In this problem, your task is to analyze a lead balloon. The balloon in question

Question

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

Explanation / Answer

Part A)

The weight of the balloon including helium, lead, basket and rigging.

The volume of a sphere is 4/3r3

The weight of the helium is found by Fw = Vg

Fw = (4/3)()(10)3(.179)(9.8) = 7348 N

The volume of the lead is 4/3(10.00025)3 - 4/3(10)3 = .3142 m3

Fw = Vg = (.3142)(11300)(9.8) = 34791 N

The weight of the basket and rigging = 295 X 9.8 = 2891 N

The total weight = (7348) + (34791) + (2891) = 45030 N

Part B)

V = 4/3r3 = (4/3)()(10)3 = 4189 m3

Part C)

FB = Vg = (4189)(1.28)(9.8) = 52547 N

Part D)

Max payload = 52547 - 40530 = 12017 N

Yes, it can lift a payload of 7.5 X 103 N

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