184_projects:artemis_last_hope_24 [Projects & Practices in Physics]

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===== Project: Accelerator Emergency =====

==== Kick Off Questions ====
  - What is the loop rule equation? When using the loop rule, what is a "loop"?
  - What is the node rule equation? When using the node rule, what is a "node"?
  - What steps do you need to follow to use the loop & node rules to solve a circuit? (Hint: these were in the readings)

==== Main Problem ====
With your help, the FTOE staff were able to re-start the hawkion accelerator.  But after a few minutes of operation, the control screen goes blank and a message from Manny the conspiracy theorist appears!  He's convinced that the storms around Lakeview are caused by his strange creatures in the woods, and that the hawkion accelerator is somehow attracting them to Lakeview.  He's hacked the accelerator control system so that the device will malfunction and blow itself up.

Accelerator operations director Melissa Lewis decides to shut the accelerator down, but just as she gives the order, there's a huge bang and warning lights start going off everywhere.  Several systems start to lose power and there's a risk that the hawkion containment systems may fail, with potentially catastrophic consequences for Lakeview.  After a quick investigation, it turns out that the circuit that controls all of the key systems is currently drawing too much current from the main battery. 

The new intern, Solomon Tobb, proposes a risky but possibly brilliant solution: to dump the hawkion beam into an absorber rather than slowing the particles down gradually.  He wants to take two batteries from another project at the lab and use them to help power the accelerator and the beam dump cooling system at the same time. In addition to the 230 V main battery, he says you can use project I.A.N.'s primary battery ($V_{bat1}$), which delivers 140 V, and its backup battery ($V_{bat2}$), which will provide another 5 V, to keep the accelerator working long enough to steer the particles into the beam dump. 

From the accelerator schematics you find the following resistances for different components that need to be powered in order to dump the beam safely: 
  * Monitor Lights: $R_{ML}=100\;\Omega$
  * Control System: $R_{CS}=700\;\Omega$ 
  * Beam Dump Cooling: $R_{BDC}=950\;\Omega$ 
  * Electromagnetic Calorimeter System: $R_{ECS}=500\;\Omega$ 
  * Accelerator Magnets: $R_{AM}=300\;\Omega$ 
  * Magnetic Containment System: $R_{MCS}=425\;\Omega$

Will this circuit work without drawing any more than the 0.35 A from the main battery? 

 {{ 184_projects:hawkioncircuit_1.jpg?600 }}


<WRAP info>
=== Learning Goals ===
  * Use resistor combination rules to simplify a complex circuit (or parts of a complex circuit)
  * Recognize when resistor combination rules do not apply
  * Use loop rule and current rule to analyze a complex circuit
</WRAP>

==== Wrap Up Questions ====
  - When using the loop rule, how do you decide if you have a voltage gain or a voltage drop for a battery?  What about for a resistor?
  - How would you explain the node rule conceptually? (e.g. in plain English to a roommate or someone not in this class)
  - How would you explain the loop rule conceptually? (e.g. in plain English to a roommate or someone not in this class)
  - When using the loop and node rules, you end up with more equations than the number of unknowns. How do you pick which equations to use?
  - If you have time at the end - you can [[:184_projects:level_up_r| revisit the challenge problem from Week 6]]