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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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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