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)