Forces and Energy Changes: Elastic Deformation

Forces applied to objects can cause deformation, which is a change in the object’s shape.
Deformation may be elastic or inelastic. When an object deforms elastically, it returns to its original shape when the force is removed.
Hooke’s Law states that for an elastically deforming material, the force applied is directly proportional to the extent of deformation or change in length.
In the context of Hooke’s Law, the extent of deformation is also known as the strain on the object.
The constant of proportionality in Hooke’s Law is referred to as the spring constant and denoted by ‘k’. It measures the stiffness of the object.
The formula F = kx represents Hooke’s Law, where F is the applied force, k is the spring constant, and x is the extension.
The spring constant is measured in Newtons per metre (N/m). A high spring constant indicates a stiff object that is hard to deform.
The limit of proportionality is the maximum force before the object no longer follows Hooke’s Law and is unlikely to return to its original shape.
Energy is stored in an elastically deforming object, known as elastic potential energy. It is potential energy because it can be transformed into other forms of energy.
The elastic potential energy can be calculated using the formula 1/2kx^2, where k is the spring constant, and x is the extension.
A force-extension graph can illustrate an object’s behaviour under different loads. The graph shows a linear region, the limit of proportionality, and the elastic limit.
Beyond the limit of proportionality, the object deforms inelastically and does not return to its original shape when the force is removed.
Finally, it’s important to remember that not all objects obey Hooke’s Law. Some materials, such as rubber, do not have a linear relationship between force and extension.