university of guyana faculty of natural sciences depart. of math, phys & stats phy 110 –...

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UNIVERSITY OF GUYANA

FACULTY OF NATURAL SCIENCES

DEPART. OF MATH, PHYS & STATS

PHY 110 – PHYSICS FOR ENGINEERS

LECTURE 12(THURSDAY, NOVEMBER 17,

2011)

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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.

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

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3.1 Elasticity

Physics by Robert Hutchings, 2nd Edition, pg 386.

Intermolecular Forces between Two Atoms:

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3.1 Elasticity

Inter-molecular Force:For separation distance d between the two atoms:

a) d = d0 , no force exists between the atoms.

b) d > d0, the force is attractive and long range.

c) d < d0, the force is repulsive and short range.

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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

A

F

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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.

oL

L

LoL

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3.1 Stress and Strain

Physics - A Concise Revision Course for CXC by Leslie Clouden, pg 15.

Intermolecular Forces and Hooke’s Law:

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3.2 Stress/Strain Relationship

Advanced Physics Through Diagrams by Stephen Pople, pg 66

Graph of Stress against Strain:

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3.2 Stress/Strain Relationship

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.

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3.2 Stress/Strain Relationship

Physics by Robert Hutchings, 2nd Edition, pg 408.

Stress/Strain Graphs: Copper and Glass

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3.2 Stress/Strain Relationship

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.

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3.2 Stress/Strain Relationship

Physics by Robert Hutchings, 2nd Edition, pg 408.

Stress/Strain Graphs: Rubber

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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.

LF

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3.3 Hooke’s Law

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.

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3.3 Hooke’s Law

Physics - A Concise Revision Course for CXC by Leslie Clouden, pg 15.

Extension-Force Graphs: Steel & Rubber

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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:

oL

L

A

F

V

W21)(2

1

)(21 LFW

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3.4 Work Done

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

o

o

ALV

LFW

L

L

A

F

V

W

2

1

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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.

)(21 LFW

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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)

LA

FLYE o

/

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3.4 Work Done

Physics by Robert Hutchings, 2nd Edition, pg 406.

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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.

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END OF LECTURE