What is Hook's law: Definition and 16 Discussions

Hooke's law is a law of physics that states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, Fs = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram. He published the solution of his anagram in 1678 as: ut tensio, sic vis ("as the extension, so the force" or "the extension is proportional to the force"). Hooke states in the 1678 work that he was aware of the law since 1660.
Hooke's equation holds (to some extent) in many other situations where an elastic body is deformed, such as wind blowing on a tall building, and a musician plucking a string of a guitar. An elastic body or material for which this equation can be assumed is said to be linear-elastic or Hookean.
Hooke's law is only a first-order linear approximation to the real response of springs and other elastic bodies to applied forces. It must eventually fail once the forces exceed some limit, since no material can be compressed beyond a certain minimum size, or stretched beyond a maximum size, without some permanent deformation or change of state. Many materials will noticeably deviate from Hooke's law well before those elastic limits are reached.
On the other hand, Hooke's law is an accurate approximation for most solid bodies, as long as the forces and deformations are small enough. For this reason, Hooke's law is extensively used in all branches of science and engineering, and is the foundation of many disciplines such as seismology, molecular mechanics and acoustics. It is also the fundamental principle behind the spring scale, the manometer, the galvanometer, and the balance wheel of the mechanical clock.
The modern theory of elasticity generalizes Hooke's law to say that the strain (deformation) of an elastic object or material is proportional to the stress applied to it. However, since general stresses and strains may have multiple independent components, the "proportionality factor" may no longer be just a single real number, but rather a linear map (a tensor) that can be represented by a matrix of real numbers.
In this general form, Hooke's law makes it possible to deduce the relation between strain and stress for complex objects in terms of intrinsic properties of the materials it is made of. For example, one can deduce that a homogeneous rod with uniform cross section will behave like a simple spring when stretched, with a stiffness k directly proportional to its cross-section area and inversely proportional to its length.

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  1. A

    I Is Hooke's law really not working, or is it me being dummy?

    Hello everyone, I'm a new member, and you might see me around from now on. I'm now on a path to understanding the mathematics behind a complicated mechanical machine. My knowledge is basically what I learned during my school days and also during university courses, and for me, it was mostly...
  2. Hajarmq

    Rotation and spring force exercise

    Summary:: Calculating the inclination angle A stick is on two springs with spring constants D1=500N/m and D2=300N/m. Consider the stick is without mass and can rotate around the point E, which is distant from spring 1 with 0,1m and from spring 2 with 0,8m. A force F=100N pulls the stick up...
  3. michael872940

    Can I determine mass & spring k from graph of wave, t, a, & vectors?

    Classical problems for hookes law generally give either mass or spring constant. What if I have a graph of a wavelike structure that is oscillating which I can use to measure for example: T (period), t (time), Δx (displacement), v (velocity), a (acceleration) and other variables is this...
  4. L

    Object on a vertical Ring with spring attached

    picture: https://ibb.co/k5P0GG Two objects slide without friction on a circular ring of radius R, oriented in a vertical plane. The heavier object (of mass 3m) is attached to a spring with an unstretched length of zero (admittedly an unphysical assumption) and spring constant k. The fixed end of...
  5. aatari

    Understanding Mass-Spring Behavior in Zero Gravity

    Hi Guys, So I am using the following simulation for this activity (Mass and Springs). The concept I need help with is to understand why when attaching a mass, the spring moves downward when the gravity is zero? If there is no gravity my limited understanding is that spring should not move...
  6. T

    Quadratic equation for maximum compression of a spring

    Homework Statement A 1.2 kg block is dropped from a height of 0.5 m above an uncompressed spring. The spring has a spring constant k = 160 N/m and negligible mass. The block strikes the top end of the spring and sticks to it Find the compression of the spring when the speed of the block...
  7. harini07

    Hooke's law and wave velocity related problem

    Homework Statement The extension in a string, obeying hooke’s law is Y when wave velocity in it is V. if extension is increased to 1.5Y, then wave velocity V’ becomes? 1) V' =V. 2)V'= 1.22V . 3)V'=1.5V. 4) V'=0.75V. Homework Equations wave velocity= frequency*wave length. The Attempt at a...
  8. C

    Solving Catapult Project: Finding Spring Constant

    I'm doing a catapult project but I'm sort of confused. I need to find the spring constant in order to get the elastic potential energy. The force of pulling back the catapult lever to 36 degrees above the horizontal is 4.2 N. Right before the lever is at rest, 90 degrees, the force is 1.4 N. One...
  9. H

    What did I miss in my energy and hook's law homework calculation?

    Homework Statement A 205 g cube slides down a ramp starting from rest as shown in the figure below. The ramp has a 46° slope. After falling a distance of 92 cm, the cube strikes a spring of spring constant k = 21 N/m. Find the maximum compression of the spring when the coefficient of kinetic...
  10. P

    Why do we call the constant of proportionality in hook's law as Young's Modulus?

    Why do we call the constant of proportionality in hook's law as Young's Modulus and not as Young's coefficient? Is there any difference in Modulus and coefficient in engineering context?
  11. G

    Understanding Hook's Law and Compression of Springs

    Homework Statement If a person holds a 30cm spring and compress on it with a force of 100 N (where k = 1000 N/m), by how much is the spring shortened. Homework Equations Hooks ' Law: F = -k* deltaX The Attempt at a Solution The answer for this is 10 cm: 10 = -1000...
  12. ~christina~

    Understanding the Relationship Between Spring and Hook's Law

    [SOLVED] Spring and Hook's law spring question
  13. P

    Solving Hook's Law Problems with Gravity

    hi everyone, I'm stuck on a problem that uses Hook's law but it's not straight forward. What must i do when there is an object pulled by an another object and connected with a spring. do i have to combine the force due to gravity on each of the object? can someone tell me a reference site for...
  14. S

    Hook's Law: Mass & Streaching Value Calculation

    What formula should I use for this question? I'm thinking hook's law, but It doesn't seem to fit. A mass is attached to a spring that has a constant of 100 N/m. The mass vibrates with a frequency of 2 Hz. I have to find the value of the mass and how far it streaches. I know I can use...
  15. R

    How can i define Hook's Law interm of Tensor

    How can i define "Hook's Law interm of Tensor" i want to define hoos's law interm of tensor:confused: how cn i define it can you all friends help me?o:) i will be thanksfull to all of you
  16. R

    How to Demonstrate Hooke's Law with a Spring and Weights

    hi, i am just having some problems with understanding the hook's law lab, if anyone has a "hook's law" can you please post it or you can email it to me. here is my address. dino_679@hotmail.com Thanks i will really appreciate it. undefined