August 21, 2004

Sink or Float? (P.2)

As promised in a previous post, I am providing my observations on the soda cans, and more. Read on to find out what sinks, what floats, why, and the limitations of the displacement method.

  1. a 12 oz. can of Coke
    • Coke sinks. Although the bubble inside the can causes one end to pop up so that it sits more or less upright in the bottom of the tub.
  2. a 12 oz. can of Diet Coke w/ Lime
    • Diet Coke floats!
  3. a 12 oz. can of C2 (half the sugar of regular Coke)
    • C2 Floats!
  4. a 12 oz. can of ginger ale
    • The 12 oz. Can of ginger ale sinks.
  5. an 8 oz. can of ginger ale
    • The 8 oz. Can of ginger ale… floats!

So, in summary, we have the sugar-containing sodas sinking and the non-sugar or part-sugar sodas floating. Except for the 8 oz. can.

Why does the 8 oz. can float? My theory is that the headspace in the cans (the big gas bubble) is constant for this style can. So the gas bubble in the smaller can is a larger percentage of the volume of the can.

Of course, one way to describe whether something is going to sink of float is by its density. Pure water has a density of 1 gram/cubic centimeter. Anything with a higher density will sink. Anything with a lower density will float.

I set out to determine the densities of the various cans. Measuring the mass was easy—I own an Ohaus electronic self-calibrating scale that has gram precision. I used the displacement method to measure the volume of a 12 oz. can (obviously, it’s more than 12 oz. all together) and also of an 8 oz. can.

Unfortunately, I do not have an accurate way of measuring volume down to the milliliter, which is what I would need for this. Or, I would need to use a much larger vessel and immerse a larger number of cans at once. Either way, you’ll see that I did not get an accurate volume measurement.

I measured the 12 oz. can to be about 390 ml. I measured the 8 oz. can to be about 275 ml.

Here are the mass measurements:

  1. a 12 oz. can of Coke = 384g
    • density calculated at 384g/390ml = .985 g/cm3
  2. a 12 oz. can of Diet Coke w/ Lime = 371g
    • 371g/390ml = .951 g/cm3
  3. a 12 oz. can of C2 (half the sugar of regular Coke) = 374g
    • 374g/390ml = .959 g/cm3
  4. a 12 oz. can of ginger ale = 384g
    • 384g/390ml = .985 g/cm3
  5. an 8 oz. can of ginger ale = 263g
    • 263g/275ml = .956 g/cm3

See the problem?

All of them are less than 1. That means they’d all be floating. I know the mass measurements were good, so it means my sloppy attempt at the displacement method was off. But these values are so closely clustered that we can use our experimental results to get a better estimate of the volume of one of these cans.

The closest two cans that had different results were the C2 and the regular Coke. C2 is 374g. Coke is 384g. So a sanity check for the volume of the can is between 374 and 384 cm3. My 390ml measurement is off by at least 6ml. That is no surprise, since I was trying to read it off the side of a fairly wide-mouth vessel with gradations of 50ml.

Perhaps I should put a graduated cylinder on my wish list.

In any case, if we have the volume estimated at 379cm3 (right in the middle of our range, for lack of a better guess) then we get these densities:

  1. a 12 oz. can of Coke — 384g/379ml = ~ 1.013 g/cm3
  2. a 12 oz. can of Diet Coke w/ Lime — 371g/379ml = ~ .979 g/cm3
  3. a 12 oz. can of C2 — 374g/379ml = ~ .987 g/cm3
  4. a 12 oz. can of ginger ale — 384g/379ml = ~ 1.013 g/cm3

(We still don’t have a more accurate volume for the smaller can, sadly)

How could I get a more accurate volume measurement with only my scale?

I could puncture a hole in one of the cans and drain out the contents. Then, I could cut a small, regular shaped hole around my puncture, small enough to cover with some good waterproof tape but large enough to admit sand. Then, I could add sand to the can up to a total weight of 375g and see if that sinks. I could successively add a gram of sand at a time until it sinks. The volume of the can would be around the sink/float crossover point, where the can is neutrally buoyant. At that point the grams and the cubic centimeters (or, milliliters) would be equal.

Maggie and Chuck both wondered how much of a difference salt water would make (both knowing that salt water is more dense). The answer is “a good bit of difference.” Surface ocean water is generally considered to be 1027 kg/m3 — around 3% salt and 1.03 g/cm3 for our purposes.

Every one of the cans above is less dense than surface ocean water and would float.

Since I drink my beer from bottles, no beer was used in this experiment. At least, not in the measurements.

Posted by James at August 21, 2004 12:02 PM
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