Forces and elasticity

    AQA
    GCSE

    Forces applied to an object result in deformation, categorized as elastic (reversible) or inelastic (permanent) depending on the material's limit of proportionality. Hooke's Law governs the linear relationship between force and extension ($F=ke$), where the spring constant ($k$) represents stiffness. The work done in stretching an object is stored as elastic potential energy ($E_e = \frac{1}{2}ke^2$), calculable from the area under a force-extension graph up to the limit of proportionality.

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    Objectives
    4
    Exam Tips
    4
    Pitfalls
    4
    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 the applied force up to the limit of proportionality
    • Credit the calculation of the spring constant ($k$) by determining the gradient of the linear section of a force-extension graph
    • Award 1 mark for correctly converting extension from centimetres to metres before substitution into the elastic potential energy equation
    • Credit responses that identify the area under the force-extension graph as representing the work done or elastic potential energy stored
    • Award 1 mark for explaining that inelastic deformation results in the object not returning to its original shape after forces are removed

    Marking Points

    Key points examiners look for in your answers

    • Award 1 mark for stating that extension is directly proportional to the applied force up to the limit of proportionality
    • Credit the calculation of the spring constant ($k$) by determining the gradient of the linear section of a force-extension graph
    • Award 1 mark for correctly converting extension from centimetres to metres before substitution into the elastic potential energy equation
    • Credit responses that identify the area under the force-extension graph as representing the work done or elastic potential energy stored
    • Award 1 mark for explaining that inelastic deformation results in the object not returning to its original shape after forces are removed

    Examiner Tips

    Expert advice for maximising your marks

    • 💡Always calculate extension explicitly ($L_{new} - L_{original}$) before using formulae; examiners frequently provide total length to trap unwary candidates
    • 💡When determining the spring constant from a graph, draw a large triangle on the linear section to minimise percentage uncertainty in your gradient calculation
    • 💡Check the units on graph axes immediately; if extension is given in mm or cm, convert to metres to ensure the spring constant unit is N/m
    • 💡For Higher Tier, remember that the area under a non-linear force-extension graph still represents work done, even if $F=ke$ no longer applies

    Common Mistakes

    Pitfalls to avoid in your exam answers

    • Substituting the total length of the spring instead of the extension (stretched length minus original length) into the equation $F=ke$
    • Failing to square the extension term ($e^2$) when calculating elastic potential energy, resulting in significant calculation errors
    • Misidentifying the limit of proportionality as the point where the spring breaks, rather than the point where the graph ceases to be linear
    • Confusing the gradient calculation when axes are swapped (i.e., calculating $1/k$ instead of $k$ when extension is on the y-axis)

    Key Terminology

    Essential terms to know

    Likely Command Words

    How questions on this topic are typically asked

    Calculate
    Determine
    Describe
    Explain
    Plot

    Practical Links

    Related required practicals

    • •{"code":"Required Practical 6","title":"Investigation of the relationship between force and extension for a spring","relevance":"Direct assessment of data collection, plotting force-extension graphs, and calculating spring constants"}

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