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Lesson_4.6_Printable

# Lesson_4.6_Printable - Elastic properties of materials...

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Elastic properties of materials Elasticity is the ability of an object to regain its original shape after being deformed by an external force . Steel is more elastic than rubber because steel can withstand large amount of external force before being permanently deformed. Deformation is caused by a stress. Deforming force per unit area is called stress F stress = Stress is measured in Nm -2 A A stress that produces a change in length is called a tensile stress . A stress that produces a change in volume is called compressional stress or volume stress . A stress that simply deforms the object at a certain angle is called the shear stress . 1

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When an object is subjected to a stress, it suffers a strain . The ratio of change in length to original length is called tensile strain . If L is the increase in length for an original length L , then: Tensile strain L L = Strain is a simple ratio, it has no units. The ratio of the change in volume ( V ) to the original volume ( V ) is called the bulk strain (volume strain) . Bulk strain V V -∆ = 2
Young’s modulus. The ratio of tensile stress to tensile strain is called the Young’s modulus of the material. If Y represents the Young’s modulus of a material: Tensile stress Tensile strain Y = Y is measured in Nm -2 / / F A L L = 1 FL L A Y = Solving this equation for L gives: The increase in length of a rod or wire under tensile stress is inversely proportional to the young’s modulus of the material. 3

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Bulk modulus The ratio of volume stress to volume strain is called the bulk modulus of the material. If B represents the bulk modulus of a material: Volume stress Volume strain B = / / F A V V = -∆ B is measured in Nm -2 The reciprocal of the bulk modulus ( 1/B ) is called the compressibility of the material and is represented by k . 1 k B = 4
Shear modulus. A shear stress is produced when a force is applied tangentially to a surface. Here the change in shape produced by the stress does not involve a change in volume, but involves a relative displacement of the two surfaces of the body. The shear strain is given by the tangent of the angle of deformation. l Shear strain h = 5

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Shear stress S = / F A = If S represents the shear modulus of a material: Shear strain / l h Shear modulus may also be of a torsional type resulting from the twisting action of a torque. 6
The following table lists the standard values of Young’s modulus ( Y ), bulk modulus ( B ) and shear modulus ( S ) of common materials. Material Young’s modulus (N.m -2 ) Sheer modulus (N.m -2 ) Bulk modulus (N.m -2 ) Aluminu m 7.0 × 10 10 2.4 × 10 10 7.0 × 10 10 Brass 9.0 × 10 10 3.5 × 10 10 6.1 × 10 10 Copper 11.0 × 10 10 4.2 × 10 10 14 × 10 10 Nylon 0.2 × 10 10 Steel 20 × 10 10 8.1 × 10 10 16 × 10 10 Tungsten 35 × 10 10 15 × 10 10 20 × 10 10 Water 0.2 × 10 10 7

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A 100-kg mass is suspended using a cable with a diameter of 2.0 cm. What is the stress in the cable?
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