Physics 1710 Chapter 13 Equilibrium and Elasticity

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Physics 1710Chapter 13 Equilibrium and
Elasticity

• Question
• Which will win a race down an incline?
• A ball?
• A disk?
• A ring?
• Why?

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Physics 1710Chapter 13 Equilibrium and
Elasticity

• 1' Lesson
• Static equilibrium (no translational or
  rotational acceleration) requires that all forces
  and torques to balance.
• If the acceleration due to gravity is the same
  for all particles comprising a body the center of
  mass is the center of gravity.
• The moduli of elasticity characterizes the
  stress-strain relation
• stress modulus x strain

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Physics 1710Chapter 13 Equilibrium and
Elasticity

• Equilibrium

Equilibrium means balanced. Fnet d P/dt In
equilibrium Fnet 0 Tnet d L/dt In
equilibrium Tnet 0
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Physics 1710 Chapter 13 Equilibrium and
Elasticity

• Legends of the FallHow a ladder stays up

Fnet 0
Tnet 0
Fnet 0
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Physics 1710 Chapter 13 Equilibrium and
Elasticity

• Center of Gravity
• If the acceleration due to gravity is the same
  for all parts of a body, then the center of mass
  corresponds to the center of gravity.
• Proof Ti Sxi Fgi Sxi gmgi Mg Sxi mgi
  /M Fcg xcm

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Physics 1710 Chapter 13 Equilibrium and
Elasticity

• Elasticity
• Stress the deforming force per unit area.
• Strain the unit deformation.
• Tensile stretch
• Compressive squeeze
• Shear lean
• Hydraulic pressure
• Yield permanently deformed

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Physics 1710 Chapter 13 Equilibrium and
Elasticity

• Elasticity
• Stress the deforming force per unit area.
• Strain the unit deformation.
• Stress modulus x strain
• s F/A Y e

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Physics 1710 Chapter 13 Equilibrium and
Elasticity

• Elasticity
• Stress the deforming force per unit area.
• Strain the unit deformation.
• Stress modulus x strain
• s F/A Y e

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Physics 1710 Chapter 13 Equilibrium and
Elasticity

• Elasticity
• Stress the deforming force per unit area.
• Strain the unit deformation.Tensile/Compressive
  , Youngs Modulus E
• Stress modulus x strain
• s F/A E e E ?L/L

?L
L
s
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Physics 1710 Chapter 13 Equilibrium and
Elasticity

• Elasticity
• Stress the deforming force per unit area.
• Strain the unit deformation.Shear Modulus G
• Stress modulus x strain
• s F/A G e G ?x/L

L
?x
s
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Physics 1710 Chapter 13 Equilibrium and
Elasticity

• Elasticity
• Stress the deforming force per unit area.
• Strain the unit deformation.Hydraulic Stress
  Bulk Modulus B
• Stress modulus x strain
• s F/A p B e B ?V/V

?V
V
p
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Physics 1710 Chapter 13 Equilibrium and
Elasticity

• Summary
• Static equilibrium imples that all forces and
  torques balance.
• The center of mass is often the center of
  gravity.
• The moduli of elasticity characterizes the
  stress-strain relation
• stress modulus x strain
• Stress modulus x strain
• s F/A Y e