Floating Duck with Oil and Water · USAPhO 2013 #A4
Physics · fluid-mechanics
Problem
A graduated cylinder is partially filled with water; a rubber duck floats at the surface. Oil is poured into the graduated cylinder at a slow, constant rate, and the volume marks corresponding to the surface of the water and the surface of the oil are recorded as a function of time.
[Figure: Graph showing Volume (mL) vs Time (min) from 0-10 minutes. Two curves are shown: "Volume mark at water surface" starting at about 175 mL and rising to about 275 mL, and "Volume mark at oil surface" starting at about 175 mL and rising to about 450 mL.]
Water has a density of 1.00 g/mL; the density of air is negligible, as are surface effects. Find the density of the oil.