A raft with a volume of 3.0 m^3 is made of a material with a density of rho_r =

Question

A raft with a volume of 3.0 m^3 is made of a material with a density of rho_r = 300 kg/m^3. It is set a float on a freshwater lake where the density of the water is rho_w = 1000 kg/m^3. a) Find the mass that could be put on top of the raft in order to have exactly half its volume (1.5 m^3) submerged below the surface of the lake. b) If the pressure at the surface of the lake is given by is P_atm = 1.01 times 10^5 pa, and the pressure at the bottom of the lake is 5.5 times 10^5 pa, how deep is the lake?

Explanation / Answer

here,

volume , V = 3 m^3

density of material , pr = 300 kg/m^3

density of water , pw = 1000 kg/m^3

a)

let the mass be m

equating the forces

buyoyant force = gravitational force

pw * V/2 * g = ( pr * V + m) * g

1000 * 1.5 = ( 300 * 3 + m)

m = 600 kg

the mass can be put on raft is 600 kg

b)

Patm = 1.01 * 10^5 Pa

pressure at the bottom , P = 5.5 * 10^5 Pa

let the depth be h

Patm + p * g * h = P

1.01 * 10^5 + 1000 * 9.81 * h = 5.5 * 10^5

h = 45.8 m

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