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University of Guyana Faculty of Natural Sciences Depart. of Math, PHYs & Stats

University of Guyana Faculty of Natural Sciences Depart. of Math, PHYs & Stats PHY 110 – Physics FOR ENGINEERS Lecture 12 (THURSDAY, November 17, 2011). Lecture Notes:. For this information, visit my website: http://ugphysics.weebly.com

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University of Guyana Faculty of Natural Sciences Depart. of Math, PHYs & Stats

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  1. University of Guyana Faculty of Natural Sciences Depart. of Math, PHYs & Stats PHY 110 – Physics FOR ENGINEERS Lecture 12 (THURSDAY, November 17, 2011)

  2. Lecture Notes: For this information, visit my website: http://ugphysics.weebly.com In the event of any other issues to be resolved, email: leed_3113@yahoo.com.

  3. 3.1 Elasticity Elasticity: Any material that regains its original shape (size) after experiencing a deforming force is deemed elastic. Consequently, one that does not regains its shape after deformation is said to be inelastic. For example, springs (metals), rubber are elastic but plastics are inelastic. This property is dependent on the molecular structure and behaviour of the material under consideration. In the 17thCenury, Robert Hooke was the first to investigate such behaviour.

  4. 3.1 Elasticity Intermolecular Forces between Two Atoms: Physics by Robert Hutchings, 2nd Edition, pg 386.

  5. 3.1 Elasticity Inter-molecular Force: For separation distance d between the two atoms: d = d0 , no force exists between the atoms. d > d0, the force is attractive and long range. d < d0, the force is repulsive and short range.

  6. 3.1 Stress and Strain Hooke’s Law: This law states that the stress experienced by a material is directly proportional to the strain it produces in that material provided the elastic limit is not exceeded. Stress: This is the force acting per unit area perpendicular to the area of contact. Units: Pascal (Pa) 1 Pa = 1Nm-2

  7. 3.1 Stress and Strain Strain: This is the fractional change in the length of a material. Units: None Where - Change in the length of the material. - Original length of the material.

  8. 3.1 Stress and Strain Intermolecular Forces and Hooke’s Law: Physics - A Concise Revision Course for CXC by Leslie Clouden, pg 15.

  9. 3.2 Stress/Strain Relationship Graph of Stress against Strain: Advanced Physics Through Diagrams by Stephen Pople, pg 66

  10. 3.2 Stress/Strain Relationship Points on Stress-Strain Graph: Limit of Proportionality: Prior to and at this point, stress is directly proportional strain. Elastic Limit: At this point, the material exhibits elastic behaviour (regains original shape when deforming force removed. Hooke’s Law obeyed. Yield Point: At this point, permanent deformation (Plastic Behaviour) sets in. Small increments in stress produce significant changes in strain. Breaking Point: Beyond this point, the material snaps.

  11. 3.2 Stress/Strain Relationship Stress/Strain Graphs: Copper and Glass • Physics by Robert Hutchings, 2nd Edition, pg 408.

  12. 3.2 Stress/Strain Relationship Stress-Strain Graphs: Ductile Material: It exhibits significant plastic deformation before its breaking point is reached. Brittle Material: It does not exhibit plastic deformation. As soon as the elastic limit is exceeded, the material breaks. . Hysteresis Loop: The path of extension and contraction differs thus energy is trapped in the material and is gradually released as heat.

  13. 3.2 Stress/Strain Relationship Stress/Strain Graphs: Rubber • Physics by Robert Hutchings, 2nd Edition, pg 408.

  14. 3.3 Hooke’s Law Hooke’s Law: This law states that provided that the elastic limit is not exceeded, the stress (deforming force) exerted on a material is directly proportional to the strain (extension) it produces in that material.

  15. 3.3 Hooke’s Law Experimental Verification: Standard weights are placed in the scale pan. Corresponding extensions and contractions of the spring is recorded. Extension/contraction is plotted against deforming force. Spring constant is determined from the plot.

  16. 3.3 Hooke’s Law Extension-Force Graphs: Steel & Rubber • Physics - A Concise Revision Course for CXC by Leslie Clouden, pg 15.

  17. 3.4 Work Done Work Done in Stretching a Material: This is computed by calculating the area enclosed by the curve for either the stress-strain or the deforming force- extension graphs. For Stress-Strain Graph: For Stress-Strain Graph:

  18. 3.4 Work Done Stress-Strain Graphs: Work done per unit Volume is the area of triangle.

  19. 3.4 Work Done Extension-Force Graphs: Work done is the area enclosed by the curve in the linear portion. It is the area of the triangular portion.

  20. 3.5 Young’s Modulus Modulus of Elasticity E/Y: This is the ratio of tensile stress to tensile strain. For a material that obeys Hooke’s law, the gradient of the linear portion of the stress-strain graph yields Young’s Modulus. Units: Pascal (Pa) 1 Pa = 1Nm-2 E/Y is quoted in Mega-Pascals (MPa)

  21. 3.4 Work Done • Physics by Robert Hutchings, 2nd Edition, pg 406.

  22. Lecture Notes: For this information, visit my website: http://ugphysics.weebly.com In the event of any other issues to be resolved, email: leed_3113@yahoo.com.

  23. END OF LECTURE

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