Question

If a cargo ship has a mass of 90,000,000 kg, how much water would it need to displace in order to float?

Answer 1

To float, a ship must displace a volume of water equal to its weight. The weight of the ship can be calculated using the mass and the acceleration due to gravity (approximately \(9.81 \, \text{m/s}^2\)).

First, we calculate the weight of the cargo ship:

\[
\text{Weight} = \text{mass} \times g = 90,000,000 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 882,900,000 \, \text{N}
\]

Next, we need to find out how much water needs to be displaced to equal this weight. The weight of the displaced water will be equal to the weight of the cargo ship.

The density of water is approximately \(1000 \, \text{kg/m}^3\). The weight of the displaced water can be related to its volume by the equation:

\[
\text{Weight} = \text{density} \times \text{volume} \times g
\]

Rearranging to find the volume:

\[
\text{Volume} = \frac{\text{Weight}}{\text{density} \times g}
\]

Substituting the values we know:

\[
\text{Volume} = \frac{882,900,000 \, \text{N}}{1000 \, \text{kg/m}^3 \times 9.81 \, \text{m/s}^2}
\]

Calculating this gives:

\[
\text{Volume} = \frac{882,900,000}{9810} \approx 89,900 \, \text{m}^3
\]

Therefore, the cargo ship needs to displace approximately **89,900 cubic meters** of water in order to float.