Final answer:
A force-extension graph for a metal wire shows the elastic region where Hooke's law is obeyed, followed by plastic deformation and ending at a fracture point. The unloading line demonstrates permanent deformation, and the slope of the initial linear region indicates Young's modulus.
Step-by-step explanation:
Force-Extension Graph for a Metal Wire
The force-extension graph for a metal wire showing both loading and unloading of forces represents how the metal behaves under stress and strain.
The initial straight portion of the graph up to point H indicates elastic deformation, where the wire obeys Hooke's law.
This law states that the force (F) applied to stretch or compress an object is proportional to the linear deformation (ΔL) it causes.
The slope of this region is the stiffness of the wire.
After point H and until point E, the behavior becomes nonlinear.
This area represents plastic deformation, where permanent changes occur within the material's structure.
When the force is released, as shown by the green line, the wire does not return to its original length, displaying a permanent deformation.
The intersection of this unloading line with the horizontal axis indicates the residual strain left in the wire.
The graph typically ends at a fracture point, which is the maximum stress a material can handle before failure.
The nature of a force-extension graph can tell us a lot about the material's properties, such as Young's modulus in the linear region and the proportionality limit which is the extent of elastic behavior under tensile stress.