Young's modulus
Young's modulus is a fundamental concept in physics that quantifies the stiffness of a material, defined as the ratio of stress (force per unit area) to strain (deformation relative to original length). It serves as a measure of a material's elasticity, indicating how easily it can be stretched or compressed. Developed by British physicist Thomas Young in the early 19th century, the modulus helps categorize materials based on their ability to return to their original shape after being deformed, a property crucial in various applications, including construction and manufacturing.
Materials exhibit different Young's modulus values, illustrating their varying degrees of elasticity. For instance, rubber has a significantly lower modulus compared to materials like steel or diamond, which are much stiffer. The calculations involve units such as Pascals (Pa) for stress, with common values for materials ranging widely—rubber around 0.01 x 10^9 Pa, while diamond can reach approximately 1220 x 10^9 Pa. Understanding Young's modulus is essential for engineers and designers to ensure safety and performance, as it affects decisions about material selection in structures, machinery, and everyday objects like bungee cords and cables.
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Subject Terms
Young's modulus
In physics, Young's modulus measures the stiffness of a particular material by determining the ratio of stress to strain for that material. A modulus is another name for an absolute numerical value that represents a physical property of a material. Young's modulus calculates the ease at which a material can be stretched, a property known as elasticity. It is used to describe the elastic properties of wires, pipes, bones, and many other materials. The modulus was developed by Thomas Young, a British physicist and physician who also made notable contributions to several other scientific fields. Young called his discovery the elastic modulus, but the equation later came to bear his name. In simple terms, Young's modulus can be written as E = stress/strain.
Background
Thomas Young was born in 1773 in Milverton, England. He was considered a prodigy as a child. He was said to have learned to read at age two, taught himself Latin by age six, and had learned Greek, Hebrew, Italian, and French by his mid-teens. He went on to study medicine and contributed to the understanding of the human eye. Young also became a professor of physics and developed an interest in Egyptology. In 1801, he challenged the long-held theory of noted physicist Sir Isaac Newton and suggested that light traveled in waves rather than as particles. His theory was widely accepted for almost a century until it was determined that light exhibits characteristics of both waves and particles. Before his death in 1829, Young played a role in deciphering the Rosetta Stone, an artifact discovered in Egypt in 1799. The stone was instrumental in helping to translate ancient Egyptian hieroglyphics.
Overview
Young presented what he called his elastic modulus in lectures given in the early nineteenth century. It was a measure of the "passive strength," or elasticity, of a material and determined the extension or compression of a material based on the amount of force applied to it. Elasticity refers to the property of a material in which it returns to its original shape after it has been deformed through stress. A rubber band or coiled metal spring, for example, can be pulled to a certain point and will revert to its shape when the force is removed. If too much stress is applied, the rubber band or spring will snap or remain in a deformed state.
While all materials undergo some physical change when a force is applied, different materials react in different ways when subjected to force. It is much easier to notice the change in a rubber band when it is pulled; however, a bar of steel can also be stretched, although it takes considerably more force and the stretching is far less noticeable. Young's modulus is a measure of this difference. Rubber, for instance, would have a much smaller Young's modulus value than an iron beam.
Young's modulus is calculated by dividing the stress placed on a material by its strain. In most cases, a capital E, from the French élasticité, is used as a symbol of Young's modulus. Some calculations use a capital Y in honor of Young. Stress is defined as the force per unit area applied to an object. This can be determined by dividing the force by the cross-sectional area of the object. Tensile stress occurs when the forces applied to an object are directed away from each other; compressive stress occurs when those forces are directed toward each other. Strain is a measure of how much an object stretches or changes relative to its original length. To determine strain, the change in an object's length after applied with force is divided by the object's original length.
In calculating the value of Young's modulus, stress is measured in Pascal (Pa), a unit named after seventeenth-century French mathematician Blaise Pascal. A Pascal is a measure of force per unit area and is equal to one newton per square meter. A newton, named after Isaac Newton, is defined as one kilogram meter per second squared, or the force required to accelerate an object with a mass of one kilogram one meter per second.
Young's modulus can be used to determine if a steel cable is strong enough to hold the weight of passengers in an elevator by determining how far the cable will stretch before it fails. It can also be used to determine how far a bungee cord will stretch and if it is safe enough for use. The elastic limit, or yield strength, is the amount of stress a material can experience before it becomes deformed. Ultimate strength is the amount of stress a material can withstand before it breaks.
The value of the Young's modulus can vary depending on the exact composition of a given material. The elasticity of metals can change by 5 percent or more depending on their composition or if they are heated during the manufacturing process. In linear materials such as steel and glass, Young's modulus remains relatively constant over several strains. The value is less constant in nonlinear materials such as rubber.
A typical piece of rubber, for example, may exhibit a Young's modulus of .01 x 109 Pa, a value defined as .01 times 10 to the ninth power—a 1 followed by nine zeroes. Copper exhibits a Young's modulus of 120 x 109 Pa; tooth enamel has a value of 83 x 109 Pa; structural steel a value of 200 x 109; and a diamond has an approximate value of 1220 x 109 Pa.
Bibliography
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