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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  4.110 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