What is Spring energy: Definition and 39 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.

View More On Wikipedia.org
  1. A

    I How come you have to use work energy to find v0 of spring?

    If you use work energy, you can get 0.5*k*x^2 = 0.5*m*v^2 to get the velocity if you pulled the spring a distance x. How come you cannot do kx*(delta t) = m*v to get the initial velocity and what would be the delta t value?
  2. Juanda

    Classical Possible error in book (Thermodynamics: An engineering approach)

    Hello I was checking the book THERMODYNAMICS AN ENGINEERING APPROACH (the 2023 version) because I saw it recommended on the internet. I was surprised to find an error in one of their examples because it is already on the 10th edition. I'm pretty sure about the error but I wanted to confirm it...
  3. Semiclassical

    Quartic function of a non-ideal spring

    I'm stuck in a part of my problem where I need to find the roots of this function which represent turning points for a non-ideal spring.
  4. J

    Looking for some help realting to spring energy changes

    Homework Statement https://imgur.com/gallery/PQx8SmXHomework Equations EPE (elastic potential energy) = 1/2kx^2 GPE (gravitational potential energy) = mgh The Attempt at a Solution my attempt, https://imgur.com/gallery/lJDhwqD [/B] I feel like I've made progress considering the quadratic...
  5. A

    Is energy profile of a spring asymmetric with +x and -x?

    Homework Statement [/B] The problem is with part b(ii). This is an A level question so only elementary concepts are to be used. Homework Equations $$E = \frac{1}{2}kx^2 $$ The Attempt at a Solution EPE should be max at 0, 0.4, 0.8 since E is a function of $x^2$. However, mark scheme only...
  6. H

    Rubber strings pulled and realeased -- find the max height

    Homework Statement Homework EquationsThe Attempt at a Solution I tried to find constant k f = k ##\Delta##x 1/2 * 9,8 = k * 0,1 k = 49 N/m is rubber string the same as spring? Ep + EK at 0,1 meter = Ek + EP at 0,3 m 1/2 k x^2 + 0 = 1/2 k x^2 + 1/2 mv^2 v^2 = 2*49(0,08) v = 7*0,4 = 2,8...
  7. X

    Is My Understanding of Spring Energy Conversions Accurate?

    Hi guys, I'm currently trying to study the energy conversions of a spring - can someone tell me if my understanding of it is completely correct or not? Thank you so much! I made it as detailed as I could: One complete oscillation of a spring: The spring starts off stationary, meaning it has no...
  8. Y

    Help in Homework - Kinetic Energy

    Homework Statement Problem: http://imgur.com/a/Sw2zA Hi all, I was given this problem as homework and I have almost no clue on how to solve it. I have tried for some time with no luck. Homework Equations We learned about kinetic and potential energy as well as work. W = F*d W = delta KE PE =...
  9. V

    How to apply the First Law of Thermodynamics to this problem?

    Homework Statement A spring (k = 500 N/m) supports a 400 g mass which is immersed in 900 g of water. The specific heat of the mass is 450 J/kg and of water is 4184 J/kg. The spring is now stretched 15 cm and, after thermal equilibrium is reached, the mass is released so it vibrates up and...
  10. X

    How do energy conversions in a spring work during one complete oscillation?

    Hi, I'm having trouble understanding the energy conversions in a spring. I know that whilst a spring is being deformed, it gains elastic potential energy and at maximum deformation it has max elastic potential energy. But, does a spring have maximum kinetic energy at its un-deformed state? if...
  11. M

    Spring Energy System: Finding Total Energy with User-Selected Position (x,y)

    Homework Statement The picture is too tough to draw online, so I've attached a picture of it. The illustrated mechanism shows two springs both with a known spring constant ##k## and rest length of ##2R##. One end of the top spring is fixed above a wheel and the other end is attached to the...
  12. R

    Maximum speed of a cylinder dropped on a spring

    Homework Statement Cylinder A (mass = 5kg) is released from rest at a height h =100mm above a spring of stiffness k = 1.8 kN/m. Determine, (i) the maximum compression of the spring, (ii) the spring deflection when the cylinder’s velocity is a maximum, and, (iii) the maximum velocity of the...
  13. 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...
  14. H

