Density and pressure

Define density, its equation and SI base unit

The mass per unit volume

ρ = m/V

ρ = density, kgm^-3

m = mass, kg

V = volume, m³

Define pressure, its equation, its standard and SI base unit

Normal force exerted on a surface per unit cross sectional area

P = F/A

P = pressure, Pa, Pascal, Nm^-2, kgm^-1s^-2

F = force, N

A = cross sectional area,m²

How do we measure the mass and volume of different objects?

Mass - ALWAYS measured with a scale

Volume -

Liquids, measuring cylinders

Regular solid, Vernier callipers to measure each side length and use the volume formula

Irregular solid, object fully submerged in a measuring cylinder or eureka can, change in volume = volume of object

Describe pressure in fluids using a column of fluid and its formula

It experiences pressure due to the weight of the fluid, making the pressure is the same in all direction and the formula is

P = hρg

P = pressure, Pa, kgm^-1s^-2

h = height of fluid column, m

ρ = density of fluid, kgm^-3

g = acceleration of free fall, g, 9.81ms^-2

How is the equation for pressure derived using a column of fluid?

W = mg

m of column = ρ x V

W = ρVg

As the column is a cylinder V = A x h

W = ρAhg

As W = F, P = F / A

P = ρAhg / A

P = ρhg

State Archimedes principle

‘The up thrust exerted on an object immersed in a fluid, whether partially or fully submerged, is equal to the WEIGHT of the FLUID that the body DISPLACES’

What happens when an object is submerged in water and why

It experiences an upward force, up thrust. This is because the pressure at the bottom surface of the object is greater that at its top surface.

Summarise Archimedes principle and the effect it has

Weight of water displaced = up thrust of object

The object will sink if the up thrust acting up is less than the weight acting down.

The object will float if the up thrust acting up is equal to the weight acting down.