Homework Help: Buoyancy - Maximum mass a styrofoam sphere can hold in water.

1. May 17, 2012

Masschaos

1. The problem statement, all variables and given/known data
Styrofoam has a density of . What is the maximum mass that can hang without sinking from a 20.0 -diameter Styrofoam sphere in water?
Assume the volume of the mass is negligible compared to that of the sphere.

2. Relevant equations
FB = ρfVg
Fg = mg

3. The attempt at a solution
So this is as far as I can get.
The buoyancy force on the sphere is FB = ρfVg = 1000kg/m3 * pi * 0.22 * 9.8 = 333.54.
However we need to take into account the weight of the sphere.
The weight of the sphere = ρ*V = 300*pi*0.22 = 10.2
This means the net weight on the sphere is Fnet = 333.54 - (10.2*9.8) = 233.54
So the maximum weight that can be hung on the sphere must have a downward force of precisely that. mg = 233.54. m = 23.8kg.
But apparently thats not it, any pointers?

2. May 17, 2012

SHISHKABOB

well first off, the DIAMETER is 20 cm

3. May 17, 2012

Masschaos

Oh wow. Just a multitude of stupid mistakes!
The diameter is 20cm so the radius is 10cm. AND the volume of a sphere is 4/3 pi r^3, I was doing the area of a circle.
Argh, I'll hang my head in shame now.

4. May 17, 2012

SHISHKABOB

heh, don't worry, we all make mistakes like that

I even saw one of my professors do the same thing in a lecture; he used the diameter instead of radius