Introduction, Elasticity Elasticity Aggregates of matter ("stuff") can stretch, shrink, or bend if you push or pull on it Think of individual particles (atoms, molecules) connected by springs Tighter springs = stiffer Looser springs = floppier Rigid objects like steel rods behave a lot like springs Stretch them a little and release them, they'll return to their original shape Mostly they're very stiff, so you don't notice it If you stretch them a lot, part or all of the stretch can become permanent, with potentially catastrophic results Quantifying elasticity We want a way to describe the elasticity of a material that: Doesn't depend on the particular force applied - though it may depend on the type of force (squeezing, bending) Doesn't depend on the particular object being squeezed Best way to do it is to relate Stress: the deforming force per unit area (N/m^2) Strain: "unit" deformation (cm/cm) ("unit" means "dimensionless") Applied force and deformation Stress is proportional to strain in the linear region In the elastic region, the material will return to its original shape Beyond the elastic limit, you got permanent deformation Eventually the object will break completely apart F Elastic region elastic limit Three types of stress ¢L Tensile stress. Shear stress. F ¢L =Y A L F ¢x =G A L Y- Young's modulus S- Shear modulus Hydraulic stress F ¢V =B A V B- Bulk modulus Example: Young's modulus Car suspended by a steel rod: how much does it stretch? Car has mass m = 1225 kg (compact car) Rod has diameter d = 1 cm, length l = 1 m Young's modulus for steel is 200 x 10^9 N/m^2 F ¢L =Y A L F = mg = 1200N 2 A = ¼ (0:5cm) = 7:9 £ 10¡5 m2 Y = 200 £ 109 N =m2 FL = ¢L AY ¢L = 0:8mm breaking point Linear region

Introduction, Elasticity

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