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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

Mathematically, Hooke's Law can be written as F=kx.

Many materials obey this law as long as the load does not exceed the material's elastic limit.

The rate or spring constant, k, relates the force to the extension in SI units: N/m or kg/s2.
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}.
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. "
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Key Term Reference
 Hooke's law
 Appears in this related concepts: Sinusoidal Nature of Simple Harmonic Motion, Springs, and Simple Harmonic Motion
 Law
 Appears in this related concepts: Physics and Other Fields, Photon Interactions and Pair Production, and Models, Theories, and Laws
 Restoring force
 Appears in this related concepts: Energy, Intensity, Frequency, and Amplitude, Stability, Balance, and Center of Mass, and Period of a Mass on a Spring
 approximation
 Appears in this related concepts: Numerical Integration, Roundoff Error, and Uniform Electric Field
 displacement
 Appears in this related concepts: Position, Displacement, Velocity, and Acceleration as Vectors, Reference Frames and Displacement, and Interference
 elastic
 Appears in this related concepts: Internal vs. External Forces, Applications of Elasticities, and Demand Curve
 equation
 Appears in this related concepts: A General Approach, Equations and Inequalities, and Equations and Their Solutions
 equilibrium
 Appears in this related concepts: How Supply and Demand Affect Businesses, Ecology of Ecosystems, and Equilibrium
 force
 Appears in this related concepts: Newton and His Laws, Work Done by a Variable Force, and Driven Oscillations and Resonance
 machine
 Appears in this related concepts: Manufacturing, Simple Machines, and The Limits of Progressivism
 mass
 Appears in this related concepts: Physical and Chemical Properties of Matter, Mass Spectrometer, and Mass
 position
 Appears in this related concepts: Damped Harmonic Motion, Longitudinal Waves, and Graphical Interpretation
 resultant
 Appears in this related concepts: Adding and Subtracting Vectors Graphically, TwoComponent Forces, and Forces in Two Dimensions
 strain
 Appears in this related concepts: Groin Pull, Viscosity, and Sprain and Strain
 stress
 Appears in this related concepts: Reducing Workplace Stress, Thermal Stresses, and Maintaining Motivation
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Source: Boundless. “Hooke's Law.” Boundless Physics. Boundless, 27 Jun. 2014. Retrieved 24 Mar. 2015 from https://www.boundless.com/physics/textbooks/boundlessphysicstextbook/wavesandvibrations15/hookeslaw122/hookeslaw4255646/