Unit 1 Key Facts- Materials Hooke’s Law Force extension graph Elastic energy Young’s Modulus...
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Transcript of Unit 1 Key Facts- Materials Hooke’s Law Force extension graph Elastic energy Young’s Modulus...
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’ kIt is a property of the thing being stretched
The extension in the object= final length – original length
Hooke’s Law... 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 regionF proportional to ΔxUp 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
Elastic potential energy
When an elastic object is stretched it stores elastic potential energy
Elastic potential energy =0J
Force F
Extension Δx
Elastic potential energy = ½ FΔ x
Elastic potential energy is the area under the linear sections of a force-extension graph. Also related to k, EPE = ½ k Δ x2
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
Stress-strain plot: look familiar?
strain
stress
O
Hooke’s law applies, returns to original length when force removed
Elastic regionF proportional to ΔxUp 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 graphsstress
strain
Elastic Young’s modulus E
Young’s modulus 2E: this material is stiffer
stress
strain
This material is brittle after elastic limitIt just breaks
Stiff and tough
ductile
Properties of materials
Properties of materials
Properties of materials