-pi/
• Solving the infinite square well http://www.wired.com/2016/03/can-solve-quantum-mechanics-classic-particle-box-problem-code/
• History of VPython https://matterandinteractions.wordpress.com/2016/04/27/a-time-line-for-vpython-development/
• Student solves a numerical calculation on paper - https://youtu.be/pe874mvvU28
• A student solves a numerical calculation with python https://youtu.be/yyXdYeFZik0

Other Examples

• 3D mass on spring http://www.glowscript.org/#/user/rhettallain/folder/phys221/program/GStutorial4springsfullprogram/edit