184_projects:f21_project_3 [Projects & Practices in Physics]

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~~NOTOC~~

===== Project 3 =====
==== Project 3A: Building Stormchaser HQ ====
You are part of a secret organization that sends task forces to investigate strange phenomenon. The name of your particular task force is S.P.A.R.T.A.N force. Your team has been sent to investigate an abnormal storm system that has encapsulated the town of Lakeview. You and your team are racing to be on the frontline to investigate this new system and as you speed toward Lakeview you receive a call from a group of scientists working at Stormchaser HQ. They explain that they have built their new base of operations (HQ) 2 km away from the mountains, which typically gather large clouds (on average, $m=1*10^9 kg$  and $q=-150 C$) to the west of the HQ. The Lakeview scientists have calibrated the equipment on top of HQ to deal with the electric potential from the large clouds, but they are concerned about an incoming storm system that is displaying abnormal qualities. As much as they would love to collect data on this storm, if the electric potential changes by more 20 MV due to the additional clouds, the equipment will be damaged. They have received reports that the storm system is heading toward HQ from the eastern plains (where the wind can last up to 20 minutes and exert a force of 36000 N) with a mass around $m=3*10^5 kg$  and a charge between $-50 C$ and $-60 C$. (For out-of-town-ers, they like to clarify that the eastern plains are roughly 500 km away.) They know that you need immediate data on the storm and would like a recommendation from your team on whether they can keep their equipment on top of HQ or if they should take it down for this storm.
<WRAP INFO>

===Learning Goals:===
  * Understand how electric force, electric energy, electric potential, and electric field relate to one another (and be able to calculate these quantities for a system of point charges)
  * Apply energy principles to a situation with charges (energy conservation, transfer of energy, system definitions, etc.)
  * Apply momentum/force principles to a situation with charges (momentum-force relationship, force-acceleration relationship, force diagrams, etc.)
  * Think about what might change when there are multiple sources of charge in the problem
</WRAP> 


==== Project 3B: Charge the Line ====

You have become trapped in the town of Lakeview. The town and surrounding landscape are under a constant barrage of storms. Not only are people being struck by lightning within the town but any vehicle or person trying to leave the city limits of Lakeview are instantly struck by lightning. The number of deaths due to lightning strikes in Lakeview in one week is larger than the amount the whole world has seen in the last 5 years. Jo Harding, a  crazy local scientist who has had a few run-ins with storms before has an idea of putting up giant metal T's, with the base of the T inserted into the ground to try and stop the townspeople from being struck with lightning. Jo wants the base of the T to be made of wood and the horizontal top of the T to be a metal. Mayor Rachel Wando is up for reelection and is willing to listen to any ideas to stop the rising death toll but ever since the lightning storms started she has been in non-stop meetings in which electric fields are being constantly talked about and is becoming very concerned about what the electric fields would be like for these T-shaped objects. Rachel reaches out to her friends at the storm chaser HQ for a model of what the electric field will be for one of these T's after it has been struck by lightning. The code below is the beginnings of your teams work on modeling the electric field from the giant T.

<code>
## Creating the scene for the code to run in
scene.range = 2

## Constants
TotalCharge = 15 #C
pointcharge = TotalCharge/7  
k = 9e9  
vscale = 1e-4

## Objects
charge1 = sphere(pos=vec(-3,0,0), Q=pointcharge,  color=color.red,  size=5e-1*vec(1,1,1))
charge2 = sphere(pos=vec(-2,0,0), Q=pointcharge,  color=color.red,  size=5e-1*vec(1,1,1))
charge3 = sphere(pos=vec(-1,0,0), Q=pointcharge,  color=color.red,  size=5e-1*vec(1,1,1))
charge4 = sphere(pos=vec(0,0,0), Q=pointcharge,  color=color.red,  size=5e-1*vec(1,1,1))
charge5 = sphere(pos=vec(1,0,0), Q=pointcharge,  color=color.red,  size=5e-1*vec(1,1,1))
charge6 = sphere(pos=vec(2,0,0), Q=pointcharge,  color=color.red,  size=5e-1*vec(1,1,1))
charge7 = sphere(pos=vec(3,0,0), Q=pointcharge,  color=color.red,  size=5e-1*vec(1,1,1))
charges = [charge1, charge2, charge3, charge4, charge5, charge6, charge7]

## Calculation Loop 1
E = vec(0,0,0)
point = vec(0,0,0)
for c in charges:
    r = point - c.pos
field = arrow(pos=point, axis=vscale*E, color = color.cyan)

## Calculation Loop 2
x = -5
dx = 0.5
xmax = 5
while x<=xmax:
    theta = 0
    dtheta = 0.1
    R = 0
    while theta < 2*pi:
        E = vec(0,0,0)
        point = vec(x, R*sin(theta), R*cos(theta))
        field = arrow(pos=point, axis = E*vscale, color = color.green)
        theta += dtheta
    x+=dx
</code>
Complete the program above to first represent the total electric field just to the right and left of the line of charges. Then,  calculate the total electric field surrounding the line of charges.

<WRAP info>
===Learning Goals===
  * Understand what a list (or an array) does in the code and why you would want to use one
  * Understand how a "for" loop works and how it is similar/different from a "while" loop
  * Make a model of a line of charge using point charges and be able to describe how you would improve your model
  * Use superposition to calculate and visualize the electric field around a line of charge
</WRAP>