hooke's law Definition and Topics - 36 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.
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...
In every book I checked, the energy (per unit mass) of elastic deformation is derived as follows:
## \int \sigma_1 d \epsilon_1 = \frac{\sigma_1 \epsilon_1}{2} ##
and then, authors (e.g. Timoshenko & Goodier) sum up such terms and substitute ##\epsilon ## from generalised Hooke's law i.e.
##...
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/
Homework Statement
If a spring is loaded with a mass, the spring being completely vertical and the mass hanging below it there would be an extension in the spring relative to the mass applied/force applied according to hookes law. If the same spring was not vertical but coiled (similar to a...
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...
Homework Statement
Homework Equations
Kinetic Energy =1/2*m*v^2
Spring Potential Energy = 1/2*k*x^2
Gravitational Potential Energy = m*g*h
The Attempt at a Solution
I am thinking to solve this problem using energy conservation but I feel that it is not possible to apply energy conservation...
Homework Statement
Two masses m1 and m2 are joined by a spring of spring constant k. Show that the frequency of vibration of these masses along the line connecting them is
ω = √[ k(m1 + m2) / (m1*m2) ]
(Hint: Center of mass remains at rest.)
Homework Equations
f = w/2π
w = √(k/m)
F = -kx
a = -...
Homework Statement
Its a series of problems essentially basically asking questions about solving proportionality
. For example
"Hooke's Law of a spring can be described by the equation F = -kx, where F is the force exerted by a spring, K us the spring constant, and X is the amount of distance...
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...
Homework Statement
A light elastic string of natural length 0.3m has one end fixed to a point on a ceiling. To the other end of the string is attached a particle of mass M. When the particle is hanging in equilibrium, the length of the string is 0.4m.
(a) Determine, in terms of M and g (take g...
1. Homework Statement
The following problem is an example from the book ' Berkely - Waves by Frank S. Crawford Jr '.
Mass 'M' slides on a frictionless surface. It is connected to rigid walls by means of two identical springs, each of which has zero mass, spring constant 'K' and relaxed length...
Homework Statement
One end of a light elastic string of stiffness mg/l and natural length l is attached to a point O. A small bead of mass m is fixed to the free end of the string. The bead is held at O and then released so that it will fall vertically. In terms of find the greatest depth to...
I don't understand the difference between the elastic limit and the yield point. I understand that if you stretch a material within the elastic limit, then the material should return to its normal shape. However, the yield point is described as the point at which a permanent increase in length...
Abu
Thread
elastic
elastic limit
hooke's law
stress and strain
yield point
Homework Statement
A 1.00kg mass and 2.00kg mass are set gently on a platform mounted on an ideal spring of force constant 40.0 N/m. The 2.00 kg mass is suddenly removed. How high above its starting position does the 1.00 kg mass reach?
Related to it... An 87 g box is attached to a spring with...
Abu
Thread
hooke's law
mass on a spring
simple harmonic motion
spring
Homework Statement
A.[/B] Suppose I have a block of mass 'M' that is attached to a wall via spring of coefficient 'k' , the spring has rest length Xo .
Suppose I look at the problem at some time 't' such that the spring is being compressed and the block moves left ( moving towards x = 0 ) ...
Hi all,
In short: For an air leg or air spring, there is a method using a Taylor approximation to find the spring constant for very small displacements, but I can't seem to figure out how it works. I've learned that air legs don't follow Hooke's law very much at all, except for when the...
So I am doing tensile testing on an elastic electrical lead for biomedical purposes. The lead is encapsulated in an elastic tubing. Now the lead acts like a weak spring itself (coiled wire).
I'm curious, if there are two springs with different k constants "within" each-other (one inside the...
Homework Statement
A mass "m" is attached to a spring of constant "k" and is observed to have an amplitude "A" speed of "v0" as it passes through the origin.
a) What is the angular frequency of the motion in terms of "A" and "v0"?
b) Suppose the system is adjusted so that the mass has speed...
Hi
I was given the following problem in my coursework:
Homework Statement
"A spring is initially compressed by 50mm when a steel ball of mass 2kg is released from just being in contact with the uncompressed spring. Determine the spring stiffness (k) of the spring."
Homework Equations
F = mg...
Homework Statement
A car driver updates the springs of a car by replacing the old springs with stiffer ones. The old springs give an amount of 8 cm when under the car, and their length when not under the car is 29 cm.
The spring constant of the new springs is 30 % greater than that of the old...
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-...
Homework Statement
A bungee jumper of mass 60kg jumps from a bridge 24 m above the surface of the water. The rope is 12 m long and is assumed to obey Hooke's law. What should the spring constant of the rope be if the woman is to just reach the water?
Homework Equations
Ep=mgh
E=1/2 kx^2
The...
For Hooke's Law, why is there a negative in F = -k*x? Is it because k is the reaction force against the force applied on the spring and not the force pushing or pulling on it? For example, let's say that the origin is set where the spring ends when it's in equilibrium with no forces applied to...
I conducted a uniaxial tension test for a variety of materials but wasn't able to gather much useful axial strain data due to the extensometer continually slipping. I have axial strain data for the linear elastic region of the stress strain curve and I also have the extension of the crossbar of...
Homework Statement
Consider a spring of natural length L_0 with constant k which rests on a horizontal frictionless surface. The spring is attached at one end to a fixed post and at the other end to a mass m. Suppose the spring is rotating around the post in a circle with angular velocity w...
Homework Statement
Consider the following classic problem: we have a rod in the vertical position with a pivot at its midpoint and a spring attached to the bottom of the rod, perpendicular to the rod. The is rotated through a small angle theta to the vertical, and released. Find the period of...
How does one arrive at the following equation to approximate spring constant for solids... using Hooke's Law
F ∝-x ⇒ F = -kx
and strain∝stress
?
k = (m/a2) × (K/ρ)½
where
k≡spring constant
m ≡ mass of a single atom
a ≡ atomic spacing
K ≡ bulk modulus
ρ ≡ density
Hi,
About elastic and plastic materials:
All materials exhibit elastic deformation up to a certain limit, beyond which they exhibit plastic deformation.
Some materials, such as plasticine, have extremely tiny elastic regions, so we call them 'plastic materials'.
Some, like rubber, have large...
As another of my personal music projects, I have wondered if it would not be possible to calculate the 'feel' of a drumhead (i.e. the amount of 'give' expressed as transverse displacement 'z' that an equally pre-tensioned circular membrane of radius 'r' experiences when struck on its plane at a...