A boat floating in fresh water displaces water weighing 35.6 kN. (a) What is the weight of the water this boat displaces when floating in salt water of density 1.10 x 10^3 kg/m^3? (b) What is the difference between the volume of fresh water displaced and the volume of salt water displaced?

a) Hey, the boat weighs the same and must displace the same mass of water, fresh or salt, exactly 35.6 kN. Of course it must displace a greater volume of the less dense fresh water and therefore will float lower in the fresh water than in the salt water. The difference in volume will be in the ratio of the densities ( 1.1 / 1.0 ) in this case). By the way that is very salty salt water indeed.

To find the weight of the water the boat displaces in salt water, we need to first calculate the volume of water displaced in fresh water and then use the density of salt water to find the weight of the same volume of salt water.

(a) Weight of water displaced in salt water:
Given weight of water displaced in fresh water = 35.6 kN

To find the weight of salt water displaced, we can use the equation:

Weight = density * volume * gravity

where density is the density of salt water (1.10 x 10^3 kg/m^3), volume is the volume of water displaced, and gravity is the acceleration due to gravity (9.8 m/s^2).

We can rearrange this equation to solve for volume:

Volume = Weight / (density * gravity)

Substituting the given values:

Volume = (35.6 kN) / (1.10 x 10^3 kg/m^3 * 9.8 m/s^2)
Volume = (35.6 x 10^3 N) / (1.10 x 10^3 kg/m^3 * 9.8 m/s^2) (since 1 N = 1 kg * m/s^2)
Volume ≈ 3.26 m^3

Now, we can find the weight of the salt water displaced using the volume:

Weight of salt water displaced = density * volume * gravity
Weight of salt water displaced = 1.10 x 10^3 kg/m^3 * 3.26 m^3 * 9.8 m/s^2
Weight of salt water displaced ≈ 35.6 kN

Therefore, the weight of the water this boat displaces when floating in salt water is approximately 35.6 kN.

(b) To find the difference between the volume of fresh water displaced and the volume of salt water displaced, we can subtract the volumes:

Difference in volume = Volume in fresh water - Volume in salt water
Difference in volume = Volume in fresh water - (35.6 kN / (1.10 x 10^3 kg/m^3 * 9.8 m/s^2))

Substituting the given values:

Difference in volume ≈ Volume in fresh water - 3.26 m^3

Please provide the volume of water displaced in fresh water to calculate the difference in volumes.

To answer these questions, we need to understand some basic principles of fluid mechanics and buoyancy.

(a) The weight of the water displaced by the boat can be calculated using Archimedes' principle, which states that the buoyant force experienced by an object immersed in a fluid is equal to the weight of the fluid displaced by the object.

To find the weight of the water displaced in salt water, we can use the density of the saltwater and the weight of the water displaced in fresh water.

First, we need to convert the weight of the water displaced in fresh water from kilonewtons (kN) to kilograms (kg):

Weight in kg = Weight in kN × 1000

Given that the weight in kN is 35.6 kN, the weight in kg is:

Weight in kg = 35.6 kN × 1000 = 35,600 kg

Now, we can use the formula for the weight of the water displaced:

Weight of water displaced = Density of salt water × Volume of water displaced

The density of salt water is given as 1.10 x 10^3 kg/m^3.

To find the volume of water displaced in salt water, we rearrange the formula:

Volume of water displaced = Weight of water displaced / Density of salt water

Substituting the values, we get:

Volume of water displaced = 35,600 kg / 1.10 x 10^3 kg/m^3

Now we can calculate the volume of water displaced.

(b) To find the difference between the volume of fresh water displaced and the volume of salt water displaced, we subtract the two volumes:

Difference in volume = Volume of fresh water displaced - Volume of salt water displaced

Using the values calculated in part (a), we can find the answer.

Let's now calculate the solution step by step.

(a) Weight of the water displaced in salt water:
Weight in kg = 35.6 kN × 1000 = 35,600 kg

Volume of water displaced = 35,600 kg / (1.10 x 10^3 kg/m^3)
Calculate the result.

(b) Difference in volume = Volume of fresh water displaced - Volume of salt water displaced
Substitute the values calculated in part (a) into the equation above.
Calculate the result.

Please provide the values calculated in part (a) so that we can continue and calculate the difference in volume in part (b).