Physics clicker question: partially- and fully-submerged objects

Physics 205A, Spring Semester 2009
Cuesta College, San Luis Obispo, CA

(Adapted from Fig. 2.1, p. 11, Mazur, Peer Instruction: A User's Manual, Prentice-Hall, Inc., 1997)

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

Two objects (same volumes, same densities) are held either half- or fully-submerged in a tank of water. It is not known whether these two objects are both lighter or denser than water.

Which object has the greatest bouyant force exerted on it?
(A) Object X.
(B) Object Y.
(C) (There is a tie.)
(D) (Depends on whether both these two objects are lighter or denser than water.)
(E) (I'm lost, and don't know how to answer this.)

Sections 30880, 30881
(A) : 5 students
(B) : 25 students
(C) : 2 students
(D) : 1 student
(E) : 0 students

This question was asked again after displaying the tallied results with the lack of consensus, with the following results. No comments were made by the instructor, in order to see if students were going to be able to discuss and determine the correct answer among themselves.

Sections 30880, 30881
(A) : 1 student
(B) : 30 students
(C) : 1 student
(D) : 1 student
(E) : 0 students

Correct answer: (A)

The bouyant force on an object is given by:

F_B = rho*g*V,

where rho is the density of the fluid, and V is the volume displaced by the object--the volume of the object that is submerged under the surface of the liquid. Thus regardless of the density of the objects, and whether the hands are lifting or pushing down on these objects, the submerged object experiences a greater bouyant force than the partially submerged object.

Pre- to post- peer-interaction gains:
pre-interaction correct = 76%
post-interaction correct = 91%
Hake, or normalized gain = 63%