What is Hooke's Law? (article) | Khan Academy
We know that the Young's modulus of an object is defined as the ratio We also know that Hooke's law, which can be applied to any linear. Our aim here is to relate these curves to Young's modulus and Hooke's law. But how can curves like these give a linear relation between the force applied and. Physics. Hooke's law, F = kx, where the applied force F equals a constant k of Hooke's law in this form, see bulk modulus; shear modulus; Young's modulus.
However, this is not an absolute classification: For example, as the linear theory implies reversibilityit would be absurd to use the linear theory to describe the failure of a steel bridge under a high load; although steel is a linear material for most applications, it is not in such a case of catastrophic failure. In solid mechanicsthe slope of the stress—strain curve at any point is called the tangent modulus.
What is Hooke's Law?
It can be experimentally determined from the slope of a stress—strain curve created during tensile tests conducted on a sample of the material. Directional materials[ edit ] Young's modulus is not always the same in all orientations of a material. Most metals and ceramics, along with many other materials, are isotropicand their mechanical properties are the same in all orientations.
However, metals and ceramics can be treated with certain impurities, and metals can be mechanically worked to make their grain structures directional. These materials then become anisotropicand Young's modulus will change depending on the direction of the force vector. Anisotropy can be seen in many composites as well.
Is There A Relationship Between Young's Modulus And Spring Constant? | Physics Forums
For example, carbon fiber has a much higher Young's modulus is much stiffer when force is loaded parallel to the fibers along the grain. Other such materials include wood and reinforced concrete. Engineers can use this directional phenomenon to their advantage in creating structures.
It corresponds to a linear approximation to F rpassing through the point r0,0where r0 is the unstressed length. Integrating Hooke's law gives a potential energy U r that is parabolic about the minimu at r0.
Hooke's law thus corresponds to the green linedrawn on the F r plot and the green parabola on the U r plot. The insets on each graph show close-ups of these approximation, and show that the approximations are poor for deformations of more than a few percent. While discussing this graph, let's observe that, although the Hooke's law approximation for U r is symmetrical about its minimum, these curves and more realistic curves are not.
This asymmetry about the minimum in U r is responsible for the thermal expansion of most condensed phases: At finite temperatures, the atoms are not found exactly at the minimum of U, because they have finite kinetic energy due to their thermal motion. Oversimplifying in the interests of brevity, we can argue that the average value of U at a value above the minimum lies to the right of the minimum, and increases as more thermal energy is added.
Deriving Young's modulus from atomic forces The curves shown above are simple polynomials.
They are analytical approximations to realistic interatomic forces, but will illustrate how to relate atomic properties to macroscopic material properties. Consider the potential where A, B, n and m are constants that we shall discuss below.
Using 2 and rearranging: We can substitute this value into 1 to get the minimum value U r0. In a diatomic molecule, this value would give an estimate of the binding energy but, as it's more complicated for a crystal, we'll leave that calculation aside. The sketch shows a simple model of a crystalline solid.
Is There A Relationship Between Young's Modulus And Spring Constant?
In the horizontal x axis, the interatomic separation is r. In both perpendicular directions, the separation is y, as shown in this sketch.SOM part 4 -Hooke's Law explained in HINDI - Young's modules of elasticity -
Young's modulus Y for a material is defined as the ratio of tensile stress to tensile strain.