What is Force constant: Definition and 52 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. F

    Maximum displacement in mass spring system

    Homework Statement A block is suspended by an ideal spring of the force constant K. If the block is pulled down by applying a constant force F and if maximum displacement of the block from its initial position of rest is X then, find the value of X. Homework Equations mg + F = XK + K(mg/K)...
  2. O

    What's the importance of a spring force constant of 1634N/m?

    Hi I'm new here and I've checked everywhere on google but I can't seem to find a website that'll tell me the spring force constant of items. Also what things would be in the range of a spring force constant of 163.427 N/m/
  3. D

    Problem with solving for force constant k of spring?

    The question is stated as the following: When a 3.60 kg object is placed on top of a vertical spring, the spring compresses a distance of 2.83 cm. What is the force constant of the spring? The correct answer was acquired by using the equation F = mg = -kx, where k is the spring constant and x...
  4. Muthumanimaran

    Bond Strength and Force constant

    Homework Statement Homework EquationsThe Attempt at a Solution (a) Total energy is $$E=\frac{-e^2}{4\pi\epsilon_{0}R}-\frac{B}{R^{5/6}}$$ Taking derivative of E with respect to R and equating it to zero when R=R0 yields, i.e, $$\frac{dE}{dR}{\bigg|}_{R=R_0}=0$$ when R=R0 yields...
  5. N

    How weight affects surface bending over time

    Very dumb classic mechanics question here: The other day I caught sight of a trivial objects arrangement: a basketball placed on top of a 6-sided cardboard box on the floor, and I wondered how the weight of the hollowed sphere could cause bending on the supported, flat top surface of the box...
  6. M

    A spring with a force constant

    Homework Statement Homework Equations These are the equations he provided. The Attempt at a Solution I actually have no idea how to do them. So any help would be much appreciated.
  7. D

    What should be the force constant of the spring?

    Homework Statement You are asked to design spring bumpers for the walls of a parking garage. A freely rolling 1100 kg car moving at 0.66 m/s is to compress the spring no more than 9.0×10−2m before stopping. What should be the force constant of the spring? Assume that the spring has negligible...
  8. Simanto Rahman

    Relation Between Spring Constant and Angular Velocity

    I was going through Periodic Motion chapter of my book and came across an equation while defining the relation between Time Period of on oscillating particle and force constant. k/m=w2 which was applied in, T = 2xpie/angular velocity can anyone please help me define this equation. I can't seem...
  9. A

    Determine the force constant of the rubber band

    Homework Statement From the experiment I did my force was equal to 0.0686N +/- 0.00196N and my x (rubber band stretch) was equal to 0.003m +/-0.002. The question asks to determine the force constant k +/- ∆k. Homework Equations F = kx k = F/x ∆k = |k| ∆x/x +∆y/y The Attempt at a Solution k...
  10. L

    Units of Force Constant

    Homework Statement A molecule is a harmonic oscillator, and has a fundamental frequency of 1000 cm−1 and a reduced mass of 10.0 amu. From this, determine the magnitude of the force constant, and express it in units of aJ ˚A−2 (atto joules per angstrom). Homework Equations ω=√(k/mr) The...
  11. Essence

    Why does the force of a spring = -kx

    I know this is an idealization, but I'm wondering if there is a reason this idealization works so well. Is it related to the coil of the spring or the bonds between each atom in the spring? I have considered using ## F = \frac{kq_1q_2Nsin\left(\theta \right)}{r^2} ## Where: ##...
  12. I

    What is the Force Constant k of a Spring?

    Homework Statement A 4.50 ✕ 10^5 kg subway train is brought to a stop from a speed of 0.500 m/s in 0.900 m by a large spring bumper at the end of its track. What is the force constant k of the spring? M- 4.50E5 kg IV- .5m/s FV- 0m/s Homework Equations k=mg/x F=-kx PE = (.5)kx^2The Attempt at...
  13. Sneakatone

    How to find force of a spring given force constant and length

    A spring with a constant force k=150 N/m has a relaxed length of 0.21 m. a) what force must you exert to strength this spring to 2.0 times its length? I used the equation F=kx F=150(2*0.21)=63 but the answer is wrong b) what force must you exert to compress this spring to 0.30 its...
  14. P

    Force constant of a spring

    Homework Statement if a spring of force constant k is cut into two halves, will the force constant of each of the two new spring remain the same ,that is ,for same force will the extension be same for the new spring as the original spring Homework Equations The Attempt at a Solution
  15. X

    Calculate Force Constant of Spring: Vibrational Frequency 7.00/s

    Homework Statement Two 3.5 g masses are attached by a spring has a vibrational frequency of 7.00 s-1. Calculate (a) the force constant of the spring; (b) the zero point energy; (c) the potential energy if the maximum displacement is 0.5 cm.Homework Equations k=((2πcω)^2)μ E=(1/2)hcw (NOTE...
  16. D

    Coulomb's constant, electric force constant

    Coulomb's Law states F = q**2/ r**2 q= statCoulombs In SI units, F = Ke (q**2/r**2) q= Coulombs I read that 1 C = 2.997 x 10E+09 statC Then Ke = 8.987 x 10E+09 (1) Does anyone know where the conversion for C to statC came from? (2) and how you get the Ke from those values...
  17. C

