A boat floating in fresh water displaces water weighing 35.6 kN. (a) What is the weight of the w

step 1 So here we know that for part A, according to Archimedes principle, we know that it makes it cle

A boat floating in fresh water displaces water weighing 35.6...

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

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

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Key Concepts

Volume Determination from Weight and Density

When the weight of the displaced fluid is known, the volume can be calculated using the formula: Volume = Weight / (Density × g), where g is the acceleration due to gravity. This concept is fundamental for comparing displacements in fluids of varying densities, such as fresh water versus salt water.

Archimedes' Principle

This principle states that any object wholly or partially immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced. It is crucial for understanding why a floating object displaces a volume of water whose weight corresponds to its own weight, regardless of the fluid’s density.

Density

Density is defined as the mass per unit volume of a substance and plays an essential role in determining the volume of fluid displaced by a floating object. A higher fluid density means that a smaller volume is needed to produce the same weight, which affects calculations regarding displacement in different fluids.

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