Hooke's law
Hooke's law, introduced by Robert Hooke in 1678, describes the relationship between the force applied to a spring and its extension or compression. According to this law, the extension of a spring is directly proportional to the force exerted on it, as long as the spring operates within its elastic limit. This principle can be mathematically expressed as F = –kx, where F is the applied force, k is the spring constant, and x represents the displacement of the spring from its equilibrium position. The spring constant varies among different springs, indicating their stiffness; more rigid springs have higher constants.
Hooke’s law explains how a spring will stretch or compress in response to weights, illustrating that doubling the weight will double the spring's displacement. However, it's crucial to note that if a spring is stretched or compressed beyond its elastic limit, it may lose its elasticity and become permanently deformed. This concept highlights the importance of understanding material limits in various applications, from engineering to everyday items like toys. Hooke's law is foundational in fields such as physics and engineering, emphasizing the interplay between force and displacement in elastic materials.
Hooke's law
Considered a Renaissance man and a jack-of-all-trades, Robert Hooke officially introduced the scientific law that bears his name in 1678. Hooke's law, also known as the law of elasticity, states that the extension of a spring is proportional to the force applied to it. Hooke's law applies only to springs stretched or compressed within their elastic limit. The discovery of the law of elasticity is just one of Robert Hooke's many contributions to the world of science.
Life of Robert Hooke
Born in Freshwater, Isle of Wight, England, on July 18, 1635, Robert Hooke was the youngest child of John and Cecily Hooke. Hooke was a sickly child, but what he lacked in physical health he compensated for in mental vigor. Early in life he demonstrated a talent for mechanics, often building completely workable mechanical gadgets.
Following his father's death in 1648, Hooke moved to London and began to attend the Westminster School, where he studied Greek, Latin, and mathematics. Five years later, he entered Christ Church College at Oxford University. At Oxford, Hooke supplemented his income by working as an assistant to chemist Robert Boyle. Hooke's mechanical inclinations proved quite helpful. At Boyle's request, Hooke created an improved air pump, which allowed Boyle to establish his ideal gas law in 1662.
Hooke may have served a supporting role in the discovery of Boyle's law early in his career, but he achieved many of his own successes later. Perhaps his most well-known published work is Micrographia (1665), in which he recorded the results of his experiments with a microscope. Micrographia includes incredibly detailed and precise sketches of microscopic specimens, such as plants, molds, and insects. Among these is an artistic rendering of a microscopic view of cork, which revealed Hooke's discovery that plants are formed from blocklike structures. Hooke is credited with naming these structures “cells.” As early as the 1660s Hooke presented lectures about planetary movement, and later communications between Hooke and Sir Isaac Newton provide evidence suggesting that the former almost certainly contributed to the latter's development of the law of universal gravitation.
Throughout his long career, Hooke dabbled in many fields of study, ranging from astronomy and geology to physics and architecture. He investigated everything from fossils and crystals to comets and planets, conducted countless experiments, and developed or improved upon numerous inventions. Following London's Great Fire of 1666, he served as both a surveyor and an architect and helped oversee the city's reconstruction. Despite his substantial contributions to the world of science (and the world in general), Hooke is remembered most for his law of elasticity, perhaps because it bears his name. Hooke died in London on March 3, 1703.
Overview of Hooke's Law
Hooke published the details of his law of elasticity in Lectures de Potentia Restitutiva, or of Spring Explaining the Power of Springing Bodies in 1678. However, he first discovered the law in 1676 and mentioned it as an anagram at the end of his A Description of Helioscopes, and Some Other Instruments. When rearranged, the anagram ceiiinosssttuv reveals the Latin phrase Ut tensio, sic vis, which means "as the extension, so the force." Hooke explains in Lectures de Potentia Restitutiva, "The power of any spring is in the same proportion with the tension thereof." In other words, the length to which the spring extends or compresses (also called the displacement) is proportional to the amount of force the spring exerts.
Hooke's law may be expressed as the mathematical formula F = –kx, where F represents the applied force, k represents the spring constant, and x represents the displacement. The spring constant varies from one spring to another. More rigid springs have higher spring constants while more flexible springs have lower spring constants. The minus sign in the formula indicates that the direction of the force exerted by the spring opposes the direction of the displacement. If the spring is stretched to the right, the force exerted by the spring pulls to the left; if the spring is compressed to the left, the force exerted by the spring pushes to the right.
Example of Hooke's Law
To consider Hooke's law in action, imagine a spring hanging vertically from a fixed position. At rest with no forces acting upon it—also known as equilibrium—the spring shows no displacement. Attaching a one-pound weight to the bottom of the spring, however, causes the spring to stretch one inch. According to Hooke's law, then, a two-pound weight should cause the spring to stretch two inches. A three-pound weight should stretch the spring three inches, and so on. As the weights pull the spring downward, the spring pulls the weights upward (i.e., the direction of the force exerted by the spring opposes the direction of displacement). The force exerted by the spring works to restore it to equilibrium, or its resting position. For this reason, it is known as the restoring force.
It is important to note that Hooke's law applies only to springs stretched or compressed within their elastic limit. A spring stretched or compressed beyond its elastic limit loses its elasticity. Anyone who has stretched a toy Slinky just a bit too far can understand that springs extended beyond their elastic limits may become misshapen or distorted. When this occurs, the restoring force is unable to return the spring to equilibrium.
Bibliography
Holzner, Steven. "How to Calculate a Spring Constant Using Hooke's Law." For Dummies. John Wiley & Sons, Inc. 2014. Web. 4 Dec. 2014. http://www.dummies.com/how-to/content/how-to-calculate-a-spring-constant-using-hookes-la.html
"Hooke, Robert." Complete Dictionary of Scientific Biography. Vol. 6. Detroit: Charles Scribner's Sons, 2008, 481–488. Print.
Hooke, Robert. A Description of Helioscopes, and Some Other Instruments. London: John Martyn, Printer to the Royal Society, 1676, 31. Print.
"Hooke, Robert." Encyclopedia of Life Sciences. Vol. 9. Chichester, UK: Wiley, 2005, 202–203. Print.
Hooke, Robert. Lectures de Potentia Restitutiva, or of Spring Explaining the Power of Springing Bodies. London: John Martyn, Printer to the Royal Society, 1678, 1–3. Print.
"Motion of a Mass on a Spring." The Physics Classroom. The Physics Classroom. 2014. Web. 4 Dec. 2014. http://www.physicsclassroom.com/class/waves/Lesson-0/Motion-of-a-Mass-on-a-Spring
Nielsen, Michael A. "The Future of Science: Building a Better Collective Memory." The Back Page. American Physical Society. Nov. 2008. Web. 4 Dec. 2014. http://www.aps.org/publications/apsnews/200811/backpage.cfm
"Robert Hooke." Bio. A&E Television Networks. 2014. Web. 4 Dec. 2014. http://www.biography.com/people/robert-hooke-9343172#synopsis
"Robert Hooke." Famous Scientists. famousscientists.org. 15 Oct. 2014. Web. 4 Dec. 2014. http://www.famousscientists.org/robert-hooke/
"Robert Hooke." Roberthooke.org.uk. Roberthooke.org.uk. 2007. Web. 4 Dec. 2014. http://www.roberthooke.org.uk/robert‗hooke.htm