Relationship between hooke law and young modulus of elasticity

Is There A Relationship Between Young's Modulus And Spring Constant? | Physics Forums

relationship between hooke law and young modulus of elasticity

For 1D case of normal tension, it is simply the scalar relation given by the Hooke's Law SIGMA=E*STRAIN where E is the Young's Modulus. Anyway, hope more. Hooke's law of elasticity, and the value of Young's modulus, are derived from molecular But how can curves like these give a linear relation between the force. Within certain limits, the force required to stretch an elastic object such as a metal . Young's modulus can be defined at any strain, but where Hooke's law is obeyed it This is a very useful relationship to understand when thinking about the.

Steelcarbon fiber and glass among others are usually considered linear materials, while other materials such as rubber and soils are non-linear. 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.

Hooke’s Law and Modulus of Elasticity

In solid mechanicsthe slope of the stress—strain curve at any point is called the tangent modulus. 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.

  • Elasticity: Young’s modulus & Hooke’s Law
  • Young's modulus, Hooke's law and material properties
  • Young's modulus

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.

Elasticity: Young's modulus & Hooke's Law - SchoolWorkHelper

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.

relationship between hooke law and young modulus of elasticity

In the horizontal x axis, the interatomic separation is r. In both perpendicular directions, the separation is y, as shown in this sketch. Young's modulus Y for a material is defined as the ratio of tensile stress to tensile strain. However, the repulsive term is simply a convenient, differentiable function that gives a very strong repulsion.

relationship between hooke law and young modulus of elasticity

So, we have related Young's modulus to individual atomic forces and energies: Work these to the best of your abilities independently first; then we will review the problems as a class. After becoming familiar with using the new equations, we will explore Hooke's law in an associated activity Applying Hooke's Law to Cancer Detection by experimentally determining an unknown proportionality constant.

What is Hooke's Law?

After exploring Hooke's law, in the second portion of the activity, we will begin to apply what we've learned to develop a means of imaging body tissues and we will soon be able to detect malignant tumors! You will also practice graphing prepared data to depict cancerous tissue. After we have mastered this material, we will have a quiz on stress, strain and Hooke's law. Please take careful notes and be sure to ask any questions you have about the example problems we will be working through.

Referring back to the legacy cycle which we discussed in the previous lesson, today's lesson constitutes the research and revise phase.

Refer back to your initial thoughts notes and record any new information that applies to solving the challenge.

What is Hooke's Law

Your goal today is to review, revise and expand your current knowledge! Now, let's learn how to detect cancer.

relationship between hooke law and young modulus of elasticity