a.The gauge pressure in a hydraulic lift is 16 atm. What is the mass
of the heaviest vehicle it can lift if the diameter of the output line
is 17 cm?
(1 atm = 1.01 ´ 105 Nm-2)


b.A 0.40 kg piece of wood floats in water but is found to sink in
alcohol, in which it has an apparent mass of 0.020 kg. What is the
density of wood?

The density of alcohol is 0.79 ´ 103 kg m-3.

a) force is pressure*area.  Area is pi*(17/2)^2 = 227 cm^2 = 0.0227
m^2.
pressure is 16*101000 N/m^2, so force is 36800 N, which, divided by
9.8 N/m^2 gives the max mass as 3750 kg.  3750 kg

b) the mass of the alcohol displaced is .38 kg, so the density of wood
is .40/.38 times that of alcohol.  .40/.38 * 790 kg/m^3 = 830 kg/m^3. 
830 kg/m^3.