The expression of Hooke's law is f = k x or △ f = k δ x, where k is a constant and is the rigidity (obstinacy) coefficient of an object. In the international system of units, the unit of F is cattle, the unit of X is meters, it is a deformation (elastic deformation), and the unit of K is cattle/meter. The stiffness coefficient is numerically equal to the elastic force of the spring when it is extended (or shortened) per unit length.
The law of elasticity is one of Hooke's most important discoveries and one of the most important basic laws of mechanics. In modern times, it is still an important basic theory of physics.
Hooke's law of elasticity points out that when the spring is elastically deformed, the elastic force Ff of the spring is directly proportional to the elongation (or compression) X of the spring, that is, F =-K X. K is the stiffness coefficient of the material, which is determined by the properties of the material. A negative sign indicates that the spring produces an elastic force opposite to its stretching (or compression) direction. In order to prove this law, Hooke also did a lot of experiments and made various shapes of elastomers with various materials.
The elastic body satisfying Hooke's law is an important physical theoretical model, which is a linear simplification of the complex nonlinear constitutive relation in the real world. Practice has proved that it is effective to some extent.
However, there are also many examples that do not satisfy Hooke's law. The significance of Hooke's law lies not only in its description of the relationship between elastic deformation and force, but also in its creation of an important research method: linear simplification of complex nonlinear phenomena in the real world, which is common in theoretical physics.
Spring equation:
Hooke's law can accurately describe the mechanical behavior of ordinary springs when the deformation is not too large. A common example of applying Hooke's law is the spring. Within the elastic limit, the elastic force f exerted by the spring on the object has a linear relationship with the length change x of the spring.
Where is the stiffness coefficient (or stubborn coefficient) of the spring, which is determined by the nature and geometry of the spring material. A negative sign indicates that the spring produces an elastic force opposite to its stretching (or compression) direction. This elastic force is called restoring force, which means that it tends to restore the balance of the system. A spring satisfying the above formula is called a linear spring.