Hooke's Law contd.

• What does the elastic limit indicate on a Force vs. Extension graph?

  Material enters a non-linear, non-proportional region
• What does Hooke's Law state about the force needed to extend a spring?


  It is directly proportional to the extension
• What happens to the extension when the force is doubled according to Hooke's Law?


  The extension also doubles
• What is Hooke's Law in relation to the elastic limit?

  • Describes linear, proportional behavior of materials
  • Elastic limit marks the end of this behavior
• If the spring constant \( k \) is 2 N/m and a force of 4 N is applied, what is the extension?

  The extension will be 2 meters
• What is the elastic limit on a Force vs. Extension graph?

  The point where material stops linear behavior
• How does the extension change if the spring constant k is increased while applying the same force?


  The extension decreases
• What is the "limit of proportionality" in the context of this image?

  • The point at which the relationship between force and extension becomes non-linear
  • The maximum extension where the material still behaves elastically
• What is the equation of the line shown in the image?

  $x +$$y =$$4$
• What does the elastic limit represent in terms of force or extension?

  Maximum force or extension before permanent deformation
• What does the variable k represent in Hooke's Law?

  The spring constant
• Why is the distinction between limit of proportionality and elastic limit important?

  Materials can extend elastically beyond the limit of proportionality
• What is the equation of the line parallel to the given line that passes through the point (1, 3)?

  $y =$$x - 1$
• What does Hooke's Law state?

  Force is proportional to extension
• What happens to force and extension beyond the limit of proportionality?

  They no longer maintain a constant ratio
• What is the relationship between force and extension described in the image?

  • Force is proportional to extension as long as you don't go past the "limit of proportionality"
  • Beyond the limit of proportionality, the relationship is no longer linear
• What is the relationship between force and extension according to the image?

  Force is proportional to extension as long as you don't go past the "limit of proportionality"
• What does a Force vs. Extension graph illustrate?

  • Relationship between force applied and extension produced
  • Elastic limit shows transition from linear to non-linear behavior
• What is the "limit of proportionality" referred to in the image?


  The point at which the relationship between force and extension is no longer proportional
• What happens to materials beyond the limit of proportionality?

  They undergo permanent deformation
• What is the significance of point C on the graph?

  • Marks the limit of proportionality
  • Point where the curve deviates from linearity
  • Beyond this point, force and extension ratio changes
• How does the relationship between force and extension change after the "limit of proportionality" is reached?

  The relationship becomes non-linear and the material may undergo permanent deformation
• What are the key regions beyond the limit of proportionality in materials?

  • Yield point: Permanent deformation begins
  • Plastic region: Stretching without stress increase
  • Breaking point: Material fractures or breaks
• What is the Proportional Limit?


  1. Proportional Limit
• What is the limit of proportionality in Hooke's Law?

  It is the maximum extension before the spring deforms
• What is the linear region of a graph?

  Where force-extension relationship is proportional
• What law applies in the linear region of the graph?

  Hooke's Law
• What characterizes the plastic region of a material?

  Material stretches without further increase in stress
• What are the key constraints shown in the image?

  • $x +$$y \leq 4$
  • $y > x - 1$
  • $x > 1$
• What is the elastic limit?

  The maximum point before permanent deformation occurs
• How are the limit of proportionality and elastic limit related?


  They are close together but distinct points
• What is meant by the 'linear region' in the context of Hooke's Law?

  It refers to the range where force and extension are proportional
• What happens if a material is stretched beyond its elastic limit?

  It causes permanent damage to the material
• What are the behaviors and graph features of the limit of proportionality and elastic limit?

  • Limit of Proportionality:
  • Behavior: No longer F∝x
  • Graph Feature: Linear region ends
  • Elastic Limit:
  • Behavior: First permanent deformation
  • Graph Feature: Curve starts
• What happens to a spring in the linear region when force increases?

  It stretches uniformly without permanent deformation
• What is the formula representing Hooke's Law?

  F = k x
• What does Hooke's Law describe?

  The direct proportionality between force and extension
• What starts the curve on a force-extension graph?

  The elastic limit
• What is the formula for Hooke's Law?

  $F =$$kx$
• What is the Yield Strength?


  1. Yield Strength