12.12: End-of-Chapter Applied Exercises

End-of-Chapter Applied Exercises

1. Rewrite for precision. Convert each weak statement: (a) "The tension is too high." (b) "Power dissipation seemed okay." (c) "The mass came out about right." (d) "The velocity increases in the middle."
2. Memo practice. Draft a complete six-section memo for: 9 V source, 220 Ω resistor, 0.25 W rating. Is it safe? The analysis takes one calculation; the memo takes six paragraphs.
3. Graph introduction practice. For the cable tension graph you built in Chapter 8, write two sentences introducing it in a Results section: one citing the figure, one stating the key result.
4. Conclusion rewrite. A classmate's Conclusion reads: "In conclusion, the computed power is 0.436 W and the current is 36.4 mA." Identify two problems and rewrite it.
5. TEGO prep. Before doing the TEGO homework, write a one-paragraph Purpose section as you would for a memo. Then list three candidate solutions and the primary trade-off for each.
6. Limitation practice. For each: (a) cable tension, static loading assumed; (b) resistor power, steady-state DC; (c) bracket stress using \(\sigma = F/A\) (axial only) — write a one-sentence limitation statement.
7. Professional email. Write a professional email to your instructor asking for clarification on the TEGO case study assignment. Apply the conventions from §13.9.

Answer Examples - click to expand

1. Rewrite for precision:
   1. Weak: “The tension is too high.”
      Improved: “The computed cable tension is \(14.2\text{ kN}\), which exceeds the \(10.0\text{ kN}\) cable rating by \(4.2\text{ kN}\), so the cable angle or cable size must be changed.”
   2. Weak: “Power dissipation seemed okay.”
      Improved: “The resistor dissipates \(0.172\text{ W}\), which is below the \(0.25\text{ W}\) rating; however, the design uses about \(69\%\) of the rating, so thermal margin should be considered for continuous operation.”
   3. Weak: “The mass came out about right.”
      Improved: “The calculated mass is \(448\text{ g}\), which is within \(2\%\) of the CAD mass estimate, indicating that the material density and unit conversions are consistent.”
   4. Weak: “The velocity increases in the middle.”
      Improved: “The cable car velocity increases as the car approaches midspan, reaching its maximum value near the midpoint where the distance from the nearest tower is greatest.”
2. Memo practice example:

   To: ENGR 110 Instructor
   From: Student Name
   Date: [Insert Date]
   Subject: Power Check for a \(220\text{ Ω}\) Resistor on a \(9\text{ V}\) Source

   Purpose: The purpose of this memo is to determine whether a \(220\text{ Ω}\) resistor connected to a \(9\text{ V}\) source can safely use a standard \(0.25\text{ W}\) power rating.

   Given Information: The circuit uses a \(9\text{ V}\) DC source and a \(220\text{ Ω}\) resistor. The resistor power rating is \(0.25\text{ W}\). The relevant circuit relationships are Ohm’s Law, \(I = V/R\), and resistor power, \(P = V^2/R\).

   Analysis: The current is \(I = 9\text{ V}/220\text{ Ω} = 0.0409\text{ A}\), or \(40.9\text{ mA}\). The resistor power is \(P = V^2/R = (9\text{ V})^2/220\text{ Ω} = 0.368\text{ W}\).

   Results: The resistor dissipates \(0.368\text{ W}\), which is greater than the \(0.25\text{ W}\) rating. The resistor would operate at approximately \(147\%\) of its rated power.

   Conclusion: The \(0.25\text{ W}\) resistor is not safe for this circuit. A higher power rating, such as \(0.5\text{ W}\) or greater, should be selected, or the resistance should be increased to reduce current and power dissipation.

   Recommendation: Use a resistor rated above \(0.368\text{ W}\), preferably with additional thermal margin. A \(0.5\text{ W}\) resistor is the minimum practical improvement, but a larger rating may be appropriate for continuous operation or enclosed spaces.

3. Graph introduction practice:
4. Conclusion rewrite:
   • The conclusion only repeats numerical results; it does not interpret whether the design is acceptable.
   • It does not compare the computed power to a rating, limit, or design requirement.

   Improved conclusion: The resistor dissipates \(0.436\text{ W}\), which exceeds a standard \(0.25\text{ W}\) rating and would not be safe for continuous operation. The circuit should use a resistor with a higher power rating, such as \(0.5\text{ W}\) or greater, or the resistance should be increased to reduce power dissipation.

5. TEGO prep example:

   Candidate solutions and primary trade-offs:

   • Solution A: Simple low-cost design. Primary trade-off: easiest to build and least expensive, but may provide less performance margin.
   • Solution B: Higher-performance design. Primary trade-off: better performance or reliability, but likely requires more material, cost, or assembly time.
   • Solution C: Balanced design. Primary trade-off: may not be the best in any single category, but could provide the strongest overall compromise among cost, performance, and manufacturability.
6. Limitation statements:
   1. Cable tension: This analysis assumes static loading only and does not account for dynamic effects such as swinging, shock loading, vibration, or sudden load application.
   2. Resistor power: This calculation assumes steady-state DC operation and does not account for transient behavior, temperature rise, ventilation, or changes in resistance with heating.
   3. Bracket stress: The equation \(\sigma = F/A\) assumes uniform axial loading and does not account for bending, shear, stress concentrations, buckling, or connection effects.
7. Professional email example:

   Subject: Clarification on TEGO Case Study Assignment

   Dear Professor [Last Name],

   I am working on the TEGO case study assignment and would like to clarify one requirement before I continue. For the candidate solutions section, should we compare three fully developed design alternatives, or is it acceptable to compare one main design with two smaller variations?

   I want to make sure my memo follows the assignment expectations and uses the correct level of detail. Thank you for your time and help.

   Respectfully,

   [Student Name]