Density

Density is a fundamental property of matter that describes how much mass is contained in a given volume. It is a key concept in understanding whether an object will float or sink in a fluid.

Definition of Density

Density ($ \rho $ ) is defined as the mass ($ m $) per unit volume ($ V $ ) of a substance.

$$ \rho = \frac{m}{V} $$

The standard SI unit for density is kilograms per cubic meter (kg/m³). Other common units include grams per cubic centimeter (g/cm³) and pounds per cubic foot (lb/ft³).

Why is Density Important for Floating?

Whether an object floats or sinks depends on its density relative to the density of the fluid it is in.

An object will float if its density is less than the density of the fluid. It will sink if its density is greater than the density of the fluid. If the densities are equal, the object will be neutrally buoyant and will neither float nor sink.

Calculating Density

Density can be calculated using the following formula:

$$ \rho = \frac{m}{V} $$

Where:

• $ \rho $ is the density (kg/m³, g/cm³, etc.)
• $ m $ is the mass (kg, g, etc.)
• $ V $ is the volume (m³, cm³, etc.)

Example: Determining if an Object Floats

To determine if an object will float, you need to compare the object's density to the density of the fluid it is placed in.

If $ \rho_{object} < \rho_{fluid} $, the object will float.

If $ \rho_{object} > \rho_{fluid} $, the object will sink.

If $ \rho_{object} = \rho_{fluid} $, the object will be neutrally buoyant.

Table of Densities (Approximate Values at Room Temperature)

Substance	Density (kg/m3)
Air	1.225
Water	1000
Iron	7874
Wood (Oak)	700-800
Plastic (e.g., polystyrene)	0.90 - 1.0

Experiment: Determining the Density of an Object

An experiment can be performed to determine the density of an object by measuring its mass and volume. For a regular shaped object, the volume can be easily calculated using geometric formulas. For an irregular shaped object, water displacement can be used.

Water Displacement Method:

1. Fill a graduated cylinder with a known volume of water.
2. Carefully submerge the object in the water.
3. Measure the new water level.
4. The volume of the object is the difference between the new and initial water levels.
5. Calculate the density using the formula: $ \rho = \frac{m}{V} $

Practice Problems

1. An object has a mass of 200g and a volume of 50 cm³. What is its density?
2. A block of wood has a mass of 500g and a volume of 200 cm³. Will it float in water? (Density of water = 1 g/cm³)