184_projects:sticky_stuff_24 [Projects & Practices in Physics]

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===== Project: StickyStuff and the Dust Particles =====

==== Kick Off Questions ====
  - When setting up an integral for a line of charge, what are the general steps you need to take?
  - What is dQ in the integral set up? Why do we rewrite dQ so it is in terms of dx?
  - How do you pick your bounds for your integral?
  - What quantity in your integral set up should include a variable (x, y, or z)?

==== Main Problem ====

{{  183_projects:taperoller.png?500}}

Adhesive tape is manufactured by repeatedly rolling and unrolling large sheets of plastic, which can cause there to be a charge on the surface of the tape. Why this important, you may ask?  Trapped in the town of Lakeview, the S.P.A.R.T.A.N force has been called to the premises of StickyStuff Corporation.  Local conspiracy theorist Manny Habañero has convinced the CEO of StickyStuff Corp that the crazy thunderstorms are related to strange creatures he's seen in the woods near town.  He claims they are about the size of a mountain lion and have fur like a cat, and he thinks that if he leaves strips of special tape in the areas where they've been spotted, it will collect some of their hairs and prove they're real.

Unfortunately, there has recently been a dust problem in the StickyStuff manufacturing plant. Dust particles (on average, $q=0.802 \times 10^{-14}$ C, $m=5.5 \times 10^{-8}$ g) have been accumulating on the tape as it rolls through the assembly line. The problem has been isolated to a single roller, which operates for 10 seconds at a time at a power of 100 watts (where 1 watt = 1 J/s). Using your handy-dandy-super-extender tape measure, you find that exactly 30 m of tape passes over the roller during each 10 second time period. 

The tape must be in excellent condition before being set out to collect fur samples, and your team needs to determine the requirements for a fan system that will blow away any dust that may be attracted to the tape.  You don't need to decide where the fans will be placed, but you need to determine how much force the fan needs to exert on each dust particle to prevent them from contaminating the tape.  From your adhesive engineering education, you have access to a [[https://www.alphalabinc.com/triboelectric-series/|table]] that you think may help.

<WRAP INFO>
=== Learning Goals ===
  * Create an analytic model for a line of charge
  * Be able to explain how you set up each part of the integral, $dQ$, $r$, limits, etc.
  * Explain how you used superposition in your solution
  * Understand how surfaces become charged (particularly as an insulator in this case)
</WRAP>

==== Wrap Up Questions ====
  - What is charge affinity?
  - How do you rewrite your separation vector? What is r_source? What is r_obs?
  - In the separation vector, should you have x as a variable or dx? Why?
  - How do you integrate a vector? What steps would you follow?
  - How did you use superposition today? Where is superposition represented in your equations?
  - What would change about your integral set up if you changed your origin? What would change if you moved the observation point?