Spring Constant

    OCR
    GCSE

    The spring constant ($k$) serves as a quantitative measure of the stiffness of an elastic object, defined by the ratio of force to extension within the limit of proportionality, as governed by Hooke's Law. Mastery of this concept requires the analysis of force-extension characteristics, distinguishing between elastic and plastic deformation, and identifying the point of failure. Furthermore, the spring constant is intrinsic to the calculation of elastic potential energy ($E_e = \frac{1}{2}ke^2$), linking mechanical forces to energy storage systems.

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    Objectives
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    Exam Tips
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    Pitfalls
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    Key Terms
    5
    Mark Points

    What You Need to Demonstrate

    Key skills and knowledge for this topic

    • Award 1 mark for stating that extension is directly proportional to force up to the limit of proportionality
    • Credit calculation of the spring constant (k) using the gradient of the linear section of a Force-Extension graph
    • Award 1 mark for correctly converting extension from centimetres to metres before substituting into the energy equation E = 0.5kx^2
    • Credit responses that identify the limit of proportionality as the point where the line ceases to be straight
    • Award 1 mark for linking the area under the Force-Extension graph to the work done or elastic potential energy stored

    Example Examiner Feedback

    Real feedback patterns examiners use when marking

    • "You correctly calculated the force, but check your units for extension—did you convert cm to m?"
    • "Good identification of the linear region. Now explain what happens to the spring's structure past the limit of proportionality."
    • "You used the length of the spring instead of the extension. Remember: Extension = New Length - Original Length."
    • "Excellent calculation of the gradient. To secure full marks, explicitly state that the gradient equals the spring constant."

    Marking Points

    Key points examiners look for in your answers

    • Award 1 mark for stating that extension is directly proportional to force up to the limit of proportionality
    • Credit calculation of the spring constant (k) using the gradient of the linear section of a Force-Extension graph
    • Award 1 mark for correctly converting extension from centimetres to metres before substituting into the energy equation E = 0.5kx^2
    • Credit responses that identify the limit of proportionality as the point where the line ceases to be straight
    • Award 1 mark for linking the area under the Force-Extension graph to the work done or elastic potential energy stored

    Examiner Tips

    Expert advice for maximising your marks

    • 💡When calculating work done or elastic potential energy from a graph, explicitly state that you are calculating the 'area under the line'
    • 💡Check the axes carefully: if Extension is on the y-axis and Force on the x-axis, the gradient represents 1/k, not k
    • 💡Ensure you can rearrange F=kx to find k or x, as this is a frequent 2-mark calculation on Foundation papers

    Common Mistakes

    Pitfalls to avoid in your exam answers

    • Calculating extension by using the total length of the spring rather than subtracting the original length
    • Failing to convert units from cm or mm into metres, resulting in incorrect orders of magnitude for energy calculations
    • Confusing the 'limit of proportionality' with the 'elastic limit' when describing graph features; OCR requires precise terminology regarding the linear region
    • Inverting the gradient calculation by dividing extension by force when Force is on the y-axis

    Study Guide Available

    Comprehensive revision notes & examples

    Read Study Guide

    Key Terminology

    Essential terms to know

    Hooke's Law and the definition of stiffness
    Elastic versus plastic deformation and the limit of proportionality
    Graphical analysis of Force-Extension relationships
    Calculation of Elastic Potential Energy

    Likely Command Words

    How questions on this topic are typically asked

    Calculate
    Describe
    Explain
    Determine
    Plot

    Practical Links

    Related required practicals

    • •{"code":"PAG P1","title":"Investigation of force-extension relationship for a spring","relevance":"Direct assessment of data collection and graphing skills"}

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