In 1983 , the United States began coining the one-cent piece...

In 1983 , the United States began coining the one-cent piece out of copper-clad zinc rather than pure copper. The mass of the old copper penny is $3.083 \mathrm{~g}$ and that of the new cent is $2.517 \mathrm{~g}$. The density of copper is $8.920 \mathrm{~g} / \mathrm{cm}^{3}$ and that of zinc is $7.133 \mathrm{~g} / \mathrm{cm}^{3} .$ The new and old coins have the same volume. Calculate the percent of zinc (by volume) in the new cent.

Key Concepts

Density

Density is a fundamental property of matter defined as mass per unit volume. It allows us to relate the mass and volume of materials, which is essential when comparing materials with different densities that are used to make objects of the same size.

Volume Conservation

Volume conservation refers to situations where the total volume of an object remains constant, even if the composition changes. In problems like this, where the new and old coins have the same volume, it provides a crucial constraint that helps relate the masses and densities of the different constituent materials.

Mass-Density Relationship

The relationship between mass, density, and volume (expressed as mass = density × volume) is key in solving problems that involve changes in material composition. This equation enables one to convert between mass and volume, facilitating the calculation of how much of a material is present in an object when its density is known.

Percent Composition

Percent composition, particularly by volume in this context, involves determining the fraction of an object’s total volume that is contributed by each constituent material. It is calculated by dividing the volume of the material of interest by the total volume and then converting it to a percentage. This concept is essential in materials science and engineering to analyze mixtures and composite objects.

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