3.2.4 Density and pressure

Density
The density of a substance is defined as its mass per unit volume:

ρ = m / v

Unit: kg m^-13

Okay so it doesn't explicitly state in the spec that we need to know methods of determining density but I have a feeling we should so here goes. We need to measure the mass and volume of the object. Mass can be measured using a digital balance. We can calculate the volume of regular shapes (e.g a cuboid) by taking measurement with a ruler or we can submerge irregular shapes in a measuring cylinder of water and see how much the water is displaced. Now do ρ = m / v.

Pressure
Pressure is the normal contact force exerted per unit cross-sectional area:

p = F / A

Unit: N  m^-2

Archimedes' principle
We need to know about pressure in liquids and gases too, not just in solids. Gases and liquids exert pressure on surfaces because of the constant bombardment by their molecules.

We can calculate the pressure exerted by a vertical column of a liquid using:

p = hρg

The buoyant force on submerged objects can be explained in terms of pressure differences at its upper and lower surfaces.

Force at the top surface = hρgA
Force at the bottom surface = (h + x) ρgA
Resultant upward force = (h + x)ρgA - hρgA
Upthrust = xρgA

The volume of the object is Ax and it has mass Axρ so the upthrust is equal to the weight of the fluid displaced. This is Archimedes' principle, 'when an object is immersed fully or partially in a fluid, the upward force applied by the fluid on the object is the same as the weight of the fluid displaced by the object'.

If upthrust is less than weight the object will sink. For floating objects upthrust must equal the weight of the object.