What is Spring force: Definition and 119 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

    How to calculate the stiffness of a spring wire cantilever beam?

    I am designing a small box with a lid. The box and its lid measure 100mm x 70mm x 25mm tall.. The lid is spring loaded by a suitably designed torsion spring. When the lid is closed it is latched in place horizontally. The latch mechanism consists of a fixed item in the lid and a moveable latch...
  2. P

    Difficulty in deciding when to apply work energy theorem

    This is how I tried to do it. The force required to move B up the incline is $kx$ where x is elongation and k is spring constant. we know that spring force is greater than $mg(sin\theta+\mu cos\theta)$. And we can use work-energy theorem to figure out velocity. $0.5*k*x^2=0.5*mv^2$ where...
  3. pandatime

    Finding the Right Spring Force: A Tale of Error and Redemption

    What I've done so far is find the spring force through ##F_s = -kx## ##F_s = -111*16.7## ## = -1853.7N## My conclusion was that since this is the spring force, the tension force must be just the negative of that so ##1853.7N## because the net force has to balance out, but I am horribly...
  4. hquang001

    Work by a Spring Force - Understanding Uinitial and Ufinal

    Here it writes Wby spring= Uinitial - Ufinal. So is it equal to opposite of the change in potential energy ?
  5. aspodkfpo

    Spring Force vs Height on a Trampoline

    There is a trampoline drawn here and a graph of the spring force vs height. I don't see why the spring force is decreasing at a decreasing rate with respect to height above trampoline. F= kx = k * h/sin(theta), letting theta be between the horizontal and the spring.
  6. R

    Spring force after fixating with limited stiffness

    Hi folks, I have an interesting problem here from the real world, it's a design i am working on. So I have an object that is pressed by an hydraulic press with 50kN, let's call it F_before. Then I drive in a jig to fixate it. But the part that holds the jig has a limited stiffness. Hence if I...
  7. Amik

    Spring force question with a mass suspended on a spring

    Fnet=0 kx-mg=0 k=mg/x=0,25*9.8/0.2=12.25 But answer is 25(And they use 0.1 instead of 0.2 Why?)
  8. 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...
  9. Prabs3257

    Is Equating Energies a Better Solution for Finding Extension Under Spring Force?

    Its a very basic problem and my friend suggested a solution that we should equate mg and kx ie mg=kx and just plug in m=8 and x=0.16 but i think that we should equate the energies like mgx=1/2kx^2 ie because at the point where mg will be equal to kx the mass will still have a velocity hence it...
  10. Sofa

    Issues Determining Change in Elastic Potential Energy

    I've attached a screengrab of the problem (Specifically, Part B, as indicated in the image) and my attempt at a solution. Summarized, my thinking was based on using ##-\Delta U=\frac{Kx_i^2-Kx_f^2}{2}##. After using up all my attempts, the solution, as it turns out, was U2=4.91J. No variation...
  11. E

    Does the spring force do work on the spring itself?

    Consider a spring with one end attached to a wall and the other to a free mass, which is then stretched so some potential energy U. After it has been released and has de-stretched, the change of elastic potential energy is -U which equates to the negative of the work done by the spring force on...
  12. C

    Spring force and the force of friction

    Hello, do someone have time to help me out with an assignment? My question In the answer sheet they say: What I do not understand is why m is withdrawn from both sides, since I don't see that those represent the same mass. When I did the assignment I thought m at the left side would be the...
  13. 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/
  14. jybe

    Solve Spring Force Problem: Displacement, Velocity & Acceleration

    Homework Statement A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 6.30 N is applied. A 0.540-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the origin to x = 5.00 cm and...
  15. navneet9431

    Why doesn't the Spring Force change on splitting?

    Suppose a spring of spring constant=K and Length=L is split into two parts L1 and L2, with spring constants K1 and K2 respectively. Then,why is it such that the spring force F=K1*L1=K2*L2=K*L? Please give an intuitive explanation of why the spring force doesn't change? I will be thankful for...
  16. isukatphysics69

    Find the work done by the spring force on a box

    Homework Statement Homework EquationsThe Attempt at a Solution Wspring = ∫-k*xdx limits of integration are 12 and 0 So [0 - .12^2/2]*172 = -1.24J of force Getting 1.8/2 points for this anser
  17. Y

    Im back, and with a question about spring force

    Homework Statement I feel like my numbers are wrong so I just had a general question what is a typical value for k (spring constant) for a rubber band assuming in this case that k=F/x is an equation that works for rubber bands because the number i got...idk it seems rather large Homework...
  18. jzzdrmr

    Effect of spring force on acceleration

    Okay, so I am designing a new treadle hammer and I want to know how much force a spring will add to the force of the hammer. Basically I have an 8 pound head that can either fall at the speed of gravity or be forced down by a 20lb extension spring. The attached image is not my design and I...
  19. Leah12

    What is the Elastic Potential Energy of a Toy Car's Spring?

