Buoyancy of Spheres: max mass added without sinking

[BennyQuixote]

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

F_B=p_oV_og
Volume of sphere: 4/3 π r³
p=m/V

The Attempt at a Solution

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

 

[rl.bhat]

Check the volume of the sphere.

 

[thomate1]

's Answer:

Based on the given information and equations, it seems like your attempt at a solution is correct. However, the resulting mass of 2345 kg does seem quite large and unrealistic. This could be due to various factors such as the assumption that the volume of the added mass is negligible compared to the sphere, or the use of idealized equations that do not fully account for real-world conditions.

In reality, the maximum mass that can be added to a Styrofoam sphere before it sinks in water would depend on various factors such as the shape and density of the added mass, the shape and size of the Styrofoam sphere, and the properties of the water (e.g. temperature, salinity, etc.). It may also be affected by external factors such as surface tension and air pockets on the surface of the sphere.

To accurately determine the maximum mass that can be added to a Styrofoam sphere without sinking, it would be necessary to conduct experiments and account for all the relevant variables. Additionally, it is important to note that buoyancy is not the only factor that determines whether an object sinks or floats in water. Other forces such as gravity and drag also play a role and may need to be considered in a more comprehensive analysis.

In summary, while your attempt at a solution is valid based on the given information and equations, it may not accurately reflect real-world conditions. To obtain a more accurate and realistic answer, it would be necessary to conduct experiments and account for all relevant variables.