Question

Styrofoam has a density of 300kg/m3. What is the maximum mass that can hang without sinking from a 90.0 cm -diameter Styrofoam sphere in water?Assume the volume of the mass is negligible compared to that of the sphere.

Answer 1

the system of the mass and the sphere will have to have a maximum density of 1g/cm3 to avoid sinking.

density is mass / volume

mass = mass of the sphere + the mass hanging

volume = volume of the sphere + volume of the hanging mass

but you assume the volume of the hanging mass is negligible so it is zero

therefor volume = volume of the sphere + ZERO = volume of the sphere

now we need the volume and mass of the sphere

volume of the sphere = (4/3)*pi*r³ = 4*3.14*(45)³/3 = 381510 cm³

mass of the sphere is its volume * density of the sphere

density of the sphere 300*1000/1000000 g/cm³ = 0.3 g/cm³

mass of the sphere = 381510*0.3 =114453g

now we can calculate the overall system density which should be equal to 1 g/cm^3

1 = (mass of sphere + hanging mass) / (system volume which is equal to sphere volume)

1 = (114453 + X) /381510

X =267057 g = Approximately 267.057 kg