    The force constant of the spring in a child’s toy car is 550 N/m. How much elastic potential energy is stored in the spring if the spring is compressed a distance of 0.012m? The formula for spring force is F =kx When I do 550 x 0.012m I get 6.6 but I am supposed to round my answer four decimal...
  20. SirChris93

    Find the time when the spring force reaches max magnitude

    Homework Statement Show how you use calculus to find the time when the magnitude of the Spring Force reaches its maximum. Then, when you found that time show how you calculate the Spring force at that time as well. m = 1.125kg vi = .8 m/s k = 2250 N/m x = 0m Homework Equations Fs (t) = [-mvi...
  21. A

    Minimum spring force required to keep a car level

    Homework Statement This is an attempt to solve a problem I asked about here https://www.physicsforums.com/threads/can-a-car-ever-sit-like-this.929453/ Homework Equations F = kx spring force The Attempt at a Solution using the largest angle down it can get with the front spring compressed all...
  22. C

    Solving for the internal forces and reactions

    Homework Statement I'm having a hard time finding the reactions at the supports and the force exerted by the spring. Given: 20 lbs 25 lbs 35 lbs k = 200 lb/ft lo = 2.5 ft members are 4 ft longHomework Equations ΣM ∑Fy = 0 ∑Fx = 0 The Attempt at a Solution I tried solving for the reactions...
  23. H

    How to find max velocity in a spring-mass system?

    Homework Statement Two masses connected with a spring with contant k. The string streched by l . Find the max velocity of mass m! M2 ___spring___ M1 M2--stretched by x2--____spring____--x1--M1 l = x1+ x2 2. Homework Equations F = k.l Mass1.x1 = mass2.x2 (x= displacement?) a=w^2 x v = wx Ep +...
  24. R

    Spring deflection load calculation for excavator

    1. A hydraulic cylinder equipped with a helical coil compression spring(figure is attached). The oil pressure acts the spring and moves the boom from position 1 to position 2. Maximum boom load in position 1 F1max= 16550N Minimum boom load in position 2 F2min = 18550N cylinder load...
  25. F

    Spring Force and Displacement: Understanding the Relationship

    Problem: Attempted Solution: The answer is actually (1/3)As^3+(1/2)Bs^2
  26. M

    B The Sense of Restoring Force in Vibrations

    I would like to ask about the sense of the restoring force in mechanical vibrations. Comment 2 says that resultant force is opposite the motion but I have some hesitations about it because let's think the situation that mass is moving back upward to its equilibrium position. In this case the...
  27. D

    Maximum compression in the spring

    Homework Statement Find the maximum compression in the spring, if the lower block is shifted to rightwards with acceleration of '##a##'. All the surfaces are smooth. Homework Equations $$\vec{F}=m\vec{a}$$ $$\vec{F}_{sp}=k\vec{x}$$ The Attempt at a Solution FBD of the upper block: From...
  28. astrocytosis

    Gas inside an expandable cylinder raises lid on spring

    Homework Statement An expandable cylinder has its top connected to a spring of constant 2000 N/m. The cylinder is filled with 5L of gas with the spring relaxed at a pressure of 1 atmosphere and a temperature of 20C. If the lid has a cross-sectional area of 0.01m2 and negligible mass, how high...
  29. Chevreuil

    Spring+mass to do known job. How dimension? Impulse? Energy?

    Hello there, I'm working on a design project where I have come upon a mechanical problem that I'm having trouble with. Basically I'm making a kind of specialized stapler (at least I think that's a good translation...), and I want it to clamp the staplers using a mass accelerated by a spring...
  30. Mouadys

    Hooke's Law: Spring Force Negative?

    Hello, Following Hooke's law, the force applied by a string on an object attached to one of its ends is F = -kx But here is my question : if we consider the equilibrium coordinate x=0 of a horizontal string, and the string is stretched until its end reaches a coordinate x1>0. By applying hooke's...
  31. B

    What Went Wrong with Calculating Spring Force in This Physics Problem?

    Homework Statement A 5.3kg mass hangs vertically from a spring with spring constant 720N/m. The mass is lifted upward and released. Calculate the force and acceleration the mass when the spring is compressed by 0.36m. Note: I already solved for acceleration and I got the correct answer-...
  32. CK328

    Equation for spring force for a cylinder on compressed air

    Evening all, I've recently undertaken a project where my roll is to analyse the suspension of a mountain bike. The suspension unit in question is a Rock Shox Monarch RT3. To give a brief summary: The shock uses compressed air as the spring, the pressure is adjustable via an air valve. The shock...
  33. CK328

    Mathematical modeling of a mountain bike rear shock

    Evening all, I've recently undertaken a project where my roll is to analyse the suspension of a mountain bike. The suspension unit in question is a Rock Shox Monarch RT3. To give a brief summary: The shock uses compressed air as the spring, the pressure is adjustable via an air valve. The shock...
  34. P

