UNIVERSITY OF GUYANA FACULTY OF NATURAL SCIENCES DEPART. OF MATH, PHYS & STATS PHY 110 – PHYSICS FOR ENGINEERS LECTURE 12 (THURSDAY, NOVEMBER 17, 2011) 1

Lecture Notes: For this information, visit my website: In the event of any other issues to be resolved, 2

3.1 Elasticity 3 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 17 th Cenury, Robert Hooke was the first to investigate such behaviour.

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

3.1 Elasticity 5 Inter-molecular Force: For separation distance d between the two atoms: a) d = d 0, no force exists between the atoms. b) d > d 0, the force is attractive and long range. c) d < d 0, the force is repulsive and short range.

3.1 Stress and Strain 6 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

3.1 Stress and Strain 7 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.

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

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

3.2 Stress/Strain Relationship 10 Points on Stress-Strain Graph: 1. Limit of Proportionality: Prior to and at this point, stress is directly proportional strain. 2. Elastic Limit: At this point, the material exhibits elastic behaviour (regains original shape when deforming force removed. Hooke’s Law obeyed. 3. Yield Point: At this point, permanent deformation (Plastic Behaviour) sets in. Small increments in stress produce significant changes in strain. 4. Breaking Point: Beyond this point, the material snaps.

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

3.2 Stress/Strain Relationship 12 Stress-Strain Graphs: 1. Ductile Material: It exhibits significant plastic deformation before its breaking point is reached. 2. Brittle Material: It does not exhibit plastic deformation. As soon as the elastic limit is exceeded, the material breaks.. 3. Hysteresis Loop: The path of extension and contraction differs thus energy is trapped in the material and is gradually released as heat.

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

3.3 Hooke’s Law 14 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.

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

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

3.4 Work Done 17 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:

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

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

3.5 Young’s Modulus 20 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)

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

Lecture Notes: For this information, visit my website: In the event of any other issues to be resolved, 22

23 END OF LECTURE