# What is Spring constant: Definition and 450 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. ### B Why is my experimental spring constant an order of magnitude off?

I did my Physics IA on comparing the maximum height reached by a projectile (shot by a spring) and the compression of that spring. In my experiment I found the maximum height reached by a metal ball shot directly upwards in comparison to the amount the spring was compressed. To test the...
2. ### Calculating the spring force constant K

So, my question is pertaining more to a specific part of this problem than actually calculating ##P## which I get to be ##P = \frac{kh}{2} - mg##. But I need ##P## in terms of a multiple of ##mg## so I need to find ##k##. The solution attached uses the fact that when the object comes to a rest...
3. ### How Is Potential Energy Converted to Kinetic Energy in Physical Systems?

d) W=1/2kx^2=PE 41000=1/2(k)(33)^2 k=82000/(33)^2 k=75.3N/m (nowhere close to the answer) e) Potential Energy = Kinetic Energy mgh = 0.5 * m * v^2 Given: m = 26 kg g = 9.8 m/s^2 h = 160 m Solving for velocity (v): 0.5 * 26 kg * v^2 = 26 kg * 9.8 m/s^2 * 160 m v^2 = (2 * 9.8 m/s^2 * 160...
4. ### Energy stored in a double spring system

Part c) i) is no problem, clearly k/m = w^2 = (2pi f)^2, solving for k using f = 0.15, m=6.6 x 10^5 gives k=5.9 x 10^5 which is close to 6x10^5. Part ii) is causing me some issues however. Clearly the model uses two springs, of combined spring constant 6 x 10^5, therefore the spring constant of...
5. ### Calculate the spring constant of oscillating mass on a spring colliding with a wall

So I proceed as: Total time for 1 oscillation is 0.2s $$\frac{1}{\sqrt{2}}=\sqrt{2} \sin ({\omega t_1})$$ $$\sqrt{2}=\sqrt{2} \sin ({\omega t_2})$$ Therefore $$\omega t_2=\frac{\pi}{2}$$ $$\omega t_1=\frac{\pi}{6}$$ $$\omega ×2(t_1+t_2)=2×\left( \frac{\pi}{2}+\frac{\pi}{6}\right)$$ Since...
6. ### Why can we move the spring with constant speed when we apply a force?

One solution is that if we move with the same velocity as the spring does, the initial velocity of the block will be ##v## and the final will be zero, so its kinetic energy will transform into a potential energy of the spring. I would also say that we can say that if we pull the spring, we...
7. ### Spring constant formlula for Force and Work Done

Finding x by force formula - only force acting is gravity ma/-k = x (0.2)(-9.8)/185 = x 0.010594594 = x Finding x by wd formula WD_ spring = (1/2)kx^2 F x = (1/2)kx^2 2(mg)/k = x [2(0.2)(-9.8)]/ 185 = x 0.021189189 = x how come the work done and force formulas produce different values for x...
8. ### Find spring constant k using an electrical circuit

This circuit consis of two identical, parallel metal plates free to move, other than being connected to identical metal springs, a switch, and a battery with terminal voltage ##\Delta V##. With the switch open, the plates are uncharged, are separated by a distance ##d##, and have a capacitance...
9. ### Engineering The value of "k" for spring constant, is the book answer incorrect?

There is some discussion currently and I was hoping to get some opinions here. The question is in regard to a Hook's law problem. The text gives the problem as seen below. The text says the answer is 50lb/in. Several people have tried from several different approaches. Factoring the "y" equation...
10. ### B Finding the spring constant of a rope

The 7/8" Kinetic Recovery Rope like this yankum rope is the most common size used for Jeeps, Broncos, and other SUVs. I apologize for English units but that's how ropes are sold and marketed. I've talked to the biggest rope suppliers and they have no idea how to compute the rope's spring...
11. ### I Predicting the spring constant theoretically

I take a wire of metal X which has a diameter d. Let the total length of it be L and I roll it around a cylinder with diameter D to create a spring. Is it possible to predict the spring constant of this system (and relate it to the elastic constants of the metal)? Has anybody seen/heard/know a...
12. ### What is the Relationship Between Force and Spring Constant?

In question 1, the spring constant from the two formulas was not the same. When we used the first formula, we got that the spring constant was 7.83 N / m. The second formula we got that the spring constant was 8,03 N / m. In questions 2 and 3 I do not know and am unsure about how to answer...
13. ### Variable pitch spring calculations

Hi, does anyone know how to calculate the current spring constant of a variable pitch spring when under compression. Since some of its coils get inactive when compressed the stiffness is increasing and consequently “k” is changing as well, is there an equation I can use to calculate the new...
14. ### Finding Spring Constant When Given Amplitude, Time, and Mass

I averaged the masses and times (which i took the time given and divided by 10 because in the problem it says you measure the time it takes to complete 10 oscillations) then plugged them directly into the T=(2(pi)((m/k)^1/2) and got the wrong answer. This is really confusing me because I don't...
15. ### How can I use the formula k=4pi^2m/T^2 to find the mass of a bolt?

