Physics final exam problem: USS Iowa passing through Panama Canal

Physics 205A Final Exam, fall semester 2016
Cuesta College, San Luis Obispo, CA

"USS Iowa Pedro Miguel Locks"
National Archive #NN33300514 2005-06-30 PH1 JEFF HILTON
commons.wikimedia.org/wiki/File:USS_Iowa_Pedro_Miguel_Locks.jpg

One of the widest ships to pass through the Panama Canal was the USS Iowa, which has an outside width of 32.97 m. The narrowest portion of the Panama Canal is through the Pedro Miguel locks, which has an inside width of 33.53 m. Assume that the USS Iowa is entirely made of steel (coefficient of thermal expansion 12×10^–6 K^–1), the Pedro Miguel locks are entirely made of concrete (coefficient of thermal expansion 9.8×10^–6 K^–1), and that these widths were measured at 20° C. Determine whether or not it is plausible for this ship to still pass through the locks, if the ship and the canal are both at the highest reported temperature for this area of 39° C. [*][**][***][****]

[*] wki.pe/USS_Iowa_(BB-61).
[**] wki.pe/Panamax.
[***] engineeringtoolbox.com/linear-expansion-coefficients-d_95.html.
[****] wki.pe/Panama_City.

Solution and grading rubric:

• p:
  Correct. Determines/discusses:
  1. the expansion and/or new width of ship at the warmer temperature; and
  2. the expansion and/or new width of the locks at the warmer temperature; then
  3. compares either the relative difference in expansion, or the new expanded widths, and concludes that the expanded size of the ship will still fit within the expanded size of the locks.
• r:
  Nearly correct, but includes minor math errors.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least enough steps are shown that would theoretically result in a complete answer, multiple errors notwithstanding.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some garbled attempt at comparing linear thermal expansion of the ship and the locks.
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach involving methods other than linear thermal expansion.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: finali0w4
p: 28 students
r: 9 students
t: 1 student
v: 9 students
x: 1 student
y: 0 students
z: 1 student

A sample "p" response (from student):