A spherical balloon has a radius of 6.94 m and is filledwith helium. How large a

Question

A spherical balloon has a radius of 6.94 m and is filledwith helium. How large a cargo can it lift, assuming thatthe skin and structure of the balloon have a mass of 990 kg?Neglect the buoyant force on the cargo volume itself. A spherical balloon has a radius of 6.94 m and is filledwith helium. How large a cargo can it lift, assuming thatthe skin and structure of the balloon have a mass of 990 kg?Neglect the buoyant force on the cargo volume itself. How large a cargo can it lift, assuming thatthe skin and structure of the balloon have a mass of 990 kg?Neglect the buoyant force on the cargo volume itself.

Explanation / Answer

The volume of the balloon is that of a sphere V = (4/3) r3 = (4/3) 6.943 = 1400.13m3 Now the buoyancy force from the air on the balloon is equal tothe weight of the air displaced which is    B = weight of air displaced = density of air * volume * g This upward force must equal the downward force of gravity onthe balloon, so    B = weight of cargo + weight ofballoon + weight of helium B = M g +   mg    + density of helium * V * g or density of air * V * g   = M g + m g + densityof helium * V * g eliminate g everywhere    density of air * V   = M   + m   + density of helium *V plug in numbers and solve for M, the cargo mass. Get thedensity figures from your book...      1.29 * 1400.13 =  M   +   990   + 0.179 *1400.13

M = 565.54

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