Why does a trash bag float when filled with air?

Answer 1

The simple answer is that the density of air is less than the density of water. So a trashbag full of air will float on water.

The more complex answer is that floating vs sinking depends on the displacement of water.

Let's forget the trashbag, and think of a gallon milk jug.

A pint, a pound, the world around... a gallon of water weighs 8 pounds.

So, if you take a milk jug and fill it with air, it will weigh less than 8 pounds. Thus, it will displace less than 8 pounds of water and it will float.

Now, fill it completely full of water (try to eliminate all air bubbles). It might float a little bit due to the density of the plastic being less than water, but it will displace 8 lbs of water (a gallon of water), and then will essentially sink or submerge.

Now, empty the milk jug and add 4 lbs of lead shot. The jug will now displace 4 lbs of water (a half gallon) (the weight of the shot), and the rest of the jug will float.

Now try 10 lbs of lead shot. It still may have some air in the top. But, once it displaces the 8 lbs of water (1 gallon), it will have 2 more pounds of shot (which will now weigh 2 lbs in the water), and it will sink.