Question

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.)

Answer 1

Answer:

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