Hooke’s law
The force needed to stretch a spring is directly proportional to the extension of the spring from its natural length provided the elastic limit hasn’t been exceeded
Springs in parallel and series
For two springs p and q:
In parallel the effective Spring constant = Kp + Kq
In series the effective Spring constant:
1/K = 1/Kp + 1/Kq
Elastic limit
Point beyond which an object is permanently deformed/stretched
The wire is permanently stretched and suffers plastic deformation
Elasticity
The ability of a material to be deformed by a force and when the force is removed it will return to its original shape
Tensile stress
The force per unit cross sectional area
= T/A where T is tension
Unit is pascal (Pa) 1Pa = 1Nm^-2
Tensile strain
The ratio of extension to length
= dL/L where dL is extension
Strain is a ratio so has no unit
Yield point
Point at which the stress in a wire suddenly drops when the wire is subjected to increasing strain
Ultimate tensile stress/breaking stress
Tensile stress required to break a solid material
This measures the maximum stress experienced before breaking not the stress when the object does break
Gives a measure of the tensile strength
Brittle material
Will snap without any noticeable yield
Little or no plastic deformation prior to failure
E.g. Glass
Ductile material
The ability of a material to be drawn out under tension reducing the cross sectional area without cracking
For example producing copper wires
Limit of proportionality
The limit beyond which, when a wire or a spring is stretched, its extension is no longer proportional to the force that stretches it
Elastic deformation
Once the force has been removed the object will return to its original shape
Atoms move small distances relative to their equilibrium positions but without actually changing their positions - so they are able to return to equilibrium
Occurs as long as the elastic limit hasn’t been exceeded
Work done is stored as elastic strain energy
Plastic deformation
The material is permanently stretched
The atoms move positions relative to each other and when the load is removed they don’t return to their original positions
Occurs when materials are stretched past their elastic limit
Strain energy
The work done to deform an object
Why is rubber used for aeroplane tyres?
It is elastic, the area under the graph between the loading and unloading represents the net output of work that is transferred to thermal energy
This means some of the kinetic energy of the aeroplane is transferred to thermal energy, so the plane doesn’t bounce when landing
