Answers to homework problems

Chapter 11

2) density = mass/volume
   a) neutron star rho = 2.7 10^28 kg/1.2 10^3 m = 2.25 10^25 kg/m^3
   b) mass = density*volume = 2.25 10^25 kg/m^3 * 2 10^-7 m^3 = 4.5 10^18 kg

7) density of gold       rho_1 = 19300 kg/m^3
   density of quartz     rho_2 =  2660 kg/m^3
   Mass = mass(gold)+mass(quartz) = rho_1*v_1 + rho_2*v_2 = 12 kg
   Volume = volume(gold)+volume(quartz)= v_1+v_2 = 4*10^-3 m^3
   solution of these equations for volume v(gold) is
      v_1 = (Mass - rho_2*Volume)/(rho_1-rho_2)
      mass(gold)=v_1*rho_1 = 1.577 kg

14) force = pressure * surface
    F = Delta(P)*A = (1.013 10^5 Pa - 0.960 10^5 Pa) * 2*3.1 m^2 =
                   = 32860 N

41) Archimedes principle: W = volume * density * g
                              volume of a sphere = 4/3 pi r^3
    ====> r^3 = W/(g*rho*4/3*pi)= 5750 N/ (9.8 m/s^2 * 1.29 kg/m^3 *4/3*pi)=
              =108.58 m^3
          r=4.8 m