Buoyancy of Spheres: max mass added without sinking

AI Thread Summary
The discussion revolves around calculating the maximum mass that can be added to a Styrofoam sphere without it sinking in water. The density of Styrofoam is given as 300 kg/m3, and the sphere's diameter is 40 cm. The participant initially calculated the maximum mass to be 1005 kg but realized this figure was excessively large. A suggestion was made to recheck the volume calculation of the sphere, indicating a potential error in the initial approach. The conversation highlights the importance of accurate volume calculations in buoyancy problems.
BennyQuixote
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Homework Statement



Styrofoam has a density of 300 kg/m3. What is the maximum mass that can hang without sinking from a 40-cm-diameter Styrofoam sphere in water? Assume the volume of the mass is negligible compared to that of the sphere.

Homework Equations



FB=poVog
Volume of sphere: 4/3 π r3
p=m/V

The Attempt at a Solution



I tried this:
mo/3.35 m3=300 kg/m3
Therefore,
mo=1005 kg

So,
To find the exact amount of mass added to the Styrofoam sphere to sink in water:
1005k + m2/3.35 m3=1000 kg/m3

Therefore:
m2=2345 kg

This is obviously an obscenely large mass to make Styrofoam sink in water. Any help is appreciated.


Quixote
 
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Check the volume of the sphere.
 
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