Feldoh said:My claim is that the shape of the string is such that the potential energy of the sting is minimized.
K^2 said:Catenary is formed under two forces - weight and tension. Here, you made the weight negative, by attaching balloons.
Now, if you want to know why catenary is the curve made by free-hanging rope, you need to look at the differential equations for it. But it should be clear why balloons force the same shape, only upside down.
The helium-filled string floats due to the buoyancy force, which is caused by the difference in density between helium and air. Helium is less dense than air, so it rises and creates an upward force on the string, allowing it to float.
The helium-filled string stays in a straight line due to the evenly spaced helium pockets along its length. Each pocket of helium provides an equal upward force, resulting in a balanced tension along the string that keeps it straight.
The helium-filled pockets on the string are typically spaced very tightly, usually only a few centimeters apart. This close spacing ensures that the buoyancy force is evenly distributed along the entire length of the string.
The amount of weight that the helium-filled string can support depends on the length and thickness of the string, as well as the amount of helium and the strength of the material. In general, longer and thicker strings with more helium will be able to support more weight.
The behavior of the helium-filled string may vary in different environments, as factors such as temperature, air pressure, and wind can affect the buoyancy force and the overall stability of the string. It is important to carefully consider these factors when using the string in different settings.