A sample of an unknown material weighs 300.0 N in air and 200.0 N when submerged in an alcohol s

step 1 Question number nine, the weight in air is MG equal to 300 Newton. And when the sample is in alc

A sample of an unknown material weighs 300.0 N in air and...

A sample of an unknown material weighs $300.0 \mathrm{N}$ in air and $200.0 \mathrm{N}$ when submerged in an alcohol solution with a density of $0.70 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3}$. What is the density of the material? (See Sample Problem 9A.)

Key Concepts

Volume Calculation

Volume calculation in the context of submerged objects often involves using the buoyant force. By equating the buoyant force to the weight of the displaced fluid, one can determine the object's volume, provided the fluid's density is known. This volume can then be used in conjunction with the object's mass to calculate its density.

Density

Density is the measure of mass per unit volume of a substance. It is an intrinsic property that determines whether an object will sink or float in a fluid, and it is calculated by dividing the mass of the object by its volume. In problems involving submerged objects, density is often determined by relating the object's mass and the displacing fluid's properties.

Archimedes' Principle

This principle states that any object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid that is displaced by the object. It is fundamental for understanding why objects seem to weigh less when submerged and is crucial when determining physical properties such as volume or density from measurements in fluids.

Buoyant Force

The buoyant force is the net upward force exerted by a fluid on a submerged object. It is calculated as the difference between the weight of the object in air and its apparent weight when submerged. This concept is key in linking the displaced fluid's weight to the object's volume.

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