I managed to isolate k to k=4pi^2/T^2 however I don't know If I did it correctly. I am trying to use K to find the mass of a bolt. I am stuck here, not sure If i need to find all three k's and then average them out?
16. ### Multiple choice Q: Mangetic fields and Spring Constant

My attempt at a solution: Is my logic accurate/correct, and is my answer correct? I consider the forces acting to be: Restoring forces in springs parallel, and Force of the current-carrying conductor in the Magnetic field. I imagine a vertical displacement of y upwards ( direction determined...
17. ### Finding Spring Constant & Energy w/ Doubt in Exercise

Summary:: Doubt in a spring exercise Text of the exercise "a mass of ##m = 0.4 \ \text{kg} ## is attached to a spring and it oscillates horizontally with period ##T = 1.57 \text{s}##; the amplitude of the oscillation is ##d = 0.4 \text{m}##. Determine the spring constant, the total energy of...
18. ### Trouble with units for Spring Constant

I do not understand how in part a, the units for K can be N/m. If Work is in joules which is kg*m^2/s^2 and we are diving by x^2 which is m^2, then m^2 should cancel out and we should be left with kg/s^2. Kg/s^2 makes more sense because in part b when you find the work done you are multiplying...
19. ### B Why is Young's modulus constant below the limit of proportionality?

Hi all, I'm a little confused about something. Force-extension graphs and stress-strain graphs are always both straight lines up until the limit of proportionality, implying both the spring constant and the Young modulus are constant up until then. For a force-extension graph, Hooke's Law...
20. ### How to determine the spring constant in a Lennard-Jones potential

Hi, First of all I hope it doesn't bother if I ask too much question.I found the values of ##u1,u2## for 2 differents posistions ##(r1,r2 )## and I now have to determine the spring constant (k).I'm thinking about using$$F= -kx$$ with ##F = -\frac{du}{dr}## then  U = \int -kr \cdot dr...
21. ### Calculating Earth's Effective Spring Constant for its Orbit Around the Sun

My first attempt was using the period equation of a spring system. I've changed it into k=((2π)^2*m)/T^2, then put Earth's mass into "m" (5.972*10^24), then put the time required for one revolution of Earth around the Sun, 365 days into seconds, 31536000 sec, to "T" So I got (2.371*10^11 kg/s^2)...
22. ### Spring constant matrix and normal modes (4 springs and 3 masses)

We need to find the normal modes of this system: Well, this system is a little easy to deal when we put it in a system and solve the system... That's not what i want to do, i want to try my direct matrix methods. We have springs with stiffness k1,k2,k3,k4 respectively, and block mass m1, m2...
23. ### Why is my solution to finding the spring constant incorrect?

This is my scope of the question, i could think to solve it by two steps, but before, let's give name to the things. X is positive down direction. X = 0 at the initial position o the platform Mass of the falling block is m1 Mass of the platform, m2 Spring constant k Δx is the initial stretched...
24. ### A Effective Spring Constant of a Chain Polymer

Hi All, I'm doing research in magnetic nanoparticles that are coated with chain molecules (oleic acid, I believe) and I am trying to model these molecules' effective spring constant. The basic scenario is this: When a water-based ferrofluid is evaporated, it leaves behind only dried...

26. ### Need to find the spring constant to achieve Max Velocity

Hello All. I am mentoring a high school student in my area with his class project for school. He has chosen he wants to launch an object (in our case, a softball) into a 5' diameter area. The idea is to build basically an oversized slingshot using an extension spring as the source of energy. We...
27. ### How do I Calculate the Spring Constant of a Piece of PVC pipe?

Okay so, recently I got a job with my local newspaper delivering newspapers to make some money while deciding how I want to continue my educational career (I already have some college under my belt but I'm taking a semester off). All the newspapers have to be at the houses by 6 am so in order to...
28. ### What is the density of a constant? (spring constant)

Hi, I could you explain me what is the density of a constant (particurarly the spring constant, or should I say "stiffness" constant)? I guess it's a probabilty function but would like more details. I would like an answer that at first describe the concept and later refine the mathematical...
29. ### Spring Car, Acceleration Problem: Find Spring Constant

"It should be able to accelerate from rest to 20 m/s at least 50 times before the spring needs winding" -So F = -kd = -k(2.1) - d is 2.1 because it is the compression length Now, since we know the d, divide it by 50, 2.1/50 = 0.042m Basically, the spring unwinds 0.042 m 50 times for a total...
30. ### Spring constant that withstands 110 kg

Hello, I have a mass of 110 kg and I want to move it with a speed of 14 m/s by using springs. how can I determine the constant of the spring and design it? thank you!
31. ### 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/
32. ### How do you know when k in Hooke's law is positive or negativ

Homework Statement A 7.2-kg mass is hanging from the ceiling of an elevator by a spring of spring constant 150N/m whose unstretched length is 80 cm. What is the overall length of the spring when the elevator: (a) starts moving upward with acceleration 0.95m/s2 ; (b) moves upward at a steady...
33. ### Spring constant of a car on springs

Homework Statement When four people with a combined mass of 325 kg sit down in a 2000-kg car, they find that their weight compresses the springs an additional 0.55 cm. A) What is the effective force constant of the springs? B) The four people get out of the car and bounce it up and down. What...
34. ### Confused about a simple harmonic motion problem....

