## Hookes

23 Hooke's Law is determined on the basis of a very simple experiment in which a uniaxial force is applied on a specimen which has one dimension much greater than the other two (such as a rod). The elongation is measured, and then the stress is plotted in terms of the strain (elongation/length). The slope of the line is called Young's modulus.

24 Hooke anticipated some of the most important discoveries and inventions of his time but failed to carry many of them through to completion. He formulated the theory of planetary motion as a problem in mechanics, and grasped, but did not develop mathematically, the fundamental theory on which Newton formulated the law of gravitation.

His most important contribution was published in 1678 in the paper De Potentia Restitutiva. It contained results of his experiments with elastic bodies, and was the first paper in which the elastic properties of material was discussed.

" Take a wire string of 20, or 30, or 40 ft long, and fasten the upper part thereof to a nail, and to the other end fasten a Scale to receive the weights: Then with a pair of compasses take the distance of the bottom of the scale from the ground or floor underneath,, and set down the said distance, then put inweights into the said scale and measure the several stretchings of the said string, and set them down. Then compare the several stretchings of the said string, and you will find that they will always bear the same proportions one to the other that the weights do that made them".

This became Hooke's Law _

25 Because he was concerned about patent rights to his invention, he did not publish his law when first discovered it in 1660. Instead he published it in the form of an anagram "ceiinosssttuu" in 1676 and the solution was given in 1678. Ut tensio sic vis (at the time the two symbols u and v were employed interchangeably to denote either the vowel u or the consonant v), i.e. extension varies directly with force.

26 If, instead of subjecting a material to a uniaxial state of stress, we now subject it to a hydrostatic pressure p and measure the change in volume AV.

27 From the summary of Table 4.1 we know that:

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