Understanding matter
Matter is made of particles, and the arrangement and motion of those particles help explain the properties of solids, liquids, and gases.
Density
Density describes how much mass is contained within a given volume. It is useful when comparing different materials and understanding whether an object is likely to float in a fluid.
ρ = m / V
Density equals mass divided by volume.
Pressure
Pressure describes how much force acts perpendicular to a surface per unit area.
P = F / A
A smaller area produces greater pressure for the same force.
Pressure is particularly important in fluids because a fluid at rest exerts pressure in all directions.
Pressure in fluids
In a fluid at rest, pressure generally increases with depth because the fluid above contributes to the force acting on lower layers.
P = P₀ + ρgh
P₀ is the pressure at the reference surface, ρ is fluid density, g is gravitational field strength, and h is depth.
Pascal's principle
When pressure is applied to an enclosed fluid, the pressure change is transmitted throughout the fluid.
This principle is used in hydraulic systems, where a force applied to one piston can produce a larger force at another piston with a greater area.
F₁ / A₁ = F₂ / A₂
The pressure is equal throughout an ideal enclosed fluid.
Buoyancy
An object placed in a fluid experiences an upward force called buoyant force. This happens because fluid pressure is greater at greater depth.
Archimedes' principle gives a useful way to calculate this force.
Fᵦ = ρVg
The buoyant force equals the weight of the displaced fluid.
Elasticity
An elastic material can return toward its original shape after the deforming force is removed, provided the deformation stays within the material's elastic limit.
Springs provide a simple model for studying elastic behaviour.
F = −kx
k is the spring constant and x is displacement from the equilibrium position. The negative sign represents the restoring direction.
Viscosity
Viscosity describes a fluid's resistance to flow. A highly viscous fluid flows less easily than a fluid with low viscosity.
Viscosity becomes especially important when studying real fluid motion, where friction within the fluid cannot be ignored.
Why do objects float?
Whether an object floats depends on the relationship between its weight and the buoyant force acting on it.
Quick example
A material has a mass of 200 g and occupies a volume of 100 cm³. What is its density?
Using:
ρ = m / V
ρ = 200 / 100