Ch.12: Static Equilibrium and Elasticity

(Forces and Torques are balanced AND Deformation due to applied stress)

*All materials become distorted when squeezed or stretched with enough force

3 Types of Elasticity:

2) Shear DeformationF

1) Tension / Compression

F

F

3) Volume Deformation

F

L

1) Tension / Compression

A

L0

F YL

LA

0

A = area to applied force

Y = Young’s modulus (depends on the material)

*The same equation holds for compression (L = decrease in length)

Ex: Weightlifter

a) If he is lifting a total of 500 lbs, and his forearms are each .30 m long with cross sectional bone area of 6.0 x 10-4 m2, by how much does each bone compress?

b) By how much does each bone stretch if he suspends the same weight with his arms hanging downward?

2) Shear Deformation

F Sx

LA

0

S = Shear modulus (depends on the material)

Ex: Jello

.03m

.07m.07m

6.0 mmWhen a shear force of .45 N is applied

Use this information to find the shear modulus of jello

3) Volume Deformation

Pressure PForceArea

*SI unit = N/m2 = 1 Pascal

P - BV

V0

B = Bulk modulus (depends on the material)

V = change in volume

V0 = initial volume

change in pressure

Ex: Styrofoam cup

The formulas for all 3 types of elasticity can be arranged to look very similar……

Stretching: FA

YL

L 0

Shearing: FA

Sx

L 0

Volume: FA

- BV

V0

Stress Strain

Another form of Hooke’s Law

*Applies only up to the elastic limit (then it breaks)