What is k in Hooke's law?
The rate or spring constant, k, relates the force to the extension in SI units: N/m or kg/s2. Click to see full answer. Also to know is, how do you find k in Hooke's Law?
What is the formula for Hooke’s law?
Hooke’s Law Equation in Terms of Stress and Strain. According to this law, within the elastic limit, stress is proportional to the strain. Thus, Hooke’s Law equation can be expressed in terms of stress and strain; Stress α Strain or stress / strain = constant = E. Stress = Young’s modulus of elasticity × Strain. σ = E ε. Where, σ is the stress,
What are the applications of Hooke’s law?
The applications of Hooke’s Law is as given below: Most commonly, in everyday life, Hooke’s Law is applied in springs because of their elasticity. They are used not only in the engineering field but also used in the field of medical science. It is used in breathing (lungs), skin, spring beds, diving boards and cars suspension system.
What is the inverse of Hooke's law?
More frequently, the x ≡ e1 axis is taken to be the axis of symmetry and the inverse Hooke's law is written as To grasp the degree of anisotropy of any class, a universal elastic anisotropy index (AU) was formulated.
What are the units for K in physics?
The constant of proportionality k is called Coulomb's constant. In SI units, the constant k has the value. k = 8.99 × 10 9 N ⋅ m 2 /C 2. The direction of the force is along the line joining the centers of the two objects.
What is the units of spring constant?
The spring constant unit is in terms of Newton per meter (N/m).
What is spring constant k?
The spring constant, k, is a measure of the stiffness of the spring. It is different for different springs and materials. The larger the spring constant, the stiffer the spring and the more difficult it is to stretch.
What is K in F KX?
F = -kx. The proportional constant k is called the spring constant. It is a measure of the spring's stiffness.
What is the spring constant k?
Hooke’s Law: Calculating Spring Constants. … k is the spring constant, in Newtons per meter (N/m), and x is the displacement of the spring from its equilibrium position. The spring constant, k, is representative of how stiff the spring is. Stiffer (more difficult to stretch) springs have higher spring constants.
How do you find the spring constant k?
W = kx. W is the weight of the added mass. Therefore, the spring constant k is the slope of the straight line W versus x plot. Weight is mass times the acceleration of gravity or W = mg where g is about 980 cm/sec2.
What happens if the spring constant increases?
A stronger spring-with a larger value of k-will move the same mass more quickly for a smaller period. As the spring constant k increases, the period decreases. … For a given mass, that means a greater acceleration so the mass will move faster and, therefore, complete its motion quicker or in a shorter period.
What does F KX mean?
F=−kx. where: x is the displacement of the spring’s end from its equilibrium position (a distance, in SI units: meters); F is the restoring force exerted by the spring on that end (in SI units: N or kg·m/s2); and. k is a constant called the rate or spring constant (in SI units: N/m or kg/s2).
What is the formula for work done?
The work is calculated by multiplying the force by the amount of movement of an object (W = F * d). A force of 10 newtons, that moves an object 3 meters, does 30 n-m of work. A newton-meter is the same thing as a joule, so the units for work are the same as those for energy – joules.
What is Hooke's equation?
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 .
What is Hooke's law in matrix notation?
It is often useful to express the anisotropic form of Hooke's law in matrix notation, also called Voigt notation. To do this we take advantage of the symmetry of the stress and strain tensors and express them as six-dimensional vectors in an orthonormal coordinate system ( e1,e2,e3) as
How are homogeneous isotropic linear elastic materials determined?
Homogeneous isotropic linear elastic materials have their elastic properties uniquely determined by any two moduli among these ; thus, given any two, any other of the elastic moduli can be calculated according to these formulas.
What is Hooke's spring law?
Hooke's spring law usually applies to any elastic object, of arbitrary complexity, as long as both the deformation and the stress can be expressed by a single number that can be both positive and negative.
Is Hooke's law analogous to other laws?
Since Hooke's law is a simple proportionality between two quantities, its formulas and consequences are mathematically similar to those of many other physical laws, such as those describing the motion of fluids, or the polarization of a dielectric by an electric field .
Why is Hooke's law applied to springs?
Most commonly, in everyday life, Hooke’s Law is applied in springs because of their elasticity. They are used not only in the engineering field but also used in the field of medical science. It is used in breathing (lungs), skin, spring beds, diving boards and cars suspension system.
What is the graph of restoring force versus elongation for the spring?
The graph of restoring force versus elongation for the spring is the straight line. This straight-line shows that the elongation of a spring is directly proportional to the applied force. So we can conclude that this spring-mass system follows Hooke’s Law.
What is the property of material that permits material to be drawn out longitudinally to a reduced cross sectional area?