    Fining the force constant of a spring

    When a 9.09kg mass is placed on top of a vertical spring, the spring compresses 4.18 cm. Find the force constant of the spring. Okay I know the formula for a spring is F=-kx So k=mg/x converting the cm to m I get 4.18cm = 0.0418m So I plug in my numbers k=(9.09kg)(9.81m/s^2)/ 0.0418...
  18. N

    Why classics assumed that the force constant in two different references frames?

    hi every one :) i need a small help please ... we have tow frames and tow observers , let suppose there is a force on an object in one of the frames , so from Newton law: f=ma "a" depend on "x" distance which is not constant in the other frame , so why they assumed that it is constant...
  19. H

    Simple harmonic motion spring force constant help

    Homework Statement A spring is hung vertically from a support. A mass of 4.5 kg is hung from the lower end of the spring and is slowly lowered a distance of 22.0 cm until equilibrium is reached. This mass is then lowered to a point 15.0 cm below the equilibrium point and is then released...
  20. nukeman

    Help with calcuating force constant ?

    Homework Statement A 320 kg wooden raft floats on a lake in equilibrium. When a 75 kg man steps carefully onto the raft, it floats 3.5 cm deeper into the water. When he steps off, the raft oscillates for a while. (a) The buoyant force of the water on the raft is a restoring force that is...
  21. N

    Finding force constant, not given the value of k

    A 0.650 kg block slides on a frictionless, horizontal surface with a speed of 1.19 m/s. The block encounters an unstretched spring and compresses it 25 cm before coming to rest. (a) What is the force constant of this spring? ____ N/m (b) For what length of time is the block in contact with...
  22. H

    Spring with masses on either side - force constant and compression remain the same?

    Homework Statement A spring is compressed by 0.100m from its equilibrium position, and two blocks of masses 3kg and 5kg are resting motionless on each side on a frictionless surface. The spring has a force constant of 20 N/m, and a rope holds the block in position against the compressed...
  23. T

    Force Constant of Surgical Tubing

    The Problem: I found the force constant of surgical tubing for a catapult I have to make for physics class. However I discovered that I have to reduce the length of the tubing a few centimetres to get a longer range for the projectile. Will reducing the length change the force constant...
  24. C

    Spring Force Constant?

    Homework Statement A 100g object is suspended from a spring. When 40g are added, the spring stretches an additional 5.0cm. With the total mass of 140g, the spring is set into vertical oscillations with an amplitude of 10 cm. (a) What is the force constant of the spring? Homework...
  25. r-soy

    Find the force constant fron the graph

    Hi all Find the force constant fron the graph k = 1/0.27 = 3.70 n/m ( is this ok ) plese I want your help
  26. O

    Hooke's Law and force constant

    Homework Statement A force of 720 N stretches a certain spring a distance of 15 cm. What is its force constant? If a 60-kg mass is hung on it, how far will it stretch? Solving for Force Constant given: F (Restoring Force) = 720 N ΔL (spring's elongation) = 15 cm x (1 m / 100 cm) = 0.15 m k...
  27. M

    Hooke's Law and the force constant

    Homework Statement When a 2.90-kg object is hung vertically on a certain light spring described by Hooke's law, the spring stretches 2.93 cm. (a) What is the force constant of the spring? (b) If the 2.90-kg object is removed, how far will the spring stretch if a 1.45-kg block is hung on...
  28. R

    Quantum Mechanical Software & Force Constant for Polyatomic Molecules

    Dear all, Any quantum mechanical software (e.g., Gaussian03) can compute the fundamental frequencies (3N-6) and force constant for each frequency.. I don't understand exactly about force constant..?? For a particular mode of vibration what does this force constant mean? For a molecular with...
  29. C

    Finding Force Constant of a Spring

    Homework Statement A 1.80 kg block slides on a rough, horizontal surface. The block hits a spring with a speed of 1.95 m/s and compresses it a distance of 14.0 cm before coming to rest. If the coefficient of kinetic friction between the block and the surface is µk = 0.560, what is the force...
  30. C

    Bungee Cord Force Constant from Work?

    Homework Statement A bungee jumper jumps with a mass of 61kg jumps off of a bridge. The massless bungee cord is 25m long and beyond that length acts as a spring. The jumper reaches the lowest point 42.9m below the bridge. Find the force constant which characterizes the bungee cord. Homework...
  31. P

    Find the effective force constant ke

    This isn't really a homework problem, but I've been going over these Yale problem sets for physics 200 (http://oyc.yale.edu/physics/fundamentals-of-physics/content/resources/problem_set_3.pdf" [Broken]), and I'm having trouble with one of the questions. Homework Statement Two springs have the...
  32. R

    Finding Force Constant of Spring: 0.296 kg & 3.3 J

    Homework Statement A 0.296 kg mass is attached to a spring and executes simple harmonic motion with a period of 0.18 s. The total energy of the system is 3.3 J. Find the force constant of the spring. Answer in units of N/m.Homework Equations k=m(t/2\pi)^2The Attempt at a Solution...
  33. D

