Final answer:
To calculate a coin's density, its mass is measured in grams, and its volume is deduced from the water displaced when submerged. Density is then calculated as mass divided by volume. This method is used to verify the authenticity of coins.
Step-by-step explanation:
Calculating Coin Density
Calculating the density of a coin is an essential method in verifying its authenticity, especially in the context of ancient coins or precious metal coins. To calculate a coin's density, we need to know two key pieces of information: its mass and its volume.
The mass is typically measured in grams (g) using a precise scale, whereas the volume is determined indirectly through the water displacement method, which relies on the fact that the volume of water displaced by the submerged coin is equal to the coin's volume.
Following the example of an ancient Greek coin, the process of density calculation is straightforward. The mass of the coin is measured in air, which in this case is 8.630 g. Then, the coin is submerged in water, and its apparent mass is recorded, coming in at 7.800 g.
The difference in mass (8.630 g - 7.800 g) represents the mass of the water displaced, which is 0.830 g. Given that the density of water is 1.000 g/cm³, the volume of water (and thus the volume of the coin) is 0.830 cm³.
With the mass and volume known, the density of the coin can be found using the formula density (p) = mass (m) divided by volume (V). Substituting the measured values, we find the coin's density to be 8.630 g / 0.830 cm³, which then can be used to ascertain if the coin is made from the material it claims to be, such as gold, silver, or a lesser-valued metal. This exercise helps in determining whether the coin is authentic or a counterfeit.