What is Hookes law: Definition and 48 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. I

    Spring Problem (Hookes law)

    Homework Statement A block of mass M is hung on a vertical spring. We have to find spring constant k, x (displacement from mean position) given. Homework Equations 1/2kx^2 = mgx mg=kx The Attempt at a Solution When i conserve energy, 1/2kx^2=mgx ⇒ k= 2mg/x But when i use mg=kx, I get k=mg/x...
  2. patrickmoloney

    How Does Young's Modulus Relate to Spring Constants in Motion Equations?

    Homework Statement A particle mass m moves in a straight line on a smooth horizontal table, and is connected to two points A and B by light elastic springs of natural lengths 2l_{o} and 3l_{o} , respectively, and modulus of elasticity λ . The points A and B are a distance 6l_{o}...
  3. M

    Trying to Calculate k, using Hooke's Law

    Homework Statement The position of a 49 g oscillating mass is given by x(t)=(1.8cm)cos12t, where t is in seconds. Homework Equations k=mg/x The Attempt at a Solution I've tried working this problem multiple different ways and it is just not working for me. I used k= (.049*9.8)/.018 Is this...
  4. Elvis 123456789

    Mass within a box hung from a spring

    Homework Statement A block of mass m is placed inside a box of mass M , which is then hung from a spring with spring constant k. The system is pulled down some distance d and released at time t =0. Determine the reaction force between the block and the bottom of the box as a function of time...
  5. popopopd

    Spectroscopy hookes law, derivation?

    hi, i am a lillte confused why the equation for hookes law is 1/(2pi*c)*sqrt(k/m_reduced)? where does c come from? http://www.massey.ac.nz/~gjrowlan/intro/lecture5.pdf - slide 8. also, is there any particular reason why we use reduced mass?
  6. A

    Hookes law for stress and strain

    I need help understanding a passage in my textbook, where the form of hookes law in continuous elastic media is explained. It says: "The absence of internal directions in isotopic matter tells us that there are only two tensors available to construct a linear relation between the the stress...
  7. A

    What is the magnitude of the spring force given M,K and X

    Homework Statement 1.In a game a .12kg disk is shot across a frictionless surface . The spring is compressed by 6cm. The spring constant is 230 N/m. What is the magnitude of the spring force? 2. A piece of plastic is attached to a spring. The spring is compressed 2cm and the released. If the...
  8. S

    Did I Make a Mistake in My Spring Constant Calculation?

    The goal is to measure the spring constant of a spring and then calculate a theoretical period of the oscillation and compare the results to a real life measurement. Extension of spring A: Neutral: 52 cm 1 N: 41 cm 2 N: 30 cm F = kx k = 9.1 N/m 10 oscilliations = 9.26 seconds Calculating the...
  9. hdp12

    Problem Check: Equilibrium of Particles

    Homework Statement A continuous cable of total length 4 m is wrapped around the small pulleys at A, B, C, D. If each spring is stretched 300 mm, determine the mass m of each block. Neglect the weight of the pulleys and cords. The springs are unstretched when d=2 m. The Attempt at a Solution I...
  10. hdp12

    What is the weight of block D in this equilibrium of particles problem?

    Homework Statement Here is the problem that I am stuck on in my mechanics class. https://lh4.googleusercontent.com/ygXVjNfI4iP8xVpEjhxXZlWlDqg_VrM2gCVFLyomOVwWCfcLU78mIcPEc7hEzUqBoACIiQ=w1210-h506 Homework Equations F=-kx The Attempt at a Solution See the attached picture of my work...
  11. A

    Solving the Slinky Wave Problem: HELP!

    Homework Statement A slinky with natural length of 3.00 meters, mass of 0.750 kg, and spring constant 18.0 N/m is stretched out along a floor, each end held by a seated person. The final length is 8.2 m. One end is plucked sending a transverse pulse. Find the pulse's travel time there AND back...
  12. J

    Netforce of spring, hookes law. help

    Homework Statement An "extreme" pogo stick utilizies a spring whose uncompressed length is 46 cm and whose force constant is 1.4 x 10^4 N/m (14000). A 60 kg enthusiast is jumping on the pogo stick, compressing the spring to a length of only 5.0 cm at the bottom of her jump, Calculate; a) The...
  13. K

    Hookes Law, Finding A Springs Constant

    A spring extends by 10cm when a mass of 100g is attached to it. What is the spring constant? (calculate your answer in N/m) I have done this so far but I don't feel that it is right as the Force (F) is in grams and not Newtons: F = K x E 100 = K x 0.10 100 ÷ 0.10 = 100 K = 100 N/m...
  14. N

    Hookes law and Youngs modulus

    Homework Statement Consider a metal bar of initial length L and cross-sectional area A. The Young's modulus of the material of the bar is Y. Find the "spring constant" k of such a bar for low values of tensile strain. Express in terms of Y, L, and A. Homework Equations I know the...
  15. X

    Hookes law: Calculate the work done by compressing a spring

    Homework Statement Hookes law: Calculate the work done by compressing a spring by x distance Homework Equations W = Fd Ee = 1/2 k x^2 F = kx The Attempt at a Solution I've found two solutions, but only one is correct. I'm confused why it's the second one. First formula I...
  16. X

    Physics problem, basketball dunk (Hookes law)

    Homework Statement A 95kg basketball player slam dunks a basketball and hangs onto the rim. Find out how much the rim bends if its spring constant = 7400 N/m and the basketball rim is 2 m in the air.Homework Equations Ep = 0.5 k x^2 Ek = 0.5 m v^2 Eg = mghThe Attempt at a Solution The book got...
  17. X

    Physics problem, involving Hookes Law?

