When an object is stretched, bent or deformed the restoring force (F) is propor- tional to the displacement (s) from its equilibrium position.
The restoring force is in the opposite direction to the displacement. The law only holds true provided the object is not stretched past its elastic limit.
ROBERT HOOKE, 1635–1703 (ENGLISH) He discovered the relation- ship between elastic restoration force
and displacement, now called Hooke’s law. He assisted Robert Boyle in
discovering the relationship between pressure and volume of a gas.
ELASTIC CONSTANT
k
mg s
k elastic constant m mass g acceleration due to gravity
The constant of proportionality relating force and displacement in Hooke’s law is called the elastic constant (k).
Hooke’s law can be defined mathematically as F ks.The ‘’ in the formula indicates that the restoring force is in the opposite direction to the displacement.
HOOKE’S LAW
F ks F restoring force, k elastic constant, s displacement from equilibrium position
ELASTIC CONSTANT
The elastic constant (k) is the constant of proportionality between the applied force and the resulting displacement of a given spring.
It is a scalar quantity with an SI unit of newton per metre (N m1).
Each different spring will be compressed by a different amount by a given load depending on the stiffness of the spring and the size of the load.This load is typically a weight placed on top of the spring, in which case:
Elastic constant weight displacement
Calculating the magnitude of the restoring force For some numeric calculations it may be worth noting:
When a spring is stretched or compressed beyond its natural length (l0) to a new length (l) its displacement s (l l0).
When calculating the magnitude of the force acting on elastic bodies, such as springs, Hooke’s law may be written as:
