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Hooke's Law
Hooke's law of elasticity is an approximation that states that the extension of a spring is directly proportional to the load applied to it.
Learning Objective

Provide the mathematical expression of Hooke's law
Key Points
Term

elasticity
The property by virtue of which a material deformed under the load can regain its original dimensions when unloaded
Full Text
In mechanics (physics), Hooke's law is an approximation of the response of elastic (i.e., springlike) bodies. It states: the extension of a spring is in direct proportion with the load applied to it . For instance, in the spring is pulled downwards with either no load, F_{p}, or twice F_{p}.
Diagram of Hooke's Law
The extension of the spring is linearly proportional to the force.
Many materials obey this law of elasticity as long as the load does not exceed the material's elastic limit. Materials for which Hooke's law is a useful approximation are known as linearelastic or "Hookean" materials. Hookean materials are broadly defined and include springs as well as muscular layers of the heart. In simple terms, Hooke's law says that stress is directly proportional to strain. Mathematically, Hooke's law is stated as:
where:
 x is the displacement of the spring's end from its equilibrium position (a distance, in SI units: meters);
 F is the restoring force exerted by the spring on that end (in SI units: N or kg·m/s^{2}); and
 k is a constant called the rate or spring constant (in SI units: N/m or kg/s^{2}). When this holds, the behavior is said to be linear. If shown on a graph, the line should show a direct variation.
It's possible for multiple springs to act on the same point. In such a case, Hooke's law can still be applied. As with any other set of forces, the forces of many springs can be combined into one resultant force.
When Hooke's law holds, the behavior is linear; if shown on a graph, the line depicting force as a function of displacement should show a direct variation. There is a negative sign on the right hand side of the equation because the restoring force always acts in the opposite direction of the displacement (for example, when a spring is stretched to the left, it pulls back to the right).
Hooke's law is named after the 17th century British physicist Robert Hooke, and was first stated in 1660 as a Latin anagram, whose solution Hooke published in 1678 as Ut tensio, sic vis, meaning, "As the extension, so the force. "
Key Term Reference
 Hooke's law
 Appears in these related concepts: Work Done by a Variable Force, Sinusoidal Nature of Simple Harmonic Motion, and Springs
 Law
 Appears in these related concepts: Newton and His Laws, Mechanical Work and Electrical Energy, and Models, Theories, and Laws
 Restoring force
 Appears in these related concepts: What is Potential Energy?, Energy, Intensity, Frequency, and Amplitude, and Period of a Mass on a Spring
 approximation
 Appears in these related concepts: Area Expansion, Numerical Integration, and Roundoff Error
 displacement
 Appears in these related concepts: Position, Displacement, Velocity, and Acceleration as Vectors, Interference, and Introduction to Human Language
 elastic
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 equation
 Appears in these related concepts: A General Approach, Equations and Inequalities, and Equations and Their Solutions
 equilibrium
 Appears in these related concepts: Calculating Equilibrium Concentrations of Polyprotic Acids, Understanding and Finding the Deadweight Loss, and Balance and Determining Equilibrium
 force
 Appears in these related concepts: Work, Force, and Force of Muscle Contraction
 machine
 Appears in these related concepts: MiddleClass Reformers, Simple Machines, and The Limits of Progressivism
 mass
 Appears in these related concepts: Mass Spectrometer, Mass, and Pop Art
 position
 Appears in these related concepts: Motion with Constant Acceleration, Motion Diagrams, and Graphical Interpretation
 resultant
 Appears in these related concepts: Adding and Subtracting Vectors Graphically, Adding and Subtracting Vectors Using Components, and Forces in Two Dimensions
 strain
 Appears in these related concepts: Pulled Groin, Sprain and Strain, and Stress and Strain
 stress
 Appears in these related concepts: Thermal Stresses, Arches, Vaults, and Domes, and The Endocrine System and Stress
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Cite This Source
Source: Boundless. “Hooke's Law.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 09 Oct. 2015 from https://www.boundless.com/physics/textbooks/boundlessphysicstextbook/wavesandvibrations15/hookeslaw122/hookeslaw4255646/