    Homework Statement A 0.500 kg mass is resting to a horizontal spring constant of 45 N/m. Your lab partner pulls the spring back and releases it when you are not looking. When the spring reaches its equilibrium point (x=0) the velocity of the mass is 3.4 m/s. Find how far your partner...
  18. A

    Hookes law, the representaion of K

    In hookes law, what does the variable K represent
  19. M

    Calculating Distance Using SHM & Hookes Law

    Homework Statement The diagram show a student before and after she makes a bungee jump from a high bridge above a river. One end of the bungee cord, which is of unstretched length 25 m, is fixed to the top of a railing on the bridge. The other end of the cord is attached to the waist of the...
  20. R

    Does the Spring Continue to Stretch Indefinitely Beyond the Elastic Limit?

    Homework Statement The Attempt at a Solution Its question 1 A (III) I don't understand. I have included a copy of the question paper and the mark scheme. I understand the continuation of the straight line up to 800N however after does the line curve like the blue / red one on my...
  21. C

    Explaining Hookes Law to a GCSE Physics Student

    I am a GCSE Physics Student I was hoping somebody would be able to help me when I have been studying Hookes law, we have only looked at a basic equation extension = extented length - original length. We have also look at how the increase in mass is directly proportional to the extension until...
  22. L

    Mechanics question involving spring and hookes law.

    My lamda value is 4. What I have managed to get so far is: dV/dx=-F V=8/arctan(x/3)dx /=integrate sign! integrate by parts u=arctan(x/3), dv=dx du=3/9+x^2dx, v=x V=8/arctan(x/3)dx = 8[x.arctan(x/3)-/3x/9+x^2dx] V= 8[x.arctan(x/3)-3/2log(9+x^2)+C] Since V(0)=0 V=...
  23. C

    Using hookes law to find impulse

    Homework Statement You are given a FORCE versus TIME graph, which shows oscillations with: A= 4N at the max points period is 4s spring constant (k)= 12.3 N/m mass of block exhibiting oscillation is 4.9 kg How do you find the IMPULSE delivered to the block during the 1st 2 seconds of...
  24. K

    Work done by spring vs hookes law?

    what is wrong with this problem? http://www.cramster.com//answers-mar-10/physics/buoyancy-force-fig-14-36-spring-spring-constant-360x104-mis_811494.aspx In Fig. 14-36, a spring of spring constant 3.60x104 N/mis between a rigid beam and the output piston of a hydraulic lever.An empty...
  25. G

    Problem involving hookes law and friction

    This is a question my professor asked in class and I did not understand his explanation at all, I found your forums hoping someone would break it all down for me [PLAIN]http://i28.lulzimg.com/0cb917f809.jpg
  26. R

    How can I write a conclusion for a Hookes law experiment?

    im having bother writing the conlcusion for hookes law experiment, can anyone help or point me in the right direction ?
  27. A

    Solved: Calculate Force from Spring Constant & Rod Length

    Homework Statement given a spring constant of 2.1 x 10^6 N/m, calculate the amount of force needed to stretch a steel rod 0.001m Homework Equations f=kx The Attempt at a Solution dont know
  28. I

    Calculating Spring Compression of Ore Car on Downhill Mine Tracks

    1.An ore car of mass 38000 kg starts from rest and rolls downhill on tracks from a mine. At the end of the tracks, 6.5 m lower vertically, is a horizontally situated spring with constant 5.2 × 105 N/m. The acceleration of gravity is 9.8 m/s2 . Ignore friction. How much is the spring...
  29. L

    Solving Hookes Law: Find Spring Constant & Weight of Package

    Homework Statement The scale of a spring balance that reads from 0 to 20.7 kg is 14.9 cm long. A package suspended from the balance is found to oscillate vertically with a frequency of 1.51 Hz. (a) What is the spring constant? (b) How much does the package weigh? Homework Equations...
  30. A

    Resonant frequency of an annular ring? Hookes Law?

    Hi, I am trying to work out the resonant frequency of an annular ring, does anyone know a general equation for it? For example the ring has an outside diameter = OD and inside diameter = ID. The ring is gently clamped at the outside diameter and a force F applied evenly at the inside...
  31. P

    A question regarding power and hookes law

    Homework Statement A 2.8 m high spring has a spring constant of 12 N/m. How much power is required if the spring is compressed 1.2 m in 2.5s? Homework Equations Pe= 1/2kx^2 Power= W/t The Attempt at a Solution =1/2(12)(1.2)^2 =8.64 J so... Power = 8.64/2.5 = 3.456 watts...
  32. K

    What is the relationship between Hooke's law and compression?

