Stretching Requires ForceTake an ordinary piece of burst balloon and pull on it with your fingers. It takes a definite force to accomplish that, doesn’t it? And the task becomes more difficult the more you stretch it. We call the exertion “force.” It takes force to stretch the rubber.
Since the required force becomes greater the more you stretch the skin of balloons, it is clear the more air you blow into them, the greater the force the skin of balloons exerts against it. The greater the volume of air you attempt to put into the balloons, the more difficult the task becomes.
QuantificationThe skin becomes thinner, but more importantly, its surface area increases. Imagine, for instance, two people stretch a single square of rubber skin. One stretches it from 3 inches long to 4 inches long. The other stretches it from 3 inches wide to 4 inches wide. The area of the skin changes from 3 x 3 = 9 square inches to 4 x 4 = 16 square inches.
The volume of air within a balloon pushing out on the balloon skin provides the force required. Now the air arranges itself within the flexible balloon, to allow the most air inside without generating an increase in force.
Balloons and the ElevatorLet’s illustrate this. Imagine you wish to enter a nearly full elevator. There is precious little room left. You stand as tall as possible and keep your arms close to your side to minimize the force between your body and those of the others, as you ease in.
Surface Area and VolumeNow for molecules of air, the shape of vessel that holds the most while having the least volume is the sphere. This is because the sphere has the least surface area for the volume contained within. Mathematically, the surface area of a sphere is 4πr² where r is the radius of the sphere (one-half the diameter) and π (or pi) is approximately 3.1415926.
The volume of a sphere is 4/3 πr³. The ratio of the volume held in the balloon the surface area of the balloon, is the smallest of any object. Hence, the balloon blows up round. Mathematically, S, the surface area, divided by V, the volume, is:
S / V = (4πr²) / (4/3 πr³) = 3 / r
S over V ratio = 3 / r
S / V = 6x² / x³ = 6 / x
S over V ratio = 6 / x
Compare: Most Efficient Shape for Holding Liquids
References: ← Back to Classic Science