    Finding the spring constant of a spring in a pulley system

    Homework Statement Ok so here is the prompt: a 3kg object is fastened to a light spring over a pulley. The pulley is frictionless and its inertia may be neglected. The object is released from rest when the spring is unstretched. If the object drops 0.1 meters before stopping, find the spring...
  35. A

    Determining the Spring Constant for a Pendulum with a Spring-Loaded Launcher

    Homework Statement A pendulum, initially at equilibrium, is set into motion by a spring-loaded launcher (compressed a distance of 0.0150 m) which fires horizontally. If the mass of the pendulum bob is 0.340 kg and it rises to a maximum height 0.120 m (relative to equilibrium), what is the...
  36. CMATT

    Spring Force and kinetic energy

    A novelty clock has a 0.0109 kg mass object bouncing on a spring that has a force constant of 1.34 N/m. How many joules of kinetic energy does the object have at its maximum velocity if the object bounces 3.49 cm above and below its equilibrium position?
  37. M

    Spring force due to Axial and Torque load?

    Homework Statement The first theory shows a spring under an axial load where the Torque is given as WRcos(a) The second theory shows a spring under axial Torque. T is given as Wsin(a) Homework Equations Given in links The Attempt at a Solution A torque T would be at full strength along...
  38. L

    Can the spring constant k be used for crumple? (not spring)

    A question on my lab is find the amount of "stopping force" required to stop the egg, by determining the size of the "crumple zone" A brief description of the lab: Build a container that will keep an egg from breaking as it is dropped from the third floor of the school, your container must...
  39. A

    Solve Spring Force/Energy: Find Velocity

    I have a question that asks to find the velocity of the object attached to a horizontal spring when it is halfway to equilibrium. I am given the mass, how far the spring was stretched, and the velocity of the spring when it was released. I am unsure of what it means by halfway to equilibrium...
  40. I

    Solving Spring Force Equation: 2X

    Hello, If we have a spring at rest and has a constant k=2 N/m (at its natural length with one end at origin (x=0) and the other end held stationary) is having a force applied on it. The force varies in same way as the the spring with function 2X. My question is how is it possible to start the...
  41. A

    Friction/spring/inclined plane problem

    Homework Statement There is a block of 1kg (m1) resting frictionless on another block of 5kg (m2). m1 is connected by a horizontal spring to m2. m2 is resting on an inclined plane of 45°. Between m2 and the plane there is friction. A force of 200N is applied on m2, pushing it upwards. F=200N...
  42. Nayef

    Work-Energy principle and spring force

    A block lies on a horizontal frictionless surface, and the spring constant is 50 N/m. Initially, the spring is at its relaxed length and the block is station ary at position x = 0 .Then an applied force with a constant magnitude of 3 N pulls the block in the positive direction of the x...
  43. M

    Impact force calculation of a Full Suspension Mountain Bike

    Hello Folks! I want to find the maximum applicable force on a full suspension mountain bike and i will use this force on a FEA software structural analysis for a uni design project. This bike has a rear suspension with 400 lbs/in spring rate.Also rear wheel vertical displacement(travel amount)...
  44. 0

    Kinda silly, but what's the sign of v?

    I have a block with a certain mass attached to a spring. I pull it and then release. Spring pulls block back. When spring is back to its relaxed position, is the velocity of the block positive or negative? Exercise does provide k, mass and x, but that's not where the error is comming from...
  45. 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...
  46. Z

    Elastic Potential Energy to Aid Electromagnetic Induction

    Matter can neither be created nor destroyed...but potential energy can be converted into a different kind of energy. Let's say we have a spring with a mass connected to it. This mass is a magnet, and the apparatus is inside a copper coil. It's a horizontal magnet with friction minimized at the...
  47. E

    Calculating the Force Constant of a Bungee Cord Using Newton's Laws

    Homework Statement You've attached a bungee cord to a wagon and are using it to pull your little sister while you take her for a jaunt. The bungee's unstretched length is 1.3m and you happen to know that your little sister weighs 220N and the wagon weighs 75N. Crossing a street, you accelerate...
  48. W

    Spring force and frictionless mass vs speed

    Homework Statement A mass (m = 1.35 kg), originally at rest, sits on a frictionless surface. It is attached to one end of an unstretched spring (k = 747 N/m), the other end of which is fixed to a wall (see figure below). The mass is then pushed with a constant force to stretch the spring...
  49. G

    Torsion spring force required to open a door

    I have a heavy door that I am adding torsion springs too in order to make it easier for a human to open. -The door weighs 460lbs. -It is hinged on one side by two heavy duty hinges and uses a thrust bearing in each hinge with a friction coef. of .008 -the effective radius of the thrust bearing...
  50. B

    The effect of spring force when perpendicular to displacement?

    Homework Statement Hi everyone, I am generalizing the following problem because I disagree with how the book solves the problem. A square mass 'm' is attached to two springs with identical constants 'k', in a configuration such that the springs mount to the left/right sides of the...