Unit 1 Key Facts- Materials Hooke's Law Force extension graph

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Hooke’s Law For the visual learner: original length Fixed end object of force constant k force Final length Extension Δx
Unit 1 Key Facts- Materials Hooke’s Law Force extension graph Elastic energy Young’s Modulus Properties of materials
Hooke’s Law For a spring or elastic substance: Force applied = - k x Δx Force ‘constant’ k It is a property of the thing being stretched The extension in the object = final length – original length
For the visual learner: original length Fixed end object of force constant k force Final length Extension Δx.
Force-extension Graphs extension Force O Hooke’s law applies, returns to original length when force removed Elastic region F proportional to Δx Up to limit of proportionality Elastic limit Plastic region – here permanent deformation occurs, Yield point: Small force results in large extension Maximum force = upper tensile strength Value of force at which sample fails
Also related to k, EPE = ½ k Δ x 2.
Stress Stress (σ )is the force applied to a material per unit area σ = Force ÷ area (units Pa) It can be tensile (stretching) Or compressive (squashing) Some materials are strong in compression but weak in tension (brick)
STRAIN Strain is the ration of extension to original length of a material ε = Δ x ÷ x (no units it is a ratio)
Young’s Modulus Young’s modulus E is the ration of stress to strain E = σ ÷ ε (Units Pa same as stress) It can be found from gradient of stress-strain plot Also known as the stiffness of the material
strain stress O Hooke’s law applies, returns to original length when force removed Elastic region F proportional to Δx Up to limit of proportionality Elastic limit Plastic region – here permanent deformation occurs, Yield point: Small force results in large extension Maximum force = upper tensile strength Tensile strength Gradient of this plot is Young’s Modulus = E.
Examples of graphs stress strain Elastic Young’s modulus E Young’s modulus 2E: this material is stiffer stress strain This material is brittle after elastic limit It just breaks Stiff and tough ductile
Large force for small plastic deformation.
Properties of materials Ductile: show plastic deformation Strong: large force to break Hard: resist plastic deformation usually by denting
Properties of materials Malleable: Show large plastic deformation before cracking or breaking brittle: Break or crack with little deformation weak: Low tensile strength – breaks easily