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Mechanics & Stress Analysis*
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  • A-Level Physics


Materials can have many different properties, and experience a number of external and internal forces. The two main such forces are the tensile and compressive forces, relating to extension (stretching) and compression (squishing) respectively.

Hooke's Law

The most common example of these forces being applied are in a helical spring: these have a natural length, and are either stretched or compressed depending on direction of force applied. The distance of this deformation is called the extension (regardless of direction) and according to Hooke's law:

Extension is directly proportional to the force applied, provided the elastic limit is not passed
Hooke's Law graph, direct proportion of spring constant up to elastic limit. Plastic Deformation. A-Level Physics Revision Study Guide Notes. Engineering Notes

As you can see in the graph, the relationship is linear, where the gradient is the force constant up to the elastic limit - if this is exceeded, the object will no longer return to its initial shape, - plastic deformation has occurred. 

F = kx Force = force constant x extension

Multiple String Systems

Springs (and indeed any elastic materials) can be combined either in series or in parallel, with vastly different effects:

Spring Constant in series and parallel diagram and equations. A-Level Physics revision study guide notes. EngineeringNotes

Elastic Potential Energy

All springs, just like any object under tensile or compressive forces, store Elastic Potential Energy. This is equivalent to the work done in extending/compressing them, and since W = Fx, this is the area under a force-extension graph.

Force Extension Graph showing Area as work done energy stored in system. A-Level Physics Revision Study Guide Notes. EngineeringNotes
W = 1/2 Fx E = 1/2 Fx E = 1/2 k x^2

Stress, Strain & Young Modulus