Physics OCR Chapter 6 (Materials)

Springs and Hooke's Law

Tensile Force = Force that produces an extension

CompressiveForce that shortens an object

Hooke's Law

Springs undergo TENSILE DEFORMATION when tensile forces are exerted and COMPRESSIVE DEFORMATION when compressive forces are exerted.

Hooke's Law states that force is directly proportional to the extension.   Force = K x Extention        where K = Spring constant Nm^-1

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Force-Extenstion Graphs

Force-Extension Graphs

(http://nothingnerdy.wikispaces.com/file/view/Hooke_wire.gif/148559309/Hooke_wire.gif)

  • The straight line on the graph from the origin up to the proportional limit is where the material obeys Hooke's Law and undergoes elastic deformation meaning it will return to original shape
  • After elastic limit material undergoes plastic deformation and won't return to original shape
  • K = gradient of linear part of force-extension graph
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Elastic Potential Energy

  • When a material is stretched or compressed without passing the elastic limit the work done can be fully recovered.
  • Once the material has undergone plastic deformation some of the work done has gone into changing the atoms into new positions --> This energy is non-recoverable 
  • Work Done = Area under force-extension graph

Elastic Potential Energy

Energy  = 1/2 x Force x Extension 

Work Done = Average Force x Final Extension

A spring obeys Hooke's Law, (via substitution):

Energy = 1/2 x Force Constant x Extension^2

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Deforming Materials

Loading and Unloading

  • Materials respond differently to forces
  • Their extension increases as force increases and then decreases as force decreases
  • However, the loading curve MAY NOT BE THE SAME as the unloading curve 
  • Materials that obey Hooke's Law have linear graphs
  • Materials that do not obey Hooke's Law have Hysteresis loops
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Stress, Strain and Young's Modulus

Tensile Stress

  • Tensile stress is the force applied per cross-sectional area of the wire
  • Tensile stress = force / cross-sectional area

Tensile Strain

  • Tensile strain is the change in original length of the wire
  • Tensile strain = extension/ original length

The Young Modulus

  • Within limit of proportionality, stress is directly proportional to strain
  • The ratio of stress to strain is constant called Young Modulus
  • Young Modulus = Stress/Strain
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Stress-Strain Graphs

Stress-Strain Graphs

P = Limit of Proportionality, A linear region where the material obeys Hooke's Law

E = Elastic Limit, Materials may obey Hooke's Law bit not always, Elastic Deformation occurs up to here

Y1 & Y2 = Upper & Lower Yield, Where material extends rapidly

UTS = Maximum stress that material can withstand when being stretched before it breaks 

B = Breaking point, The point of fracture of the material is known as Breaking point

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Comments

LewesCavern

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Page 5:

Tensile Strain = extention/original length

Charliegage

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@LewesCavern Your correct my mistake its a typo. I will correct it now!

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