Elasticity: Young's modulus & Hooke's Law - SchoolWorkHelper
Dec 16, Hooke's Law and Young's Modulus Revision. 1. Hooke's Law and Young's Modulus Revision; 2. Define these terms:• Stress• Strain• Extension•. Young's modulus or Young modulus is a mechanical property that measures the stiffness of a solid material. It defines the relationship between stress (force per unit area) and strain Young's modulus represents the factor of proportionality in Hooke's law, which relates the stress and the strain. However, Hooke's law is only. Youngs modulus of elasticity of wire. For small change in the length of the wire, the ratio of the.
Students begin to learn the basic concepts required for creating a strain graph to depict cancerous tissue.
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Lecture Information In the late s, Robert Hooke stated that "The power of any springy body is in the same proportion with the extension. The law is explained by a direct proportionality between a spring's compression or expansion and the restoring force which ensues.
This law is valid within the elastic limit of a linear spring, when acting along a frictionless surface. Extending Hooke's exploration of springs, it becomes apparent that most materials act like springs with force being directly proportional to displacement. But as compared to springs, other materials possess an area which must be accounted for.
We will now explore the measures of stress and strain.
Hooke's Law and Modulus of Elasticity
The SI unit for stress is pascals Pa which is equal to 1 Newton per square meter. The Psi is an alternative unit which expresses pounds per square inch. The units of stress are equal to the units of pressure which is also a measure of force per unit area.
Stress cannot be measured directly and is therefore inferred from a measure of strain and a constant known as Young's modulus of elasticity.Elasticity & Hooke's Law - Intro to Young's Modulus, Stress & Strain, Elastic & Proportional Limit
Using this means of inferring stress, strain is a geometrical measure of deformation and Young's modulus is a measure used to characterize the stiffness of an elastic material. Strain does not carry a unit but the units of Young's modulus are Pa. Young's modulus is also used in order to predict the deflection that will occur in a statically determinate beam when a load is applied at a point in between the beam's supports. Other elastic calculations usually require the use of one additional elastic property, such as the shear modulusbulk modulus or Poisson's ratio.
What is Hooke's Law? (article) | Khan Academy
Any two of these parameters are sufficient to fully describe elasticity in an isotropic material. Linear versus non-linear[ edit ] Young's modulus represents the factor of proportionality in Hooke's lawwhich relates the stress and the strain. However, Hooke's law is only valid under the assumption of an elastic and linear response. Any real material will eventually fail and break when stretched over a very large distance or with a very large force; however all solid materials exhibit nearly Hookean behavior for small enough strains or stresses.
If the range over which Hooke's law is valid is large enough compared to the typical stress that one expects to apply to the material, the material is said to be linear.
Otherwise if the typical stress one would apply is outside the linear range the material is said to be non-linear.
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.
In solid mechanicsthe slope of the stress—strain curve at any point is called the tangent modulus.