course_planning:184_projects:s18_project_10 [Projects & Practices in Physics]

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==== Project 10A: Magnets 'n' Junk ====
Since you are investigating the mysteries of Lakeview and the surrounding area, you decide to take some time to walk into town and get to know some members of the community. As you are strolling around town, you hear a holler. "Aya!!! Hey, howdy!! Come check out this ol' piece of junk I got right here, y'all!" It's Dr. Daryn McPaddel, the town inventor/engineer who is always showing her neighbors strange contraptions that she has made, and also happens to live adjacent to Lakeview's scrapyard, which allows her to tinker and invent to her heart's delight. This is what you see:

{{youtube>lSmuqLtmuwg?large}}

All the commotion around Dr. McPaddel's magnetic crane-thing has caused some neighbors to gather and see what all the fuss is about. Some of them approach you as they scratch their heads in disbelief. "Hey, you know about electricity and magnets and whatnot, can you explain what's going on?" You agree to explain in detail how the thing works since you want to form a bond with the townsfolk. The best way would probably be with a visual, and Dr. McPaddel has already created a visual of the coil of wire inside the contraption. All that's left to do is show what the magnetic field looks like.

<code python>
GlowScript 2.7 VPython
xaxis = cylinder(pos = vec(-3, 0, 0), axis = vec(6, 0, 0), radius = 0.01, color = color.white)
yaxis = cylinder(pos = vec(0, -3, 0), axis = vec(0, 6, 0), radius = 0.01, color = color.white)
zaxis = cylinder(pos = vec(0, 0, -3), axis = vec(0, 0, 6), radius = 0.01, color = color.white)

## Setting up the constants
mu0 = 4 * pi * 10 ** -7    # magnetic constant in standard units
I = 5000                   # current in ring
R = 1                      # radius of ring
thickness = 0.05           # thickness of ring

## Drawing the ring
ring = ring(pos = vec(0, 0, 0), axis = vec(0, 0, 1), size = vec(thickness, 2 * R, 2 * R), color = color.blue)

## Splitting the ring into little pieces
N = 100                    # number of little pieces
dtheta = 2 * pi / N        # angle between adjacent little pieces
theta = 0
little_pieces = []

## Determining dl and the location for each little piece
while theta < 2 * pi:
    dl = vec(0, 0, 0)
    r_source = vec(0, 0, 0)
    
    little_piece = arrow(pos = r_source, axis = dl, color = color.green)
    little_pieces.append(little_piece)
    
    theta = theta + dtheta

## Picking some points to observe the magnetic field
observation_radii = [0, 0.4, 0.8, 1.2, 1.6]
observation_angles = [0, pi/2, pi, 3*pi/2]
observation_heights = [0]
r_obs_vectors = []

## Putting the observation points into a list
for rad in observation_radii:
    for angle in observation_angles:
        for height in observation_heights:
            r_obs = vec(rad * cos(angle), rad * sin(angle), height)
            r_obs_vectors.append(r_obs)

## Visualizing the magnetic field
for r_obs in r_obs_vectors:
    B_total = vec(0, 0, 0)
    for little_piece in little_pieces:
        r_source = little_piece.pos
        dl = little_piece.axis
        
        r_sep = vec(0, 0, 0)
        B_little_piece = vec(0, 0, 0)
        
        B_total = B_total + B_little_piece
    arrow(pos = r_obs, axis = B_total, color = color.yellow)
</code>

<WRAP Info>
=== Learning Goals ===
  * Practice the right hand rule, and make predictions for what magnetic field looks like from a ring of current
  * Relate superposition in the code to how an integral is constructed
  * Investigate the physical meaning of how an integral splits up a wire into "little pieces"
  * Practice setting up an integral for a different shape than a straight line
  * Gain some experience working in cylindrical coordinates
</WRAP>

==== Project 10B: EM-Boar Tiger Cub ====
Dr. McPaddel woke up to a great surprise this morning when she walked outside to admire the junkyard and noticed a mysterious glowing creature stuck to her magnetic crane. Apparently, in all the excitement of showing the contraption to her neighbors, she had forgotten to turn off the machine. The creature had wandered into the scrapyard over night looking for some metal to eat, and when it wandered near the crane, the metal became magnetized, and pulled the creature up into the air, where it remained stuck until Dr. McPaddel discovered it this morning. She alerted the authorities, but it was the Hawkion researchers who arrived before anyone else, to transport the creature to a research facility to learn more about it. They are thinking these animals might be responsible for the disappearance of fish from the lake and green-bellied canaries from the cliffside.

By the time you learn of all this, the creature is already at the research facility. You arrive and the scientists fill you in. They have acquired this beast to study it, but by now they have figured out Dr. McPaddel's crane snagged a young version of the monster. Because of the apparent resemblance to both boars and tigers and their electromagnetic glow the scientists at the compound have taken to calling the monsters EM-boar tigers. So you have captured an EM-boar tiger cub. It turns out that EM boar tigers are super protective of their young and they have organized to attack the Lakeview compound. Surprisingly, even though it is a government facility, there are no guns at the compound. But you are scientists and engineers godammit! You decide to construct makeshift launcher that is using magnetic force to launch projectiles so that they will leave the launcher at a speed of $300m/s$. You must construct your launcher on the floor of the laboratory and position it at an angle of 63 degrees so that it is firing out of the window of the laboratory. 

At your disposal to construct your launcher, you have access to two copper rails that can be cut to your specifications. You also have perspex that you can cut to any dimensions and chunks of aluminum that can be cut to any shape. You also have access to multiple variable power supplies that can be set to a requested current and a bunch of wires that can be cut to any length and some switches. You must outline your design, explaining the physics behind the design of the magnetic force launcher and indicating the current needed to reach an exit velocity from the launcher of $300m/s$.

{{ 183_notes:caged.jpg?700 }}