A helium balloon is to lift a payload to an altitude of (40 mathrm{~km}), where the atmospheric

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A helium balloon is to lift a payload to an altitude of \(40 \mathrm{~km}\), where the atmospheric pressure and temperature are \(3.0 \mathrm{mbar}\) and \(-25^{\circ} \mathrm{C}\), respectively. The balloon skin is polyester with specific gravity of 1.28 and thickness of \(0.015 \mathrm{~mm}\). To maintain a spherical shape, the balloon is pressurized to a gage pressure of \(0.45 \mathrm{mbar}\). Determine the maximum balloon diameter if the allowable tensile stress in the skin is limited to \(62 \mathrm{MN} / \mathrm{m}^{2}\). What payload can be carried?

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