posted by Rob .
In this problem, your task is to analyze a lead balloon. The balloon in question is a hollow sphere of diameter of 20.0 m, constructed from a lead foil 0.25 mm thick and filled with helium gas. Below the balloon, a passenger basket is suspended. The mass of the passenger basket along with the balloon's riggings is 295 kg. For various parts of this problem, you will need to know the density of lead (11,300 kg/m3), and the densities of air and helium at standard atmospheric temperature and pressure (1.28 kg/m3 and 0.179 kg/m3). (a) What is the weight of the lead balloon, including helium, lead, basket and rigging? (b) What is the volume of the air displaced by the balloon? (Ignore any air displaced by the basket and rigging.) (c) What is the buoyant force on the balloon? (d) The maximum "payload" of the balloon, the weight of the passengers and equipment it can lift, equals the net upward force on an unloaded balloon. Can this balloon lift a payload of 7.5×103 N?
Volume of sphere =π•D³/6 = 4188.8 m³,
Surface of sphere = π•D² = 1256.6 m²,
Volume of lead foil = 1256.6•0.00025 = 0.314 m³
Mass of the lead foil = ρ•V= 11300•0.314 = 3548.2 kg.
(a) Weight = mg=[m(sph)+m(passenger)+m(He)] •g=
= [3548.2+295+749.8] •9.8=45011.4 N.
(b) 4188.8 m³,
(c) F= ρ•V•g=1.28•4188.8•9.8 = 52544.3 N.
(d) Δ= 52544.3-45011.4=7532.9 N
7532.9>7500 => This balloon can lift the payload.