Question

Salt water is denser than fresh water. a ship floats in both fresh water and salt water. compared to the fresh water, the volume of water displaced in the salt water is

Answer 1

Compared to fresh water, a ship displaces less volume of salt water because salt water is denser, which means the ship will float higher in salt water.

Step-by-step explanation:

When a ship floats in both fresh water and salt water, the volume of water displaced in the salt water is less compared to fresh water. This is because salt water is denser than fresh water. According to Archimedes' Principle, an object submerged in a fluid will displace a volume of fluid equal to its own weight. Since salt water is denser, a ship doesn't need to displace as much volume of water in saltwater to equal its weight and achieve buoyancy. This is the main reason why a ship will float higher in salt water than in fresh water.

Answer 2

The ship floats in water due to the buoyancy Fb that is given by the equation:

Fb=ρgV, where ρ is the density of the liquid, g=9.81 m/s² is the acceleration of the force of gravity and V is volume of the displaced liquid.

The density of fresh water is ρ₁=1000 kg/m³.

The density of salt water is in average ρ₂=1025 kg/m³.

To compare the volumes of liquids that are displaced by the ship we can take the ratio of buoyancy of salt water Fb₂ and the buoyancy of fresh water Fb₁.

The gravity force of the ship Fg=mg, where m is the mass of the ship and g=9.81 m/s², is equal to the force of buoyancy Fb₁ and Fb₂ because the mass of the ship doesn't change:

Fg=Fb₁ and Fg=Fb₂. This means Fb₁=Fb₂.

Now we can write:

Fb₂/Fb₁=(ρ₂gV₂)/(ρ₁gV₁), since Fb₁=Fb₂, they cancel out:

1/1=1=(ρ₂gV₂)/(ρ₁gV₁), g also cancels out:

(ρ₂V₂)/(ρ₁V₁)=1, now we can input ρ₁=1000 kg/m³ and ρ₂=1025 kg/m³

(1025V₂)/(1000V₁)=1

1.025(V₂/V₁)=1

V₂/V₁=1/1.025=0.9756, we multiply by V₁

V₂=0.9756V₁

Volume of salt water V₂ displaced by the ship is smaller than the volume of sweet water V₁ because the force of buoyancy of salt water is greater than the force of fresh water because salt water is more dense than fresh water.