Question

Styrofoam has a density of 32kg/m^3. What is the maximum mass that can hang without sinking from a 70-cm diameter Styrofoam sphere in water? Assume the volume of the mass is negligible compared to that of the sphere. Express your answer to two significant figures and include the appropriate units.

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Density of water = _w = 1000 kg/m³

Density of styrofoam = = 32 kg/m³

Diameter of the styrofoam sphere = D = 70 cm = 0.7 m

Volume of the styrofoam sphere = V

V = D³/6

V = (0.7)³/6

V = 0.179 m³

Maximum mass that can hang from the styrofoam sphere without sinking it = m

To hang maximum mass from the styrofoam sphere without sinking it the whole styrofoam sphere is submerged in water because of the hanging mass.

Buoyancy force on the styrofoam sphere = F_b = _wVg

The weight of the styrofoam sphere and the mass hanging from it is supported by the buoyancy force.

mg + Vg = _wVg

m + V = _wV

m = (_w - )V

m = (1000 - 32)(0.179)

m = 173.27 kg

Rounding off to two significant figures,

m = 1.7 x 10² kg

Maximum mass that can be hanged from the styrofoam sphere without sinking it in water = 1.7 x 10² kg