    Spring energy problem at an incline with friction

    Homework Statement Homework Equations Et = Ek + Eg + Ee The Attempt at a Solution Top:[/B] Et=mgh+1/2k1 Δx12 +1/2k2Δx22 196h+400+600 = ET Bottom: Et=1/2k1Δx22+1/2k2Δx22 400+600=1000 ...and that's when I realized I must have done something wrong. Sorry, I'm kind of bad at this stuff...
  15. Ryan_m_b

    Real life examples of spring energy storage

    Tonight I've had a deceptively simple question that I've found maddeningly difficult to get an answer to. What I'm looking for is a list of springs with information on how much they can be compressed and how much energy they store. E.g.: Steel spring from company A has dimensions X, Y, Z and...
  16. blintaro

    Spring Energy Thought Experiment

    Hi guys, I work at the tutoring center of my university, and recently a student came in with a question that has been troubled me ever since. Say you have a certain mass M a distance Δχ above a massless spring. When asked how much energy this system has, you would say it has only...
  17. T

    Spring potential energy comparison

    Homework Statement A 0.10 m spring is stretched from equilibrium position to position A and then to position B as shown in the diagram below. Compared to the spring’s potential energy at A, what is its potential energy at B? Homework Equations PE = 1/2 kx^2 The Attempt at a...
  18. S

    Spring Energy (Finding Velocity)

    Homework Statement A spring AB or constant k = 2N/m is attached to a support A and to a collar of mass m=1kg. The unstretched length of the spring is 1m, Knowing that the collar is released from rest at x = x0 = 0.9 m and neglecting friction between the collar and the horizontal rod...
  19. C

    How Do You Calculate the Spring Constant in a Frictionless System?

    Homework Statement A low friction cart has a spring plunger. The plunger and spring are compressed 6.80 cm and locked in place. The cart is launched from rest up an inclined track tipped at an angle of 13.5°. When the spring is released the cart travels 76.4 cm up the incline from its...
  20. T

    What was the plane's landing speed?

    Homework Statement As a 15000 kg jet plane lands on an aircraft carrier, its tail hook snags a cable to slow it down. The cable is attached to a spring with spring constant 60000 N/m. If the spring stretches 30 m to stop the plane, what was the plane's landing speed? Homework Equations...
  21. A

    2 masses collide, one has spring. -Collision, Momentum, Spring energy

    Homework Statement Mass 1 at 10m/s collides into mass 2 at rest, which has a spring attached to it. The second mass has a spring at 200N/m and natural length L0 = 0.1m. At the instant they collide, the spring is compressed to its max amount and the masses move with the same speed V. Determine...
  22. S

    Spring energy to kinetic energy

    Homework Statement A horizontal spring with spring constant 92.2 N/m is compressed 15.5 cm and used to launch a 2.93 kg box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinetic friction of the box on the surface...
  23. J

    Rope ascension using stored spring energy

    Just looked at a video of the atlas rope ascender (google it) and thought it was pretty cool. However, I feel as though using a more "capacitive" approach and taking advantage of the fact that ascensions would not occur frequently could allow for the use of a system that slowly recharges over...
  24. 0

    Spring energy to rotational energy

    How do i convert spring energy to rotational energy? I am building a 'green device' that allows a bicycle to move forward using stored energy (compressed spring energy). So i am figuring out how do i change the spring energy stored to rotational energy so that th bike will be able to propel...
  25. G

    Spring Energy Problem Conservative forces

    Homework Statement A spring is attached to a ceiling, and has a relaxed length of 25cm. When a mass m=.80kg is attached to the spring it stretches to an equilibrium length of L0=34cm. a.)Find the Spring Constant of the Spring? b.)I lift the mass until the spring returns to its relaxed length...
  26. C

    What's wrong with this Spring Energy question?

    Homework Statement You are given a spring with some peculiar properties. Rather than the usual equation F = −kx, you find the spring is best modeled by the equation F = −kx − lambda(|x|^2)(xhat), where lambda has units of N/m^2. The unstretched length of the spring is x0. You attach the spring...
  27. G

    How Do Gravity and Spring Forces Relate in Vertical Spring Energy Calculations?

