Answer:
a. 2 m
b. 0.15 m
Explanation:
(a) By what deck does the ship sink in fresh.
water, when it loads a cargo of 4000 tonnes
We know that the upward force , U on the ship equal the weight of fresh water displaced, W = ρVg where ρ = density of fresh water = 1000 kg/m³, V = volume of water displaced and g = acceleration due to gravity.
So, U = W = ρVg
This upward force must equal the weight of the ship, W' = mg where m = mass of ship = 4000 tonnes = 4000 × 1000 kg = 4 × 10⁶ kg
So. U = W'
ρVg = mg
V = m/ρ = 4 × 10⁶ kg/10³ kg/m³ = 4 × 10³ m³
Now the volume of water displaced equals the volume occupied by the ship floating ship of cross-sectional area, A = 2000 m³ and depth in water h.
So, V = Ah
Thus h = V/A = 4 × 10³ m³/2000 m³ = 2 m
So, the ship sinks to a depth of 2 m in fresh water.
(b) if the ship + Cargo has a displacement tonnage
of 12300 tonnes; by what amount will the ship
rise in the water when it sails from fresh water
into Seawater (density of Sea water - 1025kgm⁻³
We know that the upward force , U' on the ship in fresh water equals the weight of fresh water displaced, W" = ρV'g where ρ = density of fresh water = 1000 kg/m³, V' = volume of water displaced and g = acceleration due to gravity.
So, U = W" = ρV'g
This upward force must equal the weight of the ship + cargo, W₁ = m₁g where m₁ = mass of ship + cargo = 12300 tonnes = 12300 × 1000 kg = 1.23 × 10⁷ kg
So. U' = W₁
ρV'g = m₁g
V' = m₁/ρ = 1.23 × 10⁷ kg/10³ kg/m³ = 1.23 × 10⁴ m³
Now the volume of water displaced equals the volume occupied by the ship floating ship of cross-sectional area, A = 2000 m³ and depth in fresh water h'.
So, V' = Ah'
Thus h = V'/A = 1.23 × 10⁴ m³/2000 m³ = 6.15 m
So, the ship sinks to a depth of 0.6 m in fresh water.
Also,
We know that the upward force , U" on the ship in sea water equals the weight of sea water displaced, W₂ = ρ'V"g where ρ' = density of sea water = 1025 kg/m³, V"= volume of water displaced and g = acceleration due to gravity.
So, U" = W₂ = ρ'V"g
This upward force must equal the weight of the ship + cargo, W₁ = m₁g where m₁ = mass of ship + cargo = 12300 tonnes = 12300 × 1000 kg = 1.23 × 10⁷ kg
So. U" = W₁
ρ'V"g = m₁g
V" = m₁/ρ' = 1.23 × 10⁷ kg/1.025 × 10³ kg/m³ = 1.2 × 10⁴ m³
Now the volume of water displaced equals the volume occupied by the ship floating ship of cross-sectional area, A = 2000 m³ and depth in sea water h".
So, V" = Ah"
Thus h" = V'/A = 1.2 × 10⁴ m³/2000 m³ = 6 m
So, the ship sinks to a depth of 6 m in fresh water.
So, the rise in height from fresh water to sea water is Δh = h' - h" = 6.15 m - 6 m = 0.15 m
