A spherical balloon is filled with helium. The balloon has a radius of 1.52 m, a

Question

A spherical balloon is filled with helium. The balloon has a radius of 1.52 m, and floats at rest in air. A load is suspended from the balloon. The volume of the load can be neglected, and the weight of the balloon material is also negligible. a Find the volume of the balloon, in m^3. V = ____ b) Find the mass of the load, assuming the system is at rest. m = ___ c) Find the upward acceleration of the balloon if it is filled with hydrogen rather than helium, with the mass of the load remaining unchanged. a = ___

Explanation / Answer

a) Volume of balloon = (4/3)*pi*r3 = (4/3)*pi*1.523 = 14.71 m3

b)Mass density of helium = 0.1786 kg/m3

Weight of helium = 0.1786*14.71*9.8 = 25.747 N

Mass density of air = 1.225 kg/m3

Upward buant force experienced by balloon = 1.225*14.71*9.8 = 176.594 N

Let mass of the load be m

9.8m + 25.747 = 176.594

m = 15.39 kg

c)Mass density of hydrogen = 0.08988 kg/m3

Weight of hydrogen = 0.08988*14.71*9.8 = 12.957 N

Weight of load = 15.39*9.8 = 150.822 N

Total downward force = 12.957+150.822 = 163.779 N

Upward buoyant force = 176.594 N

Net upward force = 176.594-163.779 = 12.815 N

Mass of system =( 0.08988*14.71)+15.39 = 16.712 kg

Therefore, upward acceleration = 12.815/16.712 = 0.767 m/s2

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