phy53 lecture		dr. brown		4 november 2010

more gravity 

how do we know G = 6.67 x 10^{-11} N m^2/kg^2 ?

measuring G is equivalent to measuring M_earth

Cavendish Experiment

restoring torque from torsional pendulum  \tau = -K \theta
[recall F_spring = -k x]

F_g -- torque balance

\frac{2GMmL}{d^2} = K \theta ... solve for G 



Tides
consider two equal masses lined up radially
neap and spring tides

lunar dominates solar contribution


Humans Made of water -- so let us study ...   Fluids!
microscopic view to start...

pressure = F/(unit area)
[perpendicular to the fluid]
far too many calculations to apply N2 to every molecule...get average/macroscopic picture...

define density  \rho = \frac{dM}{dV}  V = volume

Gas -- vs -- Liquid
[both fluids]
Gas :
relatively low density
weakly interacting
spread out to fill container
compressible

Liquid :
relatively high density
strongly interacting
confined by container, retain cohesion ( surface tension)
relatively incompressible

density of water
\rho_w = 1000 kg/m^3  

specific gravity  = density of material / density of water

consider glass of water
Pressure of air = 1 atm = 10^5 Pa     SI units  Newtons/meter^2 = Pascals
P(z) = \rho g z + P_air

example -- breathing through reed 2m below surface of water (very difficult)