Physics quiz question: identical blocks in different density fluids

Physics 205A Quiz 5, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 9.27, 9.31

Two objects (same volumes, same densities) either rest on the bottom of an oil-filled tank, or rest on the bottom of a water-filled tank. The density of water is greater than the density of oil. Both tanks are filled to the same level. The object submerged in __________ experiences a greater normal force.
(A) oil.
(B) water.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (A)

Both objects have the same weight force w (being the same volume and same density) downwards, but experience different upwards bouyant forces:

F_B = ρ_fluid·g·V_sub.

Submerged volume is the same for either object, as they are both fully submerged, such that the bouyant force F_B is greater for the object in water, as water has a greater fluid density ρ_fluid than oil.

From Newton's first law, since both objects are stationary, then the magnitude of the downwards weight force must be equal to the sum of the magnitudes of the upwards bouyant force and upwards normal force:

w = F_B + N.

Since the weight force w is the same for both objects, and the bouyant force F_B is larger for the object in water, then the normal force is larger for the object in oil.

Sections 70854, 70855
Exam code: quiz05t0rQ
(A) : 19 students
(B) : 12 students
(C) : 19 students
(D) : 0 students
(No response: 1 student)

Success level: 37%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.72