Hooke’s Law – Elastic Materials Stretch in Proportion to the Force Used on Them
Used in engineering, construction and materials science, Hooke’s law shows how materials deform when forces are applied.
Robert Hooke was a true polymath who invented the balance spring and escapement mechanisms in watches and clocks, built Bedlam and also named the cell in biology. Hooke was more of an experimenter than a mathematician and it was while experimenting with springs that he discovered the law for which he is most famous. Hooke’s law says that the amount by which a spring extends is proportional to the force which is acting upon it.
Materials that obey Hooke’s law are known as ‘elastic’. As well as stretching, elastic materials are characterised by the fact that they return to their original shape when the force acting on them is removed.
According to Hooke’s law, an elastic material always requires the same amount of force to stretch it by some length. This necessary force depends on the material’s elastic modulus (effectively, the material’s stiffness). A stiff material needs a large force to extend while a more pliable material needs less force.
A material that has been stretched is said to be under a strain. Strain is defined as the percentage increase in length due to stretching. The force that is applied per unit area is also known as the stress. The stiffness of a material is defined as the ratio of stress to strain.
Aside from the engineering applications of Hooke’s law, it is also of vital importance in leisure pursuits such as bungee jumping. Hooke’s law predicts how much the bungee cord will stretch when it feels the force of the jumper’s weight.
Hooke’s law is also used in navigation. Although measuring latitude is fairly straightforward by monitoring the height of the Sun or stars in the sky, measuring longitude is much harder.
In the 17th and early 18th centuries this difficulty in determining longitude put sailor’s lives at risk and so the British government offered a cash prize to anyone who could solve the technical problems of longitude measurements.
Due to the time differences that occur during travel across the globe, longitude can be measured by comparing the local time at sea with the time at some other known place (most commonly during this period Greenwich in London). The difficulty came in not knowing the time at this specified place. Clock technology in the early 18th century was not advanced and the most accurate timepieces relied on pendulums that were useless on a rolling ship.
It was British watchmaker John Harrison who came up with a solution to the problem using Hooke’s law. Harrison invented a new type of clock that relied on springs instead of a pendulum. Unfortunately the stretchiness of these springs changed with the temperature and so they were impractical on most voyages. Harrison therefore incorporated into his clock a bimetallic strip made from two different metals bonded together. The two metals would expand by different amounts as they warmed up and this would cause the strip to bend. The incorporation of the strip into the clock’s mechanism compensated for the temperature change and so Harrison’s new clock (known as a chronometer) solved the longitude problem.