Homework Statement A vertical block-spring system on Earth has a period of 6.0 s. What is the period of this same system on the moon where the acceleration due to gravity is roughly 1/6 that of earth? Homework Equations w = √(k/m) w = (2Pi)/T T = 2Pi*√(m/k)[/B] The Attempt at a Solution So...
35. ### Calculating spring constant of a spring loaded cannon

Homework Statement if you wanted to build a spring launched cannon that will shoot you over a building that is 35 m high and 30 m wide, and the cannon is being shot at 60 degrees. If the cannon can be no more than 2 m long, what spring constant do you need in the spring to make this work? here...
36. ### 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...
37. ### 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...
38. ### Block moves down incline, hits spring, find spring constant

Homework Statement [/B] The block, initially at rest, slides down the ramp and compresses the spring 0.03 m. Theta = 30 degrees L = 1.25 m M of block = 2 kg Δx = 0.03 m 1) Write the expression for the initial and final energy states 2) Find the spring constant K Homework Equations mgh...
39. ### Finding Spring Constant Without Distance

Homework Statement Spring Compressed = 20cm = .2m Decompresses and leaves the ground at a velocity of 5m/s Mass = 6.00 kg Homework Equations k = fx The Attempt at a Solution I have no idea where to go from here...
40. ### Hooke's Law Lab Spring Constant Calculation

Homework Statement I need to calculate a spring constant using measurements from a Hooke's Law Apparatus, a spring, and some weights. The weights are hung vertically from the spring and the distance is measured from the equilibrium point of the spring. If I'm solving for k, then k=F/x. I do...
41. ### The 2.5-kg wieght is released from rest -- Determine the spring constant k

Homework Statement 14.27 The 2.5-kg weight is released from rest in position A, where the two springs of stiffness k each are undeformed. Determine the largest k for which the weight would reach position B Homework EquationsThe Attempt at a Solution Hi. Can you check if I am going at...
42. ### Pushing spring from both sides - Find the spring constant

Homework Statement A spring relaxed length is 0.5[m]. It is being pushed from both sides, and contracted to 0.4[m]. The force the spring is applying outwards is 3[N] on each side. What is the spring constant k? Homework EquationsThe Attempt at a Solution I attempted drawing a force diagram...
43. R

### Calculating Work Required to Stretch a Spring by Additional Distance

Hey everyone, I'm really hoping somebody will be able to help me with this problem. I've searched all through my textbook, notes, and the Internet, but I keep getting the wrong answer. Here's the question: If it requires 6 J of work to stretch a particular spring by 2.0 cm from its...
44. W

### (Spring constant) I can't figure out what I did wrong.

Homework Statement Two springs which have spring constant of k1 and k2 respectively are vertically hung in a series. Then, a mass m is attached to the end. Find the displacement and the spring constant of this series. Homework EquationsThe Attempt at a Solution I got the displacement x1+x2...
45. ### Calculating Spring Constant From Plot of T^2 versus r^2

Homework Statement Hi, I recently performed a lab experiment for calculating the moment of inertia and spring constant of a couple of equal masses on a steel rod. I had to do this experiment at the exact same time as performing another experiment so I was unable to perform any calculations in...
46. ### How do i find the spring constant for a rope torsion spring

I have built a torsion wheel catapult (Mangonel) for an assignment,and I need to do some theoretical calculations about the displacement, velocity and time of the projectile, the problem is I don't know how to calculate the spring constant without the displacement of the spring (x) and i don't...
47. ### Calculating the Spring Constant from Force-Extension Graph

Homework Statement Force Extension in (m) 1.0 0.014. 1.5 0.032. 2.0 0.053. 2.5 0.071. 3.0 0.090. 3.5 0.110. 4.0 0.130. 4.5 0.148. 5.0 0.166...
48. ### Rubber Band Spinning in midair

Homework Statement A uniform thin circular rubber band of mass M and spring constant k has an original radius R. Now it is tossed into the air. Assume it remains circular when stabilized in air and rotates at angular speed ω about its center uniformly. Derive an expression for the new radius...
49. ### Understanding the Relationship between Spring Constant and Energy

Homework Statement Homework EquationsThe Attempt at a Solution EPE is (0.5)kx^2 Let Y have spring constant of K then X has spring constant of 2K So EPE of Y is (0.50kx^2 which is E So EPE of X must be (0.5)2kx^2 which is kx^2 which is 2E? But correct answer is E/2??
50. 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.