Force and Extension Relationship

• What quantity is represented on the x-axis of the graph?

  Extension (m)
• If a spring is easy to stretch, what can be said about its spring constant?

  It has a lower spring constant
• What does Hooke's Law state about the force needed to stretch a spring?

  It is proportional to its extension
• How does doubling the force applied to a spring affect its extension according to Hooke's Law?

  It doubles the extension
• What is the point labeled P in the image?

  The point where the force and extension curve intersect
• What is Hooke's Law, and how does this graph relate to it?

  • Hooke's Law: The force needed to extend or compress a spring by some distance is proportional to that distance
  • The graph demonstrates Hooke's Law because the force and extension have a linear relationship (F = kx)
• According to the graph, what is the extension when the force is 4 N?

  0.08 m
• What does the spring constant indicate about a spring?

  It indicates the stiffness of the spring
• What does a higher spring constant indicate?

  • The spring is harder to stretch
  • More force is needed to stretch it
• What is the x-axis labeled in the image?

  extension
• If the spring constant is $k =$$10 N / cm$ and the force is $F =$$40 N$, what is the extension $x$?


  $x =$$4 cm$
• What type of graph is created by the relationship between force and extension for a spring?

  A straight-line graph
• According to the graph, what is the force when the extension is 0.12 m?

  6 N
• What are the key features of the stress-strain curve?

  • Elastic limit
  • Yield strength
  • Ultimate strength
  • Necking
  • Fracture
  • Area under the curve = Total energy dissipation potential
• What occurs at point Q in the force-extension relationship of rubber bands and bungee cords?

  They reach the elastic limit
• What is the spring constant?

  It measures how strong a spring is
• What does the spring constant (k) represent in the equation $F =$$kx$?


  It indicates how stiff a spring is
• What happens to rubber bands and bungee cords when they are stretched initially?

  They stretch easily at first
• How does doubling the spring constant (k) affect the extension (x) when the force remains constant?

  It reduces the extension by half
• If a spring stretches 2 cm with a force of 10 N, how much would it stretch with 20 N?

  4 cm
• What is the relationship between stress and strain as shown in the stress-strain curve?

  • Elastic limit: Stress is proportional to strain (Hooke's law)
  • Yield strength: Stress at which plastic deformation begins
  • Ultimate strength: Maximum stress the material can withstand
  • Fracture: Point at which the material breaks
• In the formula F = kx, what does F represent?

  The force applied to the spring
• What is the relationship between force and extension for rubber bands and bungee cords?

  It is a complex curve
• What are the key differences between springs and rubber bands in terms of their force-extension characteristics?

  • Springs:
  • Linear relationship
  • F = kx
  • Constant stiffness (k)
  • Rubber Bands:
  • Nonlinear relationship
  • Complex curve
  • Changing stiffness
• What is the yield strength in the context of Hooke's Law?

  The point where plastic deformation begins
• In the formula F = kx, what does k represent?

  The spring constant
• What is the definition of stress?

  Stress = Force / Cross-Sectional Area
• What is the difference between the "True Stress-Strain Curve" and the "Engineering Stress-Strain Curve"?

  The true curve accounts for changes in cross-sectional area, while the engineering curve does not
• What is the y-axis labeled in the image?

  force
• How does the force required to stretch a spring relate to its spring constant?

  More force is needed for a stronger spring
• What does a higher spring constant (k) imply about a spring's behavior?

  It requires more force to stretch the spring
• What is the formula that expresses Hooke's Law?

  F = kx
• What does Area Y represent in the force-extension graph?

  Energy lost during unloading
• What does the slope of the line in the graph represent, and how is it calculated?

  • The slope represents the spring constant (k)
  • It is calculated as:
  • $k =$$\frac{\text{Force}}{\text{Extension}} =$$\frac{\Delta F}{\Delta x}$
• How could you use this graph to determine the area under the force-extension curve?

  • The area under the force-extension curve (curve R) represents the work done
  • This work done can be calculated by integrating the force-extension curve
  • The curve labeled "area X" directly gives the area under the force-extension curve
• What does the curve labeled R represent in the image?

  The relationship between force and extension
• If $k =$$20 N / cm$ and $F =$$40 N$, what is the extension $x$?


  $x =$$2 cm$
• What is the limit of proportionality in relation to Hooke's Law?

  It is the maximum force for linear extension
• What quantity is represented on the y-axis of the graph?

  Force (N)
• What is the elastic limit in Hooke's Law?

  The maximum stress before permanent deformation