R. Field 10/31/2013 University of Florida PHY 2053Page 1 Definition of Strain System Response – Linear Deformation: System Response – Volume Deformation:

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Presentation transcript:

R. Field 10/31/2013 University of Florida PHY 2053Page 1 Definition of Strain System Response – Linear Deformation: System Response – Volume Deformation: Suppose that a wire of length L is stretched by a force F then: Linear Strain = Consider an object immersed in a fluid. The fluid will exert a pressure P from all sides causing a volume deformation. Define variables the cause deformation of a material and the response of the material. Volume Strain =

R. Field 10/31/2013 University of Florida PHY 2053Page 2 Definition of Stress Linear Deformation: Volume Deformation: Suppose that a wire of length L is stretched by a force F then: Linear Stress = Consider an object immersed in a fluid. The fluid will exert a pressure P from all sides causing a volume deformation. Define variables the cause deformation of a material and the response of the material. Volume Stress = Area A

R. Field 10/31/2013 University of Florida PHY 2053Page 3 Hooke’s Law Spring Linear Restoring Force: Spring Constant k Spring Force Stress = C × Strain Generalized Hooke’s Law! Ideal Spring Constant

R. Field 10/31/2013 University of Florida PHY 2053Page 4 Stress Proportional to Strain Linear Deformation: Volume Deformation: Suppose that a wire of length L is stretched by a force F then: Stress = Y × Strain Consider an object immersed in a fluid. The fluid will exert a pressure P from all sides causing a volume deformation. Area A Stress = -B × Strain Bulk Modulus Units = Pa Young’s Modulus Units = Pa

R. Field 10/31/2013 University of Florida PHY 2053Page 5 Example Problem: Young’s Modulus Linear Deformation: A wrecking ball with mass M is to be lifted by a crane with a steel cable that has a diameter of 1.5 cm and an unstretched length of 30 m. The Young’s modulus of steel is 2.0 × Pa. Ignoring the weight of the cable itself, when the ball is lifted and held at rest the cable stretches by 1.66 cm, what is the mass M of the wrecking ball?

R. Field 10/31/2013 University of Florida PHY 2053Page 6 Example Problem: Bulk Modulus Volume Deformation: The atmospheric pressure at the surface of a clear lake is 101 kPA. By what percentage does the density of lake water increase at a depth of 1.0 km below the surface of the lake? The bulk modulus for water is 2.2×10 9 Pa? 0.445%