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Hooke's Law and Springs

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    Hooke's Law

    Hooke's law is named after British physicist Robert Hooke who published it in 1660.

    Hooke's Law states that the extension of a spring is in direct proportion with the load or force applied to it. In other words: equal weight increments stretch the spring equally (linear relationship).

    Hooke's law formula states that:


    x is the length displacement of the spring's end from its start position (units: meters)
    F is the force exerted on the spring's end (units: N or kilogram-force)
    k is the spring constant (units: N/m)

    The meaning of the constant k, in N/m, is how many newtons we need in order to stretch the spring 1m. A higher value for k means that more force or newtons are needed in order to stretch the spring 1m - in other words, a higher value means a less flexible or stiffer spring and vice versa.

    Hooke's Law Experiment

    A coil spring is hanged with a weight hanger and pointer attached to its end. Different known weights with equal increments (in this case 500g, 1000g, 1500g, 2000g according to the coil's flexibility) are hanged and the readings of the pointer with the respective weights are marked on a sheet of paper.

    The results show that equal weight increments stretch the spring equally (linear relationship) what we call Hooke's law.

    Take in account that this linear relationship between weight and length displacement of the spring is limited to the working range of the spring (too small weights will not stretch the spring at all whereas too big weights will compromise its flexibility).

    It is clear that Hooke's law is theoreticall correct for an ideal spring that has no weight, mass, or damping losses and is perfectly elastic within its working range. But for practical springs Hooke's law is only a good approximation within their working range

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    Last updated: October 2012
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