chapter 12 l2 - department of physics · pdf file11/23/09 5 condition for static equilibrium...
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Chapter 12 – Static equilibrium and Elasticity Lecture 2
• More examples • Equilibrium in an accelerated frame • Stable and unstable equilibrium • Stress and Strain
– Young’s Modulus – Shear Modulus
Physics 201 Fall 2009
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The object shown in the diagram is a cube of uniform density resting on a rough surface. The applied force F is balanced by
the frictional force F fr. When the block is on the verge of tipping, the point of application of the normal force acting on
the cube will be
A. 1 B. 2 C. 3 D. 4 E. 5
Condition for static equilibrium • Conditions for a rigid body to be in a static equilibrium:
A) Net external force must be 0: no linear acceleration
B) Net external torque must be 0: no angular acceleration
Fext = 0∑
τext∑ = 0
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Condition for static equilibrium in accelerated frame
• Conditions for a rigid body to be in a static equilibrium in a linearly accelerated frame, eg a truck moving a block.
A) Net external force must be modified to account for the linear acceleration a
B) Net external torque must be still 0: no angular acceleration
Fext = ac.m.∑
τext∑ = 0
Which of the objects is nearest to being in unstable equilibrium?
A. 1 B. 2 C. 3 D. 4 E. 5
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Stability of equilibrium
• The static equilibrium condition can be – Stable – Unstable
• In order to understand the stability condition we look at the potential energy situation
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Stress and Strain
Strain =ΔLL
• All objects are deformable by external forces
• An object may be stretched by a tensile force. The relative change in length to due to F is called strain:
• Stress is the ratio of the force F to the cross-sectional area A
Stress =FA
Strain =ΔLL
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• Sometimes when the forces are removed, the object tends to its original shape, called elastic behavior
• Large enough forces will break the bonds between molecules and also the object.
• Young’s modulus or the elastic modulus describes how much an object deforms elastically under stress:
Deformation of Solids
Y =StressStrain
=FA
ΔLL
©2008 by W.H. Freeman and Company
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11/23/09 Physics 201, UW-Madison 19
Solids – microscopic view
• Have definite volume • Have definite shape • Molecules are held in specific
locations – by electrical forces – vibrate about equilibrium
positions – Can be modeled as springs
connecting molecules
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Elastic Properties • Stress is related to the force causing the deformation
• Strain is a measure of the degree of deformation
• The elastic modulus is the constant of proportionality between stress and strain – For sufficiently small stresses, the stress is directly proportional to
the strain – The constant of proportionality depends on the material being
deformed and the nature of the deformation – The elastic modulus can be thought of as the stiffness of the
material
Elastic modulus= stressstrain
Strain =ΔLL
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Shear stress and shear strain
• The ratio of the shear force to the horizontal area that it is applied to is called
• We define shear strain
• And the shear modulus
Shear stress =FSA
Shear strain =ΔXL
= tanθ
MS =Shear stressShear strain
=FSA
ΔXL=FSA
tanθ Block of jello
Shear stress and shear strain
MS =Shear stressShear strain
=FSA
ΔXL=FSA
tanθ Block of jello
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