I like to reminisce about warm weather as I run/walk/sprint to the library on these cold, December days. This afternoon, I was thinking about how I’d really like to be on my inflatable doughnut floatie in a pool on some lovely Caribbean island instead of crying tears from frigid wind and avoiding black ice on my mission to print my essay in the ten minutes left before class. Thinking about the physics behind such luxury really keeps me going on days like these…
People, floaties, and people in floaties float on top of water because of differences in density. When I enter the water with my floatie, the volume of pool water I displace is not equal to the volume of me + floatie. If it was, my floatie and I would be completely submerged underwater. According to the sum of the forces, the buoyant force and the force of my body + floatie should cancel out to 0N; therefore, the two forces are equal:
ΣF=FB – mg=0N
ρwaterVwaterg - ρobjectVobjectg=0N
Ultimately, we can create a proportion between the densities and volumes of the water and myself + floatie:
We can use this proportion to calculate the percent of person and floatie that is underwater and above water. The percentage of person and floatie that is underwater is equal to the amount of water that was displaced when the objects entered the water.
In general, objects float because they have a have a higher buoyancy and are less dense than water. If the object weighs less than the water, then the object will float; in the same line of thought, objects heavier than water will sink. Buoyancy is also affected by air content; as in the case of me and my floatie, we float because my lungs hold air and the floatie is filled with air.