Search results
Results from the WOW.Com Content Network
In physics, Hooke's law is an empirical law which 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, F s = 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.
Where U is interatomic potential and r is the interatomic distance. This means the atoms are in equilibrium. To extend the two atoms approach into solid, consider a simple model, say, a 1-D array of one element with interatomic distance of a, and the equilibrium distance is a 0 .
For a stretched spring fixed at one end obeying Hooke's law, the elastic potential energy is Δ E p = 1 2 k ( r 2 − r 1 ) 2 {\displaystyle \Delta E_{p}={\frac {1}{2}}k(r_{2}-r_{1})^{2}} where r 2 and r 1 are collinear coordinates of the free end of the spring, in the direction of the extension/compression, and k is the spring constant.
The following table gives formula for the spring that is equivalent to a system of two springs, in series or in parallel, whose spring constants are and . [1] The compliance c {\displaystyle c} of a spring is the reciprocal 1 / k {\displaystyle 1/k} of its spring constant.)
The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law: . Young's modulus E describes the material's strain response to uniaxial stress in the direction of this stress (like pulling on the ends of a wire or putting a weight on top of a column, with the wire getting longer and the column losing height),
These are all examples of a class of problems called stiff (mathematical stiffness) systems of differential equations, due to their application in analyzing the motion of spring and mass systems having large spring constants (physical stiffness). [5] For example, the initial value problem
[1] [2] Other names are elastic modulus tensor and stiffness tensor. Common symbols include C {\displaystyle \mathbf {C} } and Y {\displaystyle \mathbf {Y} } . The defining equation can be written as
By examining the formulas for area moment of inertia, we can see that the stiffness of this beam will vary approximately as the third power of the radius or height. Thus the second moment of area will vary approximately as the inverse of the cube of the density, and performance of the beam will depend on Young's modulus divided by density cubed .