20080423

Physics quiz question: floating block of wood

Physics 5A Quiz 5, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 9.32

[3.0 points.] A block of oak wood (880 kg/m^3) floats in oil with 70.0% of its volume submerged. What is the density of the oil?
(A) 264 kg/m^3.
(B) 616 kg/m^3.
(C) 795 kg/m^3.
(D) 1.26 x 10^3 kg/m^3

Correct answer: (D)

The bouyant force on a partially submerged object is equal to the weight of the fluid displaced, F_B = rho_fluid*g*Vol_displaced, where Vol_displaced = 0.700*Vol_object. Since the object is in static equilibrium:

w = F_B
rho_object*g*Vol_object = rho_fluid*g*0.700*Vol_object,
rho_object/0.700 = rho_fluid,

which is response (D). Response (B) = 0.700*rho_object; response (A) = (1 - 0.700)*rho_object, and response (C) is 700,000/rho_object. Note that for the wood to float in oil, the density of oil must be greater than that of the wood--this condition can only be satisfied by response (D).

Student responses
Sections 4987, 4988
(A) : 0 students
(B) : 10 students
(C) : 3 students
(D) : 20 students

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