    Homework Statement I would like to know if Hooke's law applies to compression as well as tension? Meaning if the spring is stretched or compressed is the spring constant the same? Homework Equations F = -kx The Attempt at a Solution
  33. D

    Calculating work using hookes law

    Homework Statement Calculate the work done, in Joules for a system in which a muscle of 1cm^2 cross section and 10cm length is stretched to 11cm by hanging a mass on it. The muscle behaves like a spring. The spring constant for the muscle was determined by finding that the muscle exerts a...
  34. D

    Calculating Length of Arc BD with Hookes Law

    in the following question, E=65 GPa V=0.3 find the new length of the arc BD?? i have found the stresses \sigmaxx=-56Mpa \sigmayy=0 \sigmaxy=-28Mpa using hookes law i can find the strains \epsilonxx=-8.615e-5 \epsilonyy=2.58e-4 0.5*\epsilonxy=\gamma=-1.12e-3 but how do i calculate the...
  35. D

    State of stress, strain and hookes law

    in the following question i am asked to find the state of stress given the state of strain. http://lh6.ggpht.com/_H4Iz7SmBrbk/SwBtHnG3qkI/AAAAAAAAB9M/rFS_orHMbGo/Capture.JPG i went about solving this using hookes law \sigmaxx=E[(1-v)\epsilonxx + v(\epsilonyy+\epsilonzz)]/[(1+v)1-2v)] using...
  36. Z

    Student Struggling with Hookes Law - 18 Year Old Physics Student

    hi, I am a student 18 years of age, I am currently starting my first year of physics, and I've got an exam coming up, on mechanics, materials and waves i can't seem to get a grip on hookes law, could someone explain it please?
  37. E

    Restoring Forces and Hookes law

    Kate, a bungee jumper, wants to jump off the edge of a bridge that spans a river below. Kate has a mass m, and the surface of the bridge is a height h above the water. The bungee cord, which has length L when unstretched, will first straighten and then stretch as Kate falls. Assume the...
  38. G

    What is the correct calculation for the Young's modulus using Hooke's Law?

    [SOLVED] More hookes law question Homework Statement i can't get the equation to work out to the right answer of 110-130Gpa Homework Equations E=kL/A k-1.45 L=2metres A = 0.292cm The Attempt at a Solution i get 0.0099Gpa
  39. G

    Hookes law equation for all gauges of copper wire

    [SOLVED] Hookes law equation for all gauges of copper wire Homework Statement For my coursework I'm trying to find an equation using hookes law that works with all gauges of copper wire, i know that this means i will have to change the hookes law equation from F=ke to F=ake (a is not the area...
  40. E

    What Formulas Can be Used to Calculate Energy and Forces in a Spring Collision?

    1. A guy us riding a tricycle at 33kg at 12m/s when it strikes a spring and is brought to rest in 1.6m. Compute the proportionality constant and explain the type of energy, types of forces, and Hookes law applied 2. F = k(elongation) I am sure there are others. 3. my problem...
  41. A

    Exploring Hookes Law: Impact of Width on Elasticity

    Hiya, I have had to do an investigation on hookes law as part of my primary school teaching course. i am by far not the best at understanding physics. Can someone please explain to me what effect the width of a piece of elastic has on its elasticity and why? thanks
  42. A

    Hookes Law and a uniform bar

    Homework Statement A uniform bar of an iron is supported by a long, uniform hooke's law spring. The spring is cut in half and two pieces are used to support the same bar. If the whole spring stretched by 4.0cm, by how much would each half strech? Homework Equations f=Kchange in X The...
  43. A

    Hookes Law and Spring Constant: Explaining the Integral

    Hello, I'm having some problems with the spring constant "k" together with Hookes law. U=1\2kx^2 Could someone please explain how you get that integral? If you insert it in a diagram and calculate the area as a triangle you would get 1/2kx. Where does the ^2 come from?
  44. J

    K in Hookes Law vs. Spring Potential Energy

    Today in physics class we were discussing the conservation of energy using a ball on a spring as the example. When the instructor completed the problem one of the students stated that the value of K (spring constant) that we found was different (by a factor of 2) than the value of K calculated...
  45. S

    Plotting T vs M for Hookes Law: Find k

    In the equation for Hookes law what values do I consider if I was to plot for the value of k?. Would plotting T vs M give me this and would the gradient be equal to k?
  46. J

    Hookes law or simple dynamics?

    Hi, I just have a problem dealing with the background of a project I am working on in physics... I basically have a rubber band fixed at a point above the ground, from which I have masses suspended from it. So obviously, as I add more mass, the elastic is strained more and more, and stretches...
  47. H

    Analyzing Hookes Law Experiments: Taking it to the Next Step

    hi can anyone suggest a way to take an analysis of a hookes law experiment at alavel up to "the next step" at low loads there is a reduced amount of extension - can anyone suggest why? is this due to intial tensioning of teh spring in question? i have doen all of teh standard analysis i...