Question
A cube of polystyrene measuring 10 cm per side lies partially submerged in a large container of water.
1. If 90% of the polystyrene floats above the surface of the water, what is the density of the polystyrene? (Note: The density of water is 1000 kg/m3.)
2. A 0.5 kg mass is placed on the block of polystyrene. What percentage of the block now remains above water?
3. The water is poured out of the container and replaced with ethyl alcohol (density = 790 kg/m3).
1. Will the block be able to remain partially submerged in this new fluid? Explain.
2. Will the block be able to remain partially submerged in this new fluid with the 0.5 kg mass placed on top? Explain.
4. Without using a container of water, explain how you could determine the density of the polystyrene mentioned above if the material instead were spherical.
1. $100 \textrm{ kg/m}^3$
2. $40\%$
3. i) Yes, it will float, with 13% submerged. ii) Yes, it will float with 76% submerged.
4. Use a scale to measure mass and a tape measure to measure circumference, then calculate the density.
Solution Video

# OpenStax College Physics Solution, Chapter 11, Problem 3 (Test Prep for AP® Courses) (7:05)  