Chapter 13.3, Problem 32SSC

To determine

Difference between a can that sinks and a can that floats.

Answer to Problem 32SSC

Due to lower density, diet coke can float on water

Explanation of Solution

Introduction: According to Archimedes principle’, Buoyant force on submerged object (or thing) in fluid is equal to weight (or mass) of displaced of the fluidby the same object.

Whether the coke will float on water or not, it depends on the sugar quantity contain in the coke.

The regular soda coke majorly contains water of density $1\text{g/mL}$ and $39\text{g}$ of sugar (highly fructose corn syrup). Due to these two components the net density of the regular coke become higher than that of water due to which it sinks.

On the other hand, diet coke contains Aspartame (an artificial sweetener). Sweetness of this aspartame is $113$ times more than that of normal sugar. Thus, a very small quantity of aspartame ( $0.35\text{g}$ ) is used. That’s why diet cake has lower density and can easily float on water.

Conclusion:

Regular soda sinks in water whereas, diet soda floats in the water because diet sad has lower density.