When an object floats in water, it displaces a volume of water that has a weight equal to the weight of the object. If a ship has a weight of 4753 tons, how many cubic feet of seawater will it displace? Seawater has a density of 1.025 g·cm-3; 1 ton = 2000 lb. (Enter your answer in scientific notation.)

1.63*10⁻² ft³ is the volume of sea water displaced.

Explanation:

This is the Archimedes's principle, when an object floats in water, it displaces a volume of water that has a weight equal to the weight of the object.

Let's think this formulas

mass. gravity = Weight

density. gravity = Specific weight

The formula for Archimedes's principle is:

Weight of an object = Specific weight of the liquid. submerged volume

To find out the Weight of the ship, we convert the tons to kg.

4753 tons. 1kg / 1*10⁻³ tons = 4753000 kg

gravity = 9.8 m/s²

Weight of the ship = mass. gravity → 4753000 kg. 9.8 m/s² = 46579400 N

To apply the formula, we have to convert the density to kg/m³

1.025 g/cm³ → In 1cm³ we have 1.025 g

1cm³ = 1*10⁻⁶ m³

In 1*10⁻⁶ m³ we have 1.025 g

In 1m³ we would have 1.025*10⁹ g

So 1.025*10⁹ g. 1kg / 1*10⁻³ g = 1.025*10⁶ kg/m³

Let's go to the formula:

46579400 N = 1.025*10⁶ kg/m³. 9.8 m/s². Sumerged volume

46579400 N = 10045000 N/m³. Sumerged volume

46579400 N / 10045000 m³ / N = Sumerged volume → 4.63 m³

Let's make the final conversion

4.63 m³. 35.31 ft³ / 1m³ = 1.63*10⁻² ft³