A pair of equal and opposite forces is required to alter the shape of an object. Forces that produce an extension (tensile deformation) are called tensile forces and forces that shorten an object (compressive deformation) are called compressive forces.
Hooke’s Law states that the extension of a material is directly proportional to the force applied provided the elastic limit is not exceeded. Therefore,
is the force constant of the spring (SI unit Nm-1). It is also a measure of the stiffness of the spring: a spring with a higher value of will extend less for a given force. The value of the force constant is determined from the gradient of the linear region of a force-extension graph.
The force-extension characteristics of materials such as springs, rubber bands and polythene strips can be investigated by attaching the material to one end of a clamp stand, secured to the bench, with a boss and clamp. Suspended masses produce an extension that can be measured.
- Metal wire: obeys Hooke’s Law until the elastic limit is reached. The unloading path is parallel to the unloading path because the wire has been permanently extended.
- Rubber: do not obey Hooke’s Law. Return to original length after the deforming force is removed (elastic deformation), but the loading and unloading curves are different. For a “hysteresis loop”. The reduced area under the curve during unloading is due to energy lost as heat.
Polythene: does not obey Hooke’s Law. Strips stretch easily and suffer plastic deformation under relatively little force.