Suppose that a ceramic cup floats in water as in Fig. P4.5. The height of the cylindrical cup equals its diameter (2R) and its walls are thin (W ≪ R). Its rim rests at a height H above the water surface. The dimensions are large enough that surface tension is negligible.

(a) Show how to calculate the specific gravity of the ceramic (ρ_o/ρ) from R, H, and W. If W/R = 0.1 and the cup is three-quarters submerged (H = R/2), what is the value of ρ_o/ρ?

(b) Suppose that the cup in part (a) is now partly filled with water. Beyond what water depth D would it sink?

(c) For what values of ρ_o/ρ would such a cup never float, even if empty?

Transcribed Image Text:

Air P = Po Water P Ceramic Po 2R ļ ļ Figure P4.5 Ceramic cup floating in water. R H -W