Density
The density (p) of a material is its mass per unit volume, and it’s a measure of how compact a
substance is. You can calculate density using the following equation: p = m/v
Upthrust
Objects in fluids may experience a force called upthrust due to different pressures being exerted
on the surface of the object.
In order to fully understand the origin of upthrust, you should be aware of the following equation
used to calculate pressure (p):
Archimedes’ principle
Archimedes’ principle states that the upthrust experienced by an object is equal to the weight of
the fluid it displaces. Upthrust = weight of fluid displaced
fully submerged
If an object is fully submerged, then the volume of the displaced fluid is just equal to the volume
of the object.
Stokes’ law
Stokes’ law
The resistive force experienced by an object moving in a fluid is known as viscous drag force.
This force is labelled as Fa
Stokes Law conditions
The viscous drag force exerted on an object can be calculated using Stokes’ law if the following
conditions apply:
. The object is small + spherical
. The object moves at a low speed with laminar flow.
Laminar flow
Laminar flow is where the particles in a fluid move by following smooth
paths with little to no mixing between adjacent layers of the fluid.
Turbulent Flow
On the other hand, turbulent flow is where particles in the fluid mix
between layers and form separate currents, because of this, turbulent flow is often described as
chaotic.
Viscosity s increases.
Viscosity is a measure of how resistant a fluid is to deformation (e.g. caused by an object moving
through it). A fluid’s viscosity is determined by the internal frictional forces that occur between
adjacent layers of the fluid.
It is important to note that viscosity is temperature dependent:
. In (most) liquids -
As temperature increases, the viscosity of a liquid decreases.
. In gases
As temperature increases, the viscosity of a gas increases.
Hooke’s law
Hooke’s law states that extension is directly proportional to the force applied, given that the
environmental conditions (e.g temperature) are kept constant.
Young modulus
The Young modulus is a value which describes the stiffness of a material.
It is known that up to the limit of proportionality (explained below), for a material which obeys
Hooke’s law, stress is proportional to strain, therefore the value of stress over strain is constant,
this value is the Young modulus.
Stress
Stress - Force applied per unit cross-sectional area.
Strain
Strain - This is caused by stress, and is defined as the change in length over the original length.
Force-extension and force-compression graphs
Force-extension and force-compression graphs
Force-extension graphs show how the extension of an object varies with the force applied to it.
Hooke’s law can be demonstrated by a force-extension graph which is a straight line through
the origin as this shows that force and extension are directly proportional.
limit of proportionality (P)
The limit of proportionality (P) is the point after which Hooke’s law is no longer obeyed.
elastic limit (E)
The elastic limit (E) is just after the limit of proportionality and if you increase the force applied
beyond this, the material will deform plastically (be permanently stretched).
yield point
The yield point is the point at which the material begins to stretch without an increase in load.
Elastic deformation
Elastic deformation is where a material returns to its original shape once the force applied is
removed. This is because all the work done is stored as elastic strain energy.
Plastic deformation
Plastic deformation is where a material’s shape is changed permanently. This is because work is
done to move atoms apart, so energy is not only stored as elastic strain energy but is also
dissipated as heat.
Force-compressions graphs
Force-compressions graphs show how the compression of an object varies with the force
applied to it.
Solids usually behave similarly when tensile and compressive forces are applied, therefore
force-extension and force-compression graphs often look very similar. The main difference being
that beyond the elastic limit, compressed solids will buckle (suddenly change shape) and break
instead of extending plastically.
Stress-strain graphs
Stress-strain graphs are similar to force-extension graphs, however they describe the behaviour
of a material rather than the behaviour of a specific object.
Ductile
can undergo a large amount of plastic deformation before fracturing
Brittle
where a material undergoes little to no plastic deformation before fracturing (break
apart) at a low strain
Plastic
where a material will experience a large amount of extension as the load is
increased.
