Question

In part E, you'll use your answers from parts B, C, and D to find the average density of each type of penny. Recall that density is mass divided by volume.

Calculate the average density of a penny (in g/mL) made before 1982. Show your work.

Answer 1

The average density of a pre-1982 penny is calculated by dividing its mass (8.630 g) by its displaced water volume (0.830 cm³), resulting in a density of 10.398 g/mL.

Step-by-step explanation:

To find the average density of a penny made before 1982, we need to know the coin's mass and volume. The mass of the coin is given, and we can assume it displaces an equal volume of water when submerged, thus providing us with the volume. From the information provided, the volume of water displaced, Vw, is 0.830 cm³ (since the density of water is 1.000 g/cm³ and the mass of the water displaced is 0.830 g).

The formula to calculate density, p, is mass (m) divided by volume (V), which is p = m / V. The authentic mass of the pre-1982 penny in air is 8.630 g, and when submerged in water it's 7.800 g. The apparent mass loss, which is the mass of the water displaced (mw), is used to calculate the volume of the penny.

Finally, to calculate the coin's density, we take the mass of the penny (8.630 g) and divide it by the volume of the penny (0.830 cm³), giving us an average density of 10.398 g/cm³. Therefore, the density of the penny made before 1982 is 10.398 g/mL.