Solve the following problem and its parts. A spherical weather balloon is filled

Question

Solve the following problem and its parts. A spherical weather balloon is filled with hydrogen until its diameter is 10.00 m. Its total mass including the instruments it carries and the hydrogen is 25.0 kg. (The volume a sphere is given by V = 4pir^2/3 where r is the radius) (a) Find the buoyant force acting on the balloon, assuming the density of air is 1.29 kg/m^3. (b) What is the net force acting on the balloon and its instruments after the balloon is released from the ground? (c) As the balloon rises, its radius will increase, decrease or stay the same? Explain your answer.

Explanation / Answer

Radius = 5 m

Volume(V)=(4/3)*3.14*5*5*5=523.333 m3

density of air=1.225 kg/m3

Buoyant force=V*(density of air)*g=523.333*1.225*9.8

a)Buoyant force=6282.61 N

Net force acting are buoyant force upward and mg downward mg= 25*9.8= 245N   

b) Net force=6282.61-245=6037.61 N upward

c)As the balloon rises to lower pressure environment, the volume of the balloon will EXPAND so that pV stays constant as it must for an isothermal atmosphere.

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