A Boat Floats A boat floating in fresh water displaces water...

A Boat Floats A boat floating in fresh water displaces water weighing $35.6 \mathrm{kN}$. (a) What is the weight of the water that this boat would displace if it were floating in salt water with a density of $1.10 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3} ?$ (b) Would the volume of the displaced water change? If so, by how much?

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Key Concepts

Volume Displacement

The volume displacement refers to the amount of fluid displaced by an object when it is immersed. For floating objects, while the weight of the displaced fluid is constant (equal to the weight of the object), changes in the fluid's density will result in changes in the displaced volume.

Buoyant Force

The buoyant force is the upward force exerted by a fluid on an immersed object, counteracting the weight of the object. It depends directly on the weight of the displaced fluid, following Archimedes' Principle, regardless of the fluid's density.

Archimedes' Principle

This principle states that a body fully or partially submerged in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid that is displaced by the body. It is fundamental in understanding why objects float or sink, linking fluid displacement to buoyancy.

Density

Density is the measure of mass per unit volume of a substance. It plays a crucial role in determining the weight of the displaced fluid and, consequently, the buoyant force acting on an object. Variations in density between different fluids can lead to changes in the volume of fluid displaced while maintaining the same weight.

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