I
was thinking about those Lifesavers that lifeguards use to save people and how
they always float; they can really support the weight of an adult. So to begin
to think about how this is even possible let's look the phsyics of an object
floating. The following equation:

V

_{f}/V_{o}= ⍴_{o}/⍴_{f}
shows
that the fraction of an object (lifesaver) submerged is the ratio of the
object's density to its surrounding fluid (water). Now, taking into account that
we don't want our life preservers to dip too low, I looked up what's in
these lifesavers and found that they actually contain a synthetic resin called
polyurethane which is like a light foam. The density of this light foam is
about 62kg/m

^{3}which of the way less than the 1000kg/m^{3}of water. Actually, the ratio between these two densities is .062 which means that only 6.2% of the volume of this device is submerged in water when the ring is floating all by itself in the water. If we take into account the weight of a person we that would add on to the weight by 62 kilograms (that is if we assume this person has an average weight). Life preservers usually weigh about 15.5 lbs or 7 kg, so the gravitational force on a life preserver would be about 68.6 Newton's would be Wednesday. The buoyancy force would be: the density of water X the fraction of the volume of the life preserver that is submerged underwater (6.2%) X the gravitational constant. We will also assume a typical lifesaver has a volume of about 0.125 m^{3}. The buoyancy force as it floats would be 75 N. As we can see, it is less than the 676 N force of gravity. However, if the full volume of the life preserver would be submerged in the water then the buoyancy force would increase to around 1225 N. This dramatic increase is due to the full volume of the floatation device displacing the much denser water which would push the life preserver and the person on it upwards keeping them from drowning. So in the end, we have polyurethane to thank for giving the life preservers the strength to preserve our lives. Thank you polyurethane.
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