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

[Masschaos]

Homework Statement

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.

Homework Equations

F_B = ρ^fVg
F_g = mg

The Attempt at a Solution

So this is as far as I can get.
The buoyancy force on the sphere is F_B = ρ^fVg = 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 F_net = 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 that's not it, any pointers?

 

[SHISHKABOB]

well first off, the DIAMETER is 20 cm

 

[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.

 

[SHISHKABOB]

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.

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

 

[asteriatic]

Based on your calculations, it seems you have correctly determined the maximum mass that the styrofoam sphere can hold in water. However, it is important to note that this is only an approximation since the density of styrofoam can vary and the weight of the sphere itself may also vary. Additionally, there may be other factors at play such as surface tension and the shape of the mass being hung from the sphere. It would be beneficial to conduct experiments to determine the exact maximum mass that the sphere can hold under different conditions.