Question

A scuba diver searches for treasure at a depth of 20.0m below the surface of the sea. at what pressure must the scuba device deliver air to the diver? (density of sea water= 1030kg/m^3;atmospheric pressure= 1.013x10^5 pa)

another one

A king's crown is said to be solid gold but may be made of lead and covered with gold. when it is weighed in air, the scale reads 0.475 kg. when it is submerged in water the scale reads 0.437 kg.is it solid gold? if not, what percent is mass is gold? (density of gold= 19.3x10^3 kg/m^3)

Answer 1

1.
p= ρ•g•h + p (atm)=1000•9.8•20 + 101325= =2.97•10^5 Pa.
2.
(a)
m=0.475 kg, m1 =0.437 kg
m1•g = m•g – F(buoyancy) =>
m1•g = m•g – ρ(w)•V•g,
V= (m - m1)/ρ(w) = (0.475-0.437)/1000 =3.8•10^-5 m^3.

m1•g = ρ(x) •V•g – ρ(w)•V•g ,
m•g = ρ(x) •V•g,
ρ(x) = m/V = 0.475/3.8•10^-5 =12.5•10^3 kg/m^3
(b)
19.3•10^3•x +11.4•10^3•(100-x) = 12.5•10^3•100,
19.3•x+11.4•(100-x) = 12.5•100,
7.9•x = 110,
x =13.92% ≈14%.
The crown is roughly 14% gold and 86% lead.