Hooke's law in the context of "Restoring force"

A scale or balance is a device used to measure weight or mass. These are also known as mass scales, weight scales, mass balances, massometers, and weight balances.

The traditional scale consists of two plates or bowls suspended at equal distances from a fulcrum. One plate holds an object of unknown mass (or weight), while objects of known mass or weight, called weights, are added to the other plate until mechanical equilibrium is achieved and the plates level off, which happens when the masses on the two plates are equal. The perfect scale rests at neutral. A spring scale will make use of a spring of known stiffness to determine mass (or weight). Suspending a certain mass will extend the spring by a certain amount depending on the spring's stiffness (or spring constant). The heavier the object, the more the spring stretches, as described in Hooke's law. Other types of scales making use of different physical principles also exist.

Young's modulus (or the Young modulus) is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise. It is the elastic modulus for tension or axial compression. Young's modulus is defined as the quotient of the stress (force per unit area) applied to the object and the resulting axial strain (a dimensionless quantity that quantifies relative deformation) in the linear elastic region of the material. As such, Young's modulus is similar to and proportional to the spring constant in Hooke's law, but with dimensions of pressure instead of force per distance.

Although Young's modulus is named after the 19th-century British scientist Thomas Young, the concept was developed in 1727 by Leonhard Euler. The first experiments that used the concept of Young's modulus in its modern form were performed by the Italian scientist Giordano Riccati in 1782, pre-dating Young's work by 25 years. The term modulus is derived from the Latin root term modus, which means measure.

The bulk modulus (${\displaystyle K}$ or ${\displaystyle B}$ or ${\displaystyle k}$) of a substance is a measure of the resistance of a substance to bulk compression. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume.

Other moduli describe the material's response (strain) to other kinds of stress: the shear modulus describes the response to shear stress, and Young's modulus describes the response to normal (lengthwise stretching) stress. For a fluid, only the bulk modulus is meaningful. For a complex anisotropic solid such as wood or paper, these three moduli do not contain enough information to describe its behaviour, and one must use the full generalized Hooke's law. The reciprocal of the bulk modulus at fixed temperature is called the isothermal compressibility.

A spring scale, also known as a spring balance or newton meter, is a type of mechanical force gauge or weighing scale. It consists of a spring fixed at one end with a hook to attach an object at the other. It works in accordance with Hooke's law, which states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance. Therefore, the scale markings on the spring balance are equally spaced.

A spring balance can be calibrated for the accurate measurement of mass in the location in which they are used, but many spring balances are marked right on their face "Not Legal for Trade" or words of similar import due to the approximate nature of the theory used to mark the scale. Also, the spring in the scale can permanently stretch with repeated use.

The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Furthermore, it is one of the few quantum-mechanical systems for which an exact, analytical solution is known..