    Hello! I'm a bit confused as to the relationship between the magnitude of Hooke's law (F=kx) and the magnitude of gravity versus the relationship between gravitational potential energy and spring potential energy for a vertical spring system. So, here is my problem. Imagine that you place a mass...
  28. W

    Calculate Arrow Speed & Height | Spring Energy Problem Homework

    Homework Statement An archer puts a 0.30 kg arrow to the bowstring. An average force of 192 N is exerted to draw the string back 1.3 m. Assume that air resistance is negligible. (a) Assuming that all the energy goes into the arrow, with what speed does the arrow leave the bow? (b) If the...
  29. L

    Stored Spring Energy Calculation

    Hi - Would someone check my method here please? Thank you Homework Statement Two trolleys A and B, of mass 0.70kg and 0.80kg respectively, are on a horizontal track and held together by a compressed spring. When the spring is released the trolleys separate freely and A moves to the left...
  30. Q

    Exploring Spring Energy: Loss & Gain

    A spring has an unstretched length of 0.650 and a weight of 0.400kg is attached and gently lowered till eqm point is reached. The spring is then stretched by a distance of 0.200m. Loss in gpe=mgh=0.200x0.650x9.81=0.785 J Gain in EPE=0.5 Fx= 0.5 x 0.400x 9.81 x 0.200=0.392 (?) Actually I...
  31. R

    How Far Will the Cord Stretch When a 2kg Block is Suspended?

    a cord with a spring constant of 100N/m has a 2.0kg block suspended from it. the length of the cord when it is unstretched is .5m. the block is released. determine the length of the cord when it is at the maximum length of elongation. my attempt: first determine the kinetic energy of the...
  32. L

    Nonlinear spring energy problem

    Homework Statement The stretch of a nonlinear spring by an amount x requires a force F given by: F=40x-6x^2 where F is in Newtons and x is in meters. What is the change in potential energy U when the spring is stretched 2m from its equilibrium position? Homework Equations U=.5kx^2...
  33. R

    Maximum Height Reached by Block on Spring

    A block of mass 0.250 kg is placed on top of a light vertical spring of constant k = 5200 N/m and is pushed downward so that the spring is compressed 0.093 m. After the block is released, it travels upward and then leaves the spring. To what maximum height above the point of release does it...
  34. B

    What is the oscillation frequency?

    Homework Statement A spring is standing upright on a table with its bottom end fastened to the table. A block is dropped from a height of 3 cm above the top of the spring. The block sticks to the top end of the spring and then oscillates with an amplitude of 20 cm. What is the oscillation...
  35. K

    How Fast Does a Released Mass Travel After Being Stretched by Springs?

    A 10kg mass, attached by means of two springs to the ceiling, is held against the floor and is then released. How fast will it be traveling when it hits the ceiling? The spring constant of each spring is 80 N/m, and each spring has an unstretched length of 1 m. Assume that springs become loose...
  36. G

    Solving Spring Energy: Half Amplitude & Kinetic Energy %

    For an Ideal spring...At half Amplitude, what % of the energy is kinetic? I know at A the kinetic energy it instantly zero which makes max potential energy (.5kx^2) I also know that after released, at the instant passising through the equilibrium point kinetic energy is max and potential...
  37. R

    Maximizing Potential Energy in a Falling Mass-Spring System

    Hello all, I am looking for some assistance with a physics problem that I have for my physics class. Any help would be greatly appreciated because I have no idea where to start. Thank you all ahead of time for your help. The problem is: A 10-g mass is attached to the end of an...
  38. P

    Vertical spring energy transformation

    a mass is attached to a spring and released. it then oscillates in simple harmonic motion. what is the transformation of energy? i understand how it works horizontally (max Ee at the 2 ends, max Ek at the equilibrium position), but how does it work vertically now that Eg is also present...
  39. J

    How Is Spring Compression Calculated When a Mass Is Dropped on It?

    Suppose a 300g mass is dropped from a height of 40cm onto a vertical spring with spring constant 200N/m (having a light platform on top) and sticks to the platform (a) How far will the spring compress? (b) How far will the spring be stretched as the mass and spring rebound? use S.I. units. I...