Physics midterm question: rising water level in dry dock

Physics 205A Midterm 2, fall semester 2015
Cuesta College, San Luis Obispo, CA

“Cruise Ship timelapse - Extension of Braemar at Blohm+Voss”
MK timelapse GmbH
youtu.be/QirVr-pEVU4

A cruise ship rests on the floor of a dry dock with a small amount of water. As the water level rises (but not enough water to "float" the ship yet, so it is still resting on the bottom of the dry dock), discuss why the normal force of the floor on the ship decreases. Explain your reasoning using the properties of densities, volumes, forces, Newton's laws, Archimedes' principle (buoyant forces), and free-body diagrams.

Solution and grading rubric:

• p:
  Correct. Recognizes that:
  1. from Newton's first law the downwards weight force (which has a constant magnitude, as its mass remains constant) on the ship is equal to the two upwards buoyant and normal forces on the ship;
  2. as the water level rises, the amount of the ship's submerged volume increases, increasing the amount of buoyant force on the ship (Archimedes' principle);
  such that the normal force must decrease in magnitude in order for the two upwards forces to still balance the downwards weight force.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete.
• 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.
• x:
  Implementation 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: midterm02h4W6
p: 47 students
r: 10 students
t: 4 students
v: 9 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 3158):