The mass of a full can of coke is 394 g. Because it uses an artificial sweetener, the mass of a full can of diet coke is lower: only 355 g. The volume of both cans (including the outside of the can) is 359 mL. Will either can float in water when it's full? (The density of water is 1.0 g /mL

Answer 1

To determine whether each can will float in water, we will calculate the density of each can (including its contents) and compare it to the density of water, which is 1.0 g/mL.

The density (ρ) is calculated using the formula:

\[ \text{Density} (\rho) = \frac{\text{mass}}{\text{volume}} \]

1. Full can of Coke:

   • Mass = 394 g
   • Volume = 359 mL
   • Density = \(\frac{394 \text{ g}}{359 \text{ mL}} \approx 1.096 \text{ g/mL}\)

2. Full can of Diet Coke:

   • Mass = 355 g
   • Volume = 359 mL
   • Density = \(\frac{355 \text{ g}}{359 \text{ mL}} \approx 0.987 \text{ g/mL}\)

Now, we compare the calculated densities with the density of water (1.0 g/mL):

• The full can of Coke has a density of approximately 1.096 g/mL, which is greater than 1.0 g/mL. This means that the full can of Coke will not float; it will sink.

• The full can of Diet Coke has a density of approximately 0.987 g/mL, which is less than 1.0 g/mL. This means that the full can of Diet Coke will float in water.

In summary:

• Full can of Coke: sinks
• Full can of Diet Coke: floats