A 10cm x 10cm x 10cm wood block with a density of 700 kg/m^3 floats in water.

What is the distance from the top of the block to the water in cm if the water is fresh, what if it is sea water?

(a).

density of fresh water is ρ_water = 1000 kg/m³

ΣF = 0

- (ρ_wood) g (V_wood) + (ρ_water) g (v_wood) = 0

(v_wood) / (V_wood) = (ρ_wood) / (ρ_water)

(10 * 10 * h) / (10 * 10 * 10) = (700) / (1000)

h = 7 cm

the distance from the top of the block to the water is 10 - 7 = 3 cm

(b).

density of seawater is ρ_sea = 1030 kg/m³

(v_wood) / (V_wood) = (ρ_wood) / (ρ_sea)

(10 * 10 * h') / (10 * 10 * 10) = (700) / (1030)

h' = 6.79611 cm

the distance from the top of the block to the water is 10 - 6.79611 = 3.20389 cm