Physics clicker question: buoyancy comparison

Physics 5A, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Question 9.6 (extended)

Students were asked the following clicker question (Classroom Performance System, einstruction.com) at the beginning of their learning cycle:

Three objects (same volumes, but different densities) float (or do not float) in a tank of water.

[0.6 participation points.] Which object has the greatest weight?
(A) Object X.
(B) Object Y.
(C) Object Z.
(D) (More than one of the objects listed above has the greatest weight.)
(E) (I'm lost, and don't know how to answer this.)

Sections 0906, 0907
(A) : 1 student
(B) : 0 students
(C) : 29 students
(D) : 2 students
(E) : 0 students

Correct answer: (C)

Most students appealed to their intuition to determine that Object Z was the heaviest. Weight force vectors are now drawn on the diagram, and the next question is asked.

[0.6 participation points.] Which object has the greatest bouyant force exerted on it?
(A) Object X.
(B) Object Y.
(C) Object Z.
(D) (More than one of the objects listed above has the greatest bouyant force exerted on it.)
(E) (I'm lost, and don't know how to answer this.)

Sections 0906, 0907
(A) : 22 students
(B) : 3 students
(C) : 2 students
(D) : 7 students
(E) : 0 students

Correct answer: (D)

The magnitude of the bouyant force is the weight of the volume of water displaced. Object X displaces only a portion of its volume, and thus has the least amount of bouyant force exerted on it. Both Objects Y and Z are completely submerged, and thus have the same amount of bouyant force exerted on it. (However, Object Z also has a normal force exerted on it, from the bottom of the tank.)