phy53 lect			dr. brown 			16 november 2010

curve balls -- baseball

discussion -- golf balls...dimpled surface; compare to ping pong ball


leading to Young's Modulus

atoms modeled like connected by springs 
[discussion of similarity -- Leonard-Jones potential -- consider Taylor series expansion about the minimum]

single chain; two chains; block of material with cross sectional area...

F_{restoring} = - Y A/L  \Delta L = -"k_eff" \Delta L

Y = young's modulus = stress over strain = (F/A)/(\Delta L /L)

explains linear response limit, elastic limit[permanent deformation] and fracture limit


Another material response -- push rectanglular cross section at top -- shear stress and strain

Shear modulus = shear stress / shear strain = (F/A) / (\Delta x /L)

finally -- "Bulk modulus"  increase pressure -- response is change in volume

large bulk modulus => low compressibility

We can really understand springs now and where, from microscopic view of matter, Hooke's Law comes from-- so,

solve -- mass on a spring

F_x = -kx = m a = m \frac{d^2 x}{dt}

Simple Harmonic Oscillator Equation
\frac{d^2 x}{dt^2} + \frac{k}{m} x = 0

solve it   Euler equation...real part ... x(t) = x_o cos (\omega t + \delta)

next -- pendulum ... nonlinear diffy q  so, make small angle approximation   sin(\theta) approx \theta