Physics midterm question: cargo ship traveling from saltwater to freshwater ports

Physics 205A Midterm 2, fall semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 9.29(a)

"P1050821" (Tropical Fresh (TF), Tropical Seawater (T))
Darren B. Hillman
flic.kr/p/pdSe7Z

A National Park Service newsletter for the San Francisco Maritime National Historical Park describes the following scenario:

Imagine you are the captain of a gigantic cargo ship. You loaded your ship in a saltwater port in Japan, traveled across the entire Pacific Ocean, and are heading to a freshwater port in the San Francisco Bay to unload. As you travel from saltwater to freshwater, your ship's hull will sink deeper into the water[*].

Discuss why the ship will be lower in freshwater (1,002 kg/m³) than in saltwater (1,025 kg/m³). Explain your reasoning using the properties of densities, volumes, forces, Newton's laws, and Archimedes' principle (buoyant forces), and free-body diagrams.

[*] National Park Service, U.S. Department of the Interior, "Kids Fun Page—Float or Sink?" The Maritime News (July-August 2008), p. 4, nps.gov/safr/parknews/upload/maritimenews21.pdf.

Solution and grading rubric:

• p:
  Correct. Recognizes that:
  1. the mass and weight of the ship is constant;
  2. from Newton's first law the buoyant force is equal to the weight force in either case, thus the buoyant force is the same in either saltwater or freshwater;
  3. so in order to have the same buoyant force in freshwater (lower density) as in saltwater (higher density), the volume submerged must be greater for freshwater than in saltwater.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Typically only has two of the (1)-(3) points to be made in (p).
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. As (r), but one of the two points being made is garbled.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some constructive attempt at relating the buoyant force to the density of the fluid and volume displaced (Archimedes' principle) and/or Newton's first law, but typically argues that there is less buoyant force on the ship in freshwater than in saltwater.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Appeal to some other properties of fluids and densities other than Archimedes' principle and Newton's laws.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm02j0R6
p: 17 students
r: 18 students
t: 9 students
v: 17 students
x: 6 students
y: 0 students
z: 0 students

A sample "p" response (from student 7810):