GCSE Combined Science (AQA)

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Gradient of a Force-Extension Graph

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Forces Forces and elasticity

Gradient of a Force-Extension Graph

3:07 Deformations and Springs
Spec 4.5.3
Previous Spring Constant Next Work & Elastic Potential
  • Before the limit of proportionality, the extension of a spring is proportional to the force applied.
  • A force extension graph can be created by plotting extension on the Y axis and force on the X axis.
  • The graph shows that force and extension are proportional; doubling one value doubles the other.
  • The limit of proportionality is the force after which inelastic deformations occur, and force and extension are no longer proportional.
  • The gradient of the graph is equal to the reciprocal of the spring constant.
  • To calculate the gradient, choose two points and find the difference in Y and X.
  • The gradient is the difference in extension (E) over the difference in force (F).
  • Before the limit of proportionality, F = KE, where K is the spring constant.
  • K is equal to F over E, so flip the gradient to get the equation for K.
  • In exams, use this method to calculate the spring constant from a graph.
  • Example: Various weights are hung from a spring, and extension is measured and plotted on a graph.
  • To calculate the spring constant, choose two points: 7.5 N and 0.9 m, 2.5 N and 0.3 m.
  • Divide the difference in force by the difference in extension: (7.5 - 2.5) / (0.9 - 0.3) = 8.333 recurring.
  • Round the result to two significant figures: 8.3 N/m.

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