Physics 110 Lecture 24 from Chapter 9 Sections 1 to 3

1
Physics 110 Lecture 24 from Chapter 9
Sections 1 to 3

• Properties of Solids

2
Homework Assignment 24

• Problems
• Chapter 9, Problem 1 on page 311
• Chapter 9, Problem 5 on page 312
• Chapter 9, Problem 10 on page 312
• Chapter 9, Problem 17 on page 312

3
The 4 States of Matter

• Solids
• Liquid
• Gas
• Plasma

4
Solids

• Has definite volume
• Has definite shape
• Molecules are held in specific locations
• by electrical forces
• Vibrate about equilibrium positions
• Can be modeled as springs connecting molecules

5
More About Solids

• External forces can be applied to the solid and
  compress the material
• In the model, the springs would be compressed
• When the force is removed, the solid returns to
  its original shape and size
• This property is called elasticity

6
Crystalline Solid

• Atoms have an ordered structure
• An example is a crystal of salt
• Gray spheres represent Na ions
• Green spheres represent Cl- ions

7
Amorphous Solid

• Atoms are arranged almost randomly
• Examples include glass and plastic

8
Liquid

• Has a definite volume
• No definite shape
• Exists at a higher temperature than solids
• The molecules wander through the liquid in a
  random fashion
• The intermolecular forces are not strong enough
  to keep the molecules in a fixed position
• Cannot resist shearing forces

9
Gas

• Has no definite volume
• Has no definite shape
• Molecules are in constant random motion

• The molecules exert only weak forces on each
  other
• Average distance between molecules is large
  compared to the size of the molecules

10
Plasma

• Matter heated to a very high temperature
• Many of the electrons are freed from the nucleus
• Result is a collection of free, electrically
  charged ions
• Plasmas exist inside stars

11
Properties of Solids

• Density
• Elasticity
• Deformation
• Fracture Strength

12
Density

• The density of a substance of uniform composition
  is defined as its mass per unit volume
• Units are kg/m3 (SI) or g/cm3 (cgs)
• 1 g/cm3 1000 kg/m3

13
Density, cont.

• The densities of most liquids and solids vary
  slightly with changes in temperature and pressure
• Densities of gases vary greatly with changes in
  temperature and pressure

14
Density of Common Material
15
Example 1

• An unknown silvery, metallic sphere of diameter
  7.5 cm has a weight of 10 N. What possible
  material(s) could it be made from?

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Example 1

• D 7.5 cm 0.075 m
• W10 N

Possible material titanium
17
Specific Gravity

• The specific gravity of a substance is the ratio
  of its density to the density of water at 4 C
• The density of water at 4 C is 1000 kg/m3

18
Some Common Specific Gravities

• Air 0.001
• Wood 0.3-0.8
• Water 1.0
• Glass 2.5
• Aluminum 2.7
• Iron 7.9
• Lead 11.3
• Gold 19.3

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Deformation of Solids

• All objects are deformable
• It is possible to change the shape or size (or
  both) of an object through the application of
  external forces
• when the forces are removed, the object tends to
  its original shape
• This is a deformation that exhibits elastic
  behavior

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Types of Deformation
Axial
Shear
Bulk
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Stress
Stress is the Force acting per unit Area
Units of N/m2
Stress is a measure of how hard the material is
being pulled apart on an atomic level.
F
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Strain
The unit change in length or size that a body
under stress shows is called strain.
?L
?x
??
?y
L
Axial
Shear
Bulk
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Stress vs. Strain

• Stress is the force per unit area causing the
  deformation
• Strain is a measure of the amount of deformation
• The relationship between stress and stain is
  given by Hooke's law For sufficiently small
  stresses, the stress is directly proportional
  to the strain.
• where E is the material constant called the
  Modulus of Elasticity (or Young's Modulus)

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Modulus of Elasticity (or Young's Modulus)

• Modulus of Elasticity is found by performing
  material testing.
• It represents the slope of the stress-strain
  curve during elastic behavior of the test.
• A stressed body exhibits elastic behavior up to a
  point, after which it permanently deforms.

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Elastic Modulus

• also called Young's Modulus
• The elastic modulus can be thought of as the
  stiffness of the material
• A material with a large elastic modulus is very
  stiff and difficult to deform
• Analogous to the spring constant
• Units of Pascals 1 Pa 1 N/m2

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Ultimate Strength

• The maximum stress a part can withstand before it
  breaks.
• The ultimate strength is the greatest stress the
  object can withstand. The stress is based on the
  original cross sectional area.

Ult. Strength
For a ductile material, after passing the
ultimate strength the material thins and
stretches at a lower stress level before breaking
Breaking point
stress, s
Elastic limit
strain, e
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Ultimate Strength

• The maximum stress a part can withstand before it
  breaks.
• The ultimate strength is the greatest stress the
  object can withstand. The stress is based on the
  original cross sectional area.

For a brittle material, the breaking point is
just beyond its ultimate strength
Ult. Strength Breaking point
stress, s
Elastic limit
strain, e
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Shear ModulusElasticity of Shape

• Forces may be parallel to one of the objects
  faces
• The stress is called a shear stress
• The shear strain is the ratio of the horizontal
  displacement and the height of the object

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Shear Modulus, final

• S is the shear modulus (or modulus of rigidity)
• A material having a large shear modulus is
  difficult to bend

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Bulk Modulus

• Bulk Modulus characterizes the response of an
  object to uniform squeezing
• The object undergoes a change in volume without a
  change in shape

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Bulk Modulus

• The pressure, ?P, is the ratio of the force to
  the surface area
• The volume strain is equal to the ratio of the
  change in volume to the original volume

The negative sign indicates that increasing
pressure results in decreasing volume
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Common Values of Elastic Modulus,
Ultimate Strength, and Yield Strength
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Notes on Moduli

• Solids have Elastic, Shear, and Bulk moduli.
• Liquids have only Bulk moduli.
• Liquids will not support shearing or tensile
  stresses.
• The liquid will flow instead of fracture

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Example 2

• A 1.6 m long steel piano wire has a diameter of
  0.2 cm.
• a) How great is the tension if it stretches 0.30
  cm when tightened?
• b) How great a force is needed to cause the wire
  to break?

?L
L
F
F
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Example 2

• L 1.6 m
• d 0.2cm 0.002 m
• ?L 0.30 cm 0.003 m
• From table E 200x109 Pa sult
  500x106 Pa

?L
L
F
F
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Example 2 Part A
?L
L
F
F
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Example 2 Part B
?L
L
F
F