Hooke's Law

Introduction to Hooke’s Law

• Hooke’s Law is a principle of physics that states that the force (F) needed to extend or compress a spring by some distance (x) is proportional to that distance.
• It can be written mathematically as F = kx, where k is a constant factor unique to each spring, often referred to as the spring or stiffness constant.

The Spring Constant

• The spring constant (k) is a measure of elasticity for a spring or other elastic body. It is measured in newtons per meter (N/m).
• In the equation for Hooke’s Law (F = kx), a larger value of k means the spring is stiffer or harder to stretch.

Elastic Limit and Permanent Deformation

• Every spring or elastic body has a limit to the amount it can be stretched or compressed without being permanently deformed. This is known as its elastic limit.
• If a spring is deformed beyond its elastic limit, it would not return to its original shape and size when the force is removed. This is known as permanent deformation.

Energy Stored in a Spring

• Elastic potential energy is the energy stored in a stretched or compressed spring.
• The elastic potential energy is given by the equation E = 0.5 kx^2.

Graphical Representation of Hooke’s Law

• Graphs plotting the force against extension can be used to display Hooke’s Law.
• The spring constant (k) can be calculated from the graph as the gradient of the line.
• The point where the graph line deviates from a straight line represents the point of elastic limit or the limit of proportionality. Beyond this point, the spring does not obey Hooke’s Law.