Question

An object with a density of 681.0 kg/m3 and a mass of 1831.0 kg is thrown into the ocean. Find the volume that sticks out of the water. (use ρseawater = 1024 kg/m3)

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Density of seawater = _w = 1024 kg/m³

Mass of the object = M = 1831 kg

Density of the object = = 681 kg/m³

Volume of the object = V

M = V

1831 = (681)V

V = 2.689 m³

Volume of the object submerged under seawater = V_s

Buoyancy force on the object = F_b = _wV_sg

The object floats in seawater therefore the buoyancy force on the object is equal to the weight of the object.

Mg = F_b

Mg = _wV_sg

M = _wV_s

1831 = (1024)V_s

V_s = 1.788 m³

Volume of the object that sticks out of the water = V₀

V = V_s + V₀

2.689 = 1.788 + V₀

V₀ = 0.901 m3

Volume of the object that sticks out of the water = 0.901 m³