    Force constant between 2 atoms

    Homework Statement The atomic mass of tellurium is 2.12×10-25 kg, and the frequency, 7.53×1012 Hz. What is the effective force constant that connects the two atoms? Homework Equations Have no idea The Attempt at a Solution I am lost with this problem, we havn't learned it in...
  34. E

    AFM indentation - force constant

    Anyone have any reference or experience as to in which range the force constant of the cantilever should be for carrying out AFM indentation on CNT? (in UVH). Thanks, E.S
  35. B

    Force Constant given torque

    You are designing exercise equiptment to operate as shown in teh figure: where a person pulls upward on an elastic stretched length of .31m. If you would like the torque about the elbow joint to be 81 N*m in the position shown, what force constant, k, is required for the cord? ::: okay, so...
  36. Y

    Hooke's law - addition of force constant

    I need to figure out an equation that shows the relationship between the force constants of two springs that are connected together. I know that the 1/ktot = 1/k1 + 1/k2 but I have to shows all the steps to obtain this equation... I know that F = k1x1 = k2x2 = k(x1 + x2) I tried...
  37. P

    Force Constant, Springs

    Hi, I Need to know exactly how to solve this...I just can't take it anymore. The only reason I'm so into it now is because I don't get it. I promised my girlfriend I would help her and now she's annoyed because I get more into it than she does. But anyway, someone..PLEASE tell me what has to be...
  38. V

    Relating force constant and frequency to mass

    Homework Statement A body of unknown mass is attached to an ideal spring with force constant 123 N/m. It is found to vibrate with a frequency of 5.65 Hz. Find the mass of the object.Homework Equations F=-kx F=ma No idea what else... The Attempt at a Solution No idea where to start. I get...
  39. B

    Calculate Force Constant for Bungee Jumping

    Homework Statement so i have a bungee jumper starting 36m above the surface of a river from a hot air ballon. the elastic cord is attached to his waist. the unstretched length of the cord is 25m, and the student weighs 700N. calculate the required force constant of the cord if the student is...
  40. P

    Force constant of a spring launching a satellite

    You are asked to design a spring that will give a 1200 kg satellite a speed of 3.80 m/s relative to an orbiting space shuttle. Your spring is to give the satellite a maximum acceleration of 5.00g. The spring's mass, the recoil kinetic energy of the shuttle, and changes in gravitational potential...
  41. B

    Hooke's Law, Force Constant Question

    Homework Statement -How does the total force constant of two springs hung linearly compare with the individual force constants of springs. -Predict the equation that relates the total force constant, ktotal, to the individual force constants, k1 and k2, of two springs joined together...
  42. F

    K; the force constant of a spring

    Homework Statement how would you find the k (N/m) of a spring that is inclined at an angle (for ex. 30degrees)? Do you just ignore the fact that it's inclided at an angle? By the way, the spring is stretched at 8cm. Homework Equations hooke's law: F=kx The Attempt at a Solution...
  43. 7

    Calculating Spring Force Constant from a Dropped Ball

    A 86.3g ball is dropped from a height of 52.3cm above a spring of negligible mass. The ball compresses the spring to a maximum displacement of 4.9296 cm. The acceleration of gravity is 9.8m/s^2. Calculate the spring force constant k. answer in units of N/m.
  44. H

    Force constant of rear suspension of car

    Can anyone help with the formula set ups for this ? A 110 kg box is loaded into the trunk of a car. If the height of the car's bumper decreases by 13 cm, what is the force constant of the rear suspension ?
  45. E

    Calculating a force constant using kinetic and potential energy?

    You are designing a delivery ramp for crates containing exercise equipment. The crates weighing 1500 N will move at a speed of 2.00 m/s at the top of a ramp that slopes downward at an angle 24.0^\circ. The ramp exerts a kinetic friction force of 540 Non each crate, and the maximum static...
  46. P

    Equation for combined strings force constant

    Hi, you have two strings, one has force constant K1, the other Force Constant K2. You hook the two strings together. I need to see a derived euqation using K1 and K2 to find KTOTAL (the force constant when he two strings are placed together). Please keep things as simple as possible...
  47. marcus

    Using the force constant in equations

    Quantum gravity research ties into Planck units and it is possible to have variations on that theme. At one point (I think a couple of years ago) john baez was advocating that the units should be adjusted so that the central coefficient in the Einstein eqn have value one. that is the main...
  48. F

    What is the force constant of the web?

    Using sense organs in her legs, a spider can detect vibrations in the web when her prey is captured. When trapped in one web, a 1.0×10-3 kg insect causes the web to vibrate at 15 Hz. What is the force constant of the web?
  49. D

    What is the force constant of its rear suspension

    Problem- A 110-kg box is loaded into the trunck of a car. If the higher of the car's bumber decreases by 13cm, what is the force constant of its rear suspension? answer- i know the formula is Fx= -k(x) since Fx= 110 x 9.81 (110 x 9.81)/.13 =kN/m i get = 8300.77 but the answer in the...