Question

Styrofoam has a density of 300kg/m3. What is the maximum mass that can hang without sinking from a 20.0 cm -diameter Styrofoam sphere in water?

Assume the volume of the mass is negligible compared to that of the sphere.

Answer 1

Gravitational acceleration = g

Density of water = _w = 1000 kg/m³

Density of styrofoam = = 300 kg/m³

Diameter of the styrofoam sphere = D = 20 cm = 0.2 m

Volume of the styrofoam sphere = V

V = D³/6

Mass attached to the styrofoam so that the styrofoam doesn't sink = m

The styrofoam sphere will be completely submerged for maximum mass to be hanged from it.

The buoyancy force on the styrofoam sphere supports the weight of the styrofoam sphere and the mass.

_wVg = Vg + mg

m = V(_w - )

m = D³(_w - )/6

m = (0.2)³(1000 - 300)/6

m = 2.932 kg

Maximum mass that can hang without sinking the styrofoam sphere in water = 2.932 kg