Density, pressure and buoyancy

Learning objectives

Calculate density as ρ = m/V, explain how it follows from the internal structure and spacing of the particles in a substance, and use it to compare materials

Define pressure as the magnitude of the force applied perpendicular to a surface divided by the area of that surface, and explain why pressure at a point in a static fluid acts equally in all directions

Calculate absolute pressure at a depth as P = P₀ + ρgh, distinguish it from gauge pressure, and explain why the pressure depends on depth but not on the shape of the container

Explain the origin of the buoyant force as the pressure difference between the bottom and the top of a submerged object, and apply Archimedes' principle to calculate it as the weight of displaced fluid

Construct a free-body diagram for a floating or submerged object and decide whether it rises, sinks or stays in equilibrium by comparing its density with that of the fluid

Calculate the fraction of a floating object that is submerged, and design a procedure to find the density of an irregular solid from its weight in air and its apparent weight in a fluid