5.3.3 Force–Extension Graphs

• What does a force-extension graph plot against each other?

  It plots the force applied to an object against the extension or compression of the object from its natural length.
• What is the unit of force in a force-extension graph?

  Newtons (N)
• What does extension (x) represent in a force-extension graph?

  It represents the change in length of the material compared to its original length.
• What does the linear region of a force-extension graph indicate?

  It indicates that the relationship between force and extension is directly proportional.
• What is Hooke’s Law as it relates to the linear region of a force-extension graph?

  Hooke's Law states that the force is proportional to the extension, represented by the equation F=k×x.
• What does the gradient of the linear section of a force-extension graph represent?

  The gradient represents the spring constant (k).
• What is the elastic limit in a force-extension graph?

  The elastic limit is the point where the graph starts to deviate from a straight line, indicating permanent deformation.
• What happens to the material beyond the elastic limit?

  The material will not return to its original shape and will experience permanent deformation.
• What characterizes the plastic region of a force-extension graph?

  The plastic region shows that the material does not follow Hooke's Law and experiences permanent changes in shape or size.
• What does the gradient of the linear portion of the graph represent in terms of units?

  It is measured in Newtons per meter (N/m).
• How can the area under the force-extension graph be interpreted?

  The area under the graph up to the elastic limit represents the elastic potential energy stored in the material.
• How is elastic potential energy calculated for a linear graph?

  Elastic Potential Energy = 1/2 F × x.
• What are the characteristics of Graph A in a force-extension graph?

  • A straight line through the origin
  • Shows a linear relationship between force and extension
  • The spring constant (k) is constant
  • The material remains in the elastic region
• What are the characteristics of Graph B in a force-extension graph?

  • A straight line initially, but curves after reaching the elastic limit
  • Follows Hooke's Law up to the elastic limit
  • Deforms plastically after the elastic limit
• What are the characteristics of Graph C in a force-extension graph?

  • A curve that starts to deviate from a straight line almost immediately
  • Does not follow Hooke's Law
  • Deforms plastically from the start
• What are some practical applications of force-extension graphs?

  • Designing springs and shock absorbers
  • Testing materials for their elastic properties
  • Determining suitability for specific applications
• What are the key features of a force-extension graph?

  • Force vs. extension plot
  • Linear region indicates elastic behavior
  • Elastic limit marks the start of plastic deformation
  • Gradient represents spring constant (k)
  • Area under the graph represents elastic potential energy stored