Hooke's Law is a fundamental principle in physics that describes how springs behave. It states that the force needed to extend or compress a spring is directly proportional to the distance of displacement from its equilibrium position.
The mathematical expression of Hooke's Law is F equals negative k times x. Here, F represents the applied force, k is the spring constant which depends on the material properties, and x is the displacement from equilibrium. The negative sign indicates that the force is a restoring force, always acting to bring the spring back to its natural length.
The spring constant k is a measure of how stiff a spring is. A stiff spring with a large k value requires more force to compress or extend it by the same distance compared to a soft spring with a small k value. The units of the spring constant are Newtons per meter.
Hooke's Law only applies within the elastic limit of the material. Within this limit, the spring follows a linear relationship and returns to its original shape when the force is removed. Beyond the elastic limit, permanent deformation occurs and the linear relationship breaks down, entering the plastic region where the material no longer obeys Hooke's Law.
To summarize what we've learned about Hooke's Law: it describes the linear relationship between force and displacement in elastic materials. The mathematical formula F equals negative k times x shows that force is proportional to displacement. The spring constant determines how stiff the material is, and this law only applies within the elastic limit. Hooke's Law is fundamental in engineering and physics applications.