Thursday, 3 November 2016
Finishing the birthday balloon calculations
I modeled the balloon as a flattened cylinder. I calculated the volume as 0.0113 cubic metres. Air has a density of about 1.2 kg per cubic metre so mass of air displaced = 0.0135kg of air displaced so upthrust = 0.135N. Density of helium is 0.164 kg per cubic metre so there is 0.002kg of helium in the balloon. But the foil weighs something too. I calculated the surface area of the balloon as 0.301 square metres. I looked for possible thicknesses of foil on the Internet and came up with 0.03mm. Density of aluminium is 2700 kg per cubic metre giving the mass of the foil as 0.024kg. Weight of the balloon = 0.26N ie more than the upthrust so the balloon shouldn't float. The thickness must be wrong. On yesterday's post, I think the derivation of the equation was correct, so I stuck with the measured time period of 7 seconds and worked backwards to a thickness. It came out as foil of thickness 0.014mm. That doesn't sound impossible.