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Chapter 10
Simple Harmonic
Motion and Elasticity
Elastic Deformation
Because of these atomic-level “springs”, a material tends to return to its initial shape once forces have been removed.
ATOMS
FORCES
Elastic Deformation
STRETCHING, COMPRESSION, AND YOUNG’S MODULUS
L
F Y
L A
o
Young’s modulus has the units of pressure: N/m2
Elastic Deformation
Elastic Deformation
Example: Bone Compression
In a circus act, a performer supports the combined weight (1080 N) of a number of colleagues. Each thighbone of this performer has a length of 0.55 m and an effective cross sectional area of 7.7×10-4 m2. Determine the amount that each thighbone compresses under the extra weight.
Answer :
L 4.110 5 m
Elastic Deformation
SHEAR DEFORMATION AND THE SHEAR MODULUS
x
F S A
L
o
The shear modulus has the units of pressure: N/m2
Elastic Deformation
Elastic Deformation
Example: J-E-L-L-O
You push tangentially across the top surface with a force of 0.45 N. The top surface moves a distance of 6.0 mm relative to the bottom surface. What is the shear modulus of Jell-O?
Answer :
S 460 N m 2
Elastic Deformation
VOLUME DEFORMATION AND THE BULK MODULUS
V
P B
V
o
The Bulk modulus has the units of pressure: N/m2
Elastic Deformation
Stress, Strain, and Hooke’s Law
In general the quantity F/A is called the stress.
The change in the quantity divided by that quantity is called the strain: V Vo L Lo x Lo
HOOKE’S LAW FOR STRESS AND STRAIN
Stress is directly proportional to strain.
Strain is a unitless quantitiy.
SI Unit of Stress: N/m2
Stress, Strain, and Hooke’s Law
Simple Harmonic
Motion and Elasticity
Elastic Deformation
Because of these atomic-level “springs”, a material tends to return to its initial shape once forces have been removed.
ATOMS
FORCES
Elastic Deformation
STRETCHING, COMPRESSION, AND YOUNG’S MODULUS
L
F Y
L A
o
Young’s modulus has the units of pressure: N/m2
Elastic Deformation
Elastic Deformation
Example: Bone Compression
In a circus act, a performer supports the combined weight (1080 N) of a number of colleagues. Each thighbone of this performer has a length of 0.55 m and an effective cross sectional area of 7.7×10-4 m2. Determine the amount that each thighbone compresses under the extra weight.
Answer :
L 4.110 5 m
Elastic Deformation
SHEAR DEFORMATION AND THE SHEAR MODULUS
x
F S A
L
o
The shear modulus has the units of pressure: N/m2
Elastic Deformation
Elastic Deformation
Example: J-E-L-L-O
You push tangentially across the top surface with a force of 0.45 N. The top surface moves a distance of 6.0 mm relative to the bottom surface. What is the shear modulus of Jell-O?
Answer :
S 460 N m 2
Elastic Deformation
VOLUME DEFORMATION AND THE BULK MODULUS
V
P B
V
o
The Bulk modulus has the units of pressure: N/m2
Elastic Deformation
Stress, Strain, and Hooke’s Law
In general the quantity F/A is called the stress.
The change in the quantity divided by that quantity is called the strain: V Vo L Lo x Lo
HOOKE’S LAW FOR STRESS AND STRAIN
Stress is directly proportional to strain.
Strain is a unitless quantitiy.
SI Unit of Stress: N/m2
Stress, Strain, and Hooke’s Law