Ductility: It is the property of material, which permits material to be drawn-out longitudinally to a reduced cross-sectional area, because of the application of tensile force. It also can be defined as the property of material, which permits a material to be drawn-out in the form of wire.
Is Hooke's law universal?
Hooke’s Law gives accurate result only for solid bodies if the forces and deformations are small. Hooke’s Law is not a universal law. Test your Knowledge on Hookes law. Q 5. Put your understanding of this concept to test by answering a few MCQs.
What does K stand for in spring constant?
FSpring = -kx. In this equation, F is the force exerted by something stretching or compressing the spring, and x is the distance that the spring is stretched or compressed from its “rest” position. The letter k represents the “spring constant,” a number which essentially tells us how “stiff” a spring is.
How do you find the spring constant k?
Mathematically, F∝x, where F is the force applied, and x is the extension or compression of the object (usually in metres).
What is the force constant?
View this answer. In physics, a force constant is another name for a spring constant, as defined by Hooke’s law. More specifically, it is a proportionality constant…
What happens if the spring constant increases?
A stronger spring-with a larger value of k-will move the same mass more quickly for a smaller period. As the spring constant k increases, the period decreases. … For a given mass, that means a greater acceleration so the mass will move faster and, therefore, complete its motion quicker or in a shorter period.
What is the value of k constant?
The symbol k is a proportionality constant known as the Coulomb’s law constant. The value of this constant is dependent upon the medium that the charged objects are immersed in. In the case of air, the value is approximately 9.0 x 109 N • m2 / C2.
Does spring constant change with mass?
That is because the spring constant and the length of the spring are inversely proportional. That means that the original mass of 30 gm will only yield a stretch of 1 mm on the shorter spring. The larger the spring constant, the smaller the extension that a given force creates.
What does spring constant depend on?
Answer: In dealing with a coil spring the spring constant will depend on the stiffness of the spring material, the thickness of the wire from which the spring is wound and, diameter of the turns of the coil, the number of turns per unit length and the overall length of the spring.
What is the force of 3 N?
A force of 3 N is applied to a spring. The spring stretches reversibly by 0.15 m - the fact that the string stretches reversibly means that it will go back to its normal shape after the force has been removed. Calculate the spring constant.
What is the spring constant?
Spring constant is a measure of the stiffness of a spring up to its limit of proportionality or elastic limit. The limit of proportionality refers to the point beyond which Hooke's law is no longer true when stretching a material.
Overview
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 …
Formal definition
Consider a simple helical spring that has one end attached to some fixed object, while the free end is being pulled by a force whose magnitude is Fs. Suppose that the spring has reached a state of equilibrium, where its length is not changing anymore. Let x be the amount by which the free end of the spring was displaced from its "relaxed" position (when it is not being stretched). Hooke's law states that
Analogous laws
Since Hooke's law is a simple proportionality between two quantities, its formulas and consequences are mathematically similar to those of many other physical laws, such as those describing the motion of fluids, or the polarization of a dielectric by an electric field.
In particular, the tensor equation σ = cε relating elastic stresses to strains is entirely similar to the equation τ = με̇ relating the viscous stress tensor τ and the strain rate tensor ε̇ in flows of viscous fl…
Units of measurement
In SI units, displacements are measured in meters (m), and forces in newtons (N or kg·m/s ). Therefore, the spring constant k, and each element of the tensor κ, is measured in newtons per meter (N/m), or kilograms per second squared (kg/s ).
For continuous media, each element of the stress tensor σ is a force divided by an area; it is therefore measured in units of pressure, namely pascals (Pa, or N/m , or kg/(m·s ). The elements …
General application to elastic materials
Objects that quickly regain their original shape after being deformed by a force, with the molecules or atoms of their material returning to the initial state of stable equilibrium, often obey Hooke's law.
Hooke's law only holds for some materials under certain loading conditions. Steel exhibits linear-elastic behavior in most engineering applications; Hooke'…
Derived formulae
A rod of any elastic material may be viewed as a linear spring. The rod has length L and cross-sectional area A. Its tensile stress σ is linearly proportional to its fractional extension or strain ε by the modulus of elasticity E:
.
The modulus of elasticity may often be considered constant. In turn,
Linear elasticity theory for continuous media
Note: the Einstein summation convention of summing on repeated indices is used below.
Isotropic materials are characterized by properties which are independent of direction in space. Physical equations involving isotropic materials must therefore be independent of the coordinate system chosen to represent them. The strain tensor is a symmetric tensor. Since the trace of any tensor is independent of any coordinate system, the most complete coordinate-free decomposit…
Thermodynamic basis
Linear deformations of elastic materials can be approximated as adiabatic. Under these conditions and for quasistatic processes the first law of thermodynamics for a deformed body can be expressed as
where δU is the increase in internal energy and δW is the work done by external forces. The work can be split into two terms