Edexcel A Level Physics:复习笔记4.7 Force-Extension Graphs

• The way a material responds to a tensile or compressive force can be shown on a force-extension, or a force-compression graph
  • Although compression can be put into equations as a negative value, the graphs have the same shaped curves
  • Compression is plotted on the graph as a positive, increasing value

• Every material will have a unique force-extension graph depending on how brittle or ductile it is
• In the same way, materials have unique force-compression graphs, which will not be the same as their force-extension graph
  • This is because materials behave differently under tensile and compressive strain

Simple Force-Extension Graphs

Simple force-extension graph showing the Hooke's Law region, and the calculation to find k, the spring constant

• A material may obey Hooke's Law up to a point
  • This is shown on its force-extension graph by a straight line through the origin
• As more force is added, the graph may start to curve slightly

The key features of the graph are:

• The limit of proportionality
  • The point beyond which Hooke's law is no longer true when stretching or compressing a material i.e. the extension/ compression is no longer proportional to the applied force
  • The point is identified on the graph where the line starts to curve

• The elastic limit
  • The point before which a material will return to its original length or shape when the deforming force is removed
  • This point is always after the limit of proportionality
• The spring constant k is found from the gradient of the straight part of the graph

More Detailed Force-Extension Graphs

• Graphs of applied load-extension can give more detailed information about materials
  • This will apply when loads were continued well past the elastic limit

Detailed force-extension graph showing a material under loads which exceed the elastic limit

• The yield point is where the material continues to stretch even though no extra force is being applied to it
• Elastic deformation is a change of shape where the material will return to its original shape when the load is removed
• Plastic deformation occurs after the yield point
  • It is a change of shape where the material will not return to its original shape when the load is removed

Step 1: Define both terms

• • Elastic limit: point before which a material will return to its original length or shape when the deforming force is removed
  • Yield point: the point at which the continues to stretch even though no extra force is being applied to it

Step 2: Using your definitions as prompts, select the correct point on the graph

• • Elastic limit is at B because the line has curved slightly after the Hooke's law region but not started to extend with no extra force
  • Yield point is at C because the line increases in the x-direction (extension is increasing) but not in the y-direction (no extra force is being added)