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Lecture 9 Elasticity

Lecture 9 Elasticity. Peter J. Nolan, Fundamentals of college physics, Wm. C. Brown Publishers, 1993. The atomic nature of elasticity.

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Lecture 9 Elasticity

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  1. Lecture 9Elasticity Peter J. Nolan, Fundamentals of college physics, Wm. C. Brown Publishers, 1993

  2. The atomic nature of elasticity Elasticity is that property of a body by which it experiences a change in size or shape whenever a deforming force acts on the body. When the force is removed the body returns to its original size and shape. Most objects are elastic for forces up to a certain maximum, called the elastic limit. If the forces exceed the elastic limit, the object does not return to its original shape but is permanently deformed. The elastic properties of matter are a manifestation of the molecular forces that hold solids together. • Deformation types: • Stretch • Compress • Shear

  3. Hook`s law – stress and strain.

  4. Hook`s law – stress and strain. The deformation L of the wire is thus directly proportional to the magnitude of the applied force F, inversely proportional to the cross-sectional area A, and directly proportional to the original length of the wire L0 The ratio of the magnitude of the applied force to the cross-sectional area of the wire is called the stress (tensile and compressive stresses) acting on the wire, while the ratio of the change in length to the original length of the wire is called the strain of the wire stress  strain Hooke`s law of elasticity Young`s modulus of elasticity

  5. A steel wire 1 m long with a diameter d = 1 mm has a 10 kg mass hung from it. (a) How much will the wire stretch? (b) What is the stress on the wire? (c) What is the strain? 0.594 mm. (b) 1.25* 108 N/m2 (c) 0.594 10-3

  6. Hook`s law – stress and strain. Hooke`s law is only invalid below the elastic limit.

  7. Hook`s law for a spring. k is the force constant or the spring constant

  8. Hook`s law for a spring.

  9. Springs in parallel

  10. Springs in series

  11. Elasticity of shape – shear If the body returns to its original shape when the distorting stress is removed, the body exhibits the property of elasticity of shape, sometimes called shear at small deformations Shearing strain

  12. Elasticity of shape – shear stress  strain Shearing stress Hooke`s law for elasticity of shear S is the shear modulus (the torsion modulus or the modulus of rigidity). Values of S for various materials are given in table. The large the value of S, the greater the resistance to shear. The shear modulus is smaller than Young’s modulus.

  13. A sheet of copper 0.750 m long, 1 m high, and 0.500 cm thick is acted on by a tangential force of 50000 N, as shown in figure. The value of S for copper is 4.20* 1010 N/m2 .Find (a) the shearing stress, (b) the shearing strain, and (c) the linear displacement Δx (a) 3.75* 10-3 m2 (b) 3.17* 10-4 rad. (c) 0.317 mm

  14. Elasticity of volume the bulk modulus

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