S-Cool Revision Summary

S-Cool Revision Summary

Hooke's Law

Measure how a spring stretches as you apply an increasing force to it and you get:

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This shows that Force is proportional to extension. This is Hooke's law. It can be written as:

F = ke

Where:

F = tension acting on the spring

e is extension = (l-lo); l is the stretched length and lo is original length, and;

k is the gradient of the graph above. It is known as the spring constant.

The above equation can be rearranged as:

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Spring constant = Applied force/extension

If you continue to stretch a spring it eventually comes to a point where it stops obeying Hooke's Law.

Hooke's Law Diagram

The point on the graph where it stops obeying Hooke's Law is often called the 'limit of proportionality' because it is the last point at which the deformation of the material is proportional to the force acting on the material.

At about the same moment as it stops obeying Hooke's law, you will notice that if you unload the spring it won't return to its original shape. It has been permanently deformed. We call this point the elastic limit - the limit of elastic behaviour.

If a material returns to its original size and shape when you remove the forces stretching or deforming it, we say that the material is demonstrating elastic behaviour.

Permanent deformation is a sign of plastic behaviour.

Energy in deformations

To calculate the energy stored in a deformed object, find the area under the force - extension graph.

In this example:

Work = ½ force x extension = ½ x 10 x 0.02 = 0.1J

Equations

Deformation of solids

F = ke - Hooke's Law

Work (or energy Stored) = ½ force x extension

Symbols

Deformation of solids

F - Force, N

k - spring constant (or the spring stiffness). Nm-1

e - extension, m

Glossary

Breaking Stress Stress at which material breaks
Deformation Change of size (dimension) under the action of a force
Deformation (elastic) Non-permanent deformation. It disappears when the force casing it are removed i.e. object returns to zero strain condition (reversible deformation)
Deformation (plastic) Permanent deformation; material does not go its original shape after the forces causing it are removed (irreversible deformation).
Density (r) Weight per unit volume (units:kgm-3)
Elastic Behaviour a behaviour of a material exhibiting return to its original size and shape when the forces deforming it is removed (see deformation (elastic)).
Elastic Limit A limit (of stress/strain) within which a material will regain its original shape (zero strain position) after the deforming force is removed. a material will acquire a permanent deformation if stretched beyond elastic limit
Hooke's Law Law describing behaviour of elastic solids: Force is proportional to extension.
Hysteresis Phenomenon of lagging behind of any effect when the forces acting on a body are changed. Some substances like rubber show hysteresis when they are subjected to forces deforming them.
Hysteresis Loop Loop formed by two branches (loading and unloading) in force-extension and stress-strain graphs of some materials (e.g. rubber). Area of the hysteresis loop represents the energy lost during a loading unloading cycle.