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Contrary to what you might expect, a solid steel ball can
Chapter 2, Problem 99P(choose chapter or problem)
Problem 99P
Contrary to what you might expect, a solid steel ball can float on water due to the surface tension effect. Deter mine the maximum diameter of a steel ball that would float on water at 20°C. What would your answer be for an aluminum ball? Take the densities of steel and aluminum balls to be 7800 kg/m3 and 2700 kg/m3, respectively.
Questions & Answers
QUESTION:
Problem 99P
Contrary to what you might expect, a solid steel ball can float on water due to the surface tension effect. Deter mine the maximum diameter of a steel ball that would float on water at 20°C. What would your answer be for an aluminum ball? Take the densities of steel and aluminum balls to be 7800 kg/m3 and 2700 kg/m3, respectively.
ANSWER:
Solution
Introduction
Consider a solid ball is floating on water due to the surface tension effect whose weight is equal to the product of mass and force due to gravity.
Step 1
The temperature of the water is constant and is 200 C
The surface tension of water at 200 C σs =0.073 N/m
The surface tension σs =
The surface tension force F = σs A
F = σs (πD)
Weight of the solid W = mg = (ρV)g
V is the volume =
So W = ρ()g