CHAPTER 13: FLOATING AND SINKING

Why does a ship made of steel float, while a small stone sinks? Why does an egg float in salt water but sink in fresh water? The answers lie in the principles of buoyancy discovered by Archimedes over 2,000 years ago. This chapter explores the relationship between weight, volume, and density that determines whether objects float or sink. Understanding these principles is essential for naval architecture, hydrometry, and understanding the behaviour of fluids.

13.1 DENSITY AND RELATIVE DENSITY

Before we can understand floating and sinking, we must understand density.

13.1.1 Density (ρ)

Density is defined as mass per unit volume. It tells us how much matter is packed into a given space.

ρ = m / V

Where:

• ρ = density (kg/m³ in SI units, or g/cm³)
• m = mass (kg or g)
• V = volume (m³ or cm³)

Common densities:

• Water: 1000 kg/m³ = 1 g/cm³
• Ice: 920 kg/m³ (0.92 g/cm³)
• Iron: 7870 kg/m³ (7.87 g/cm³)
• Mercury: 13,600 kg/m³ (13.6 g/cm³)
• Air: 1.2 kg/m³ (at sea level)

13.1.2 Relative Density (R.D.)

Relative density (also called specific gravity) is the ratio of the density of a substance to the density of a reference substance—usually water for liquids and solids, and air for gases. Since it is a ratio, it has no units.

R.D. = (density of substance) / (density of water)

For solids and liquids:

R.D. = ρ_substance / ρ_water

Since density = m