Your team is in charge of launching a large helium weather balloon that is spher

Question

Your team is in charge of launching a large helium weather balloon that is spherical in shape, and whose radius is 2.4 m and total mass is 16.9 kg (balloon plus helium plus equipment).

(a) What is the initial upward acceleration of the balloon when it is released from sea level?
m/s2

(b) If the drag force on the balloon is given by the equation below, where r is the balloon radius, is the density of air, and v is the balloon's ascension speed, calculate the terminal velocity of the ascending balloon.

m/s

Explanation / Answer

a)

We need to use Newton’s 2nd law of motion,

Fnet = ma

Fb – Fg = ma

Vballoonairg - mg = ma

4/3**r3*airg - mg = ma

a=(4/3**r3*airg - mg)/m

a=(4/3*3.14*2.4^4*1.225*9.8 – 16.9*9.8)/16.9

a= 88.87 m/s^2 ----------(2)

b)

Plugging (2) in (1),

Fb=ma- mg = m(a-g) = 16.9*(88.87-9.8) = 1336.3 N

Fd = ½*r2v2

at terminal velocity Fnet = ma = 0

Hence Fb – mg - Fd= 0

Fd = Fb – mg

v=sqrt [(Fb – mg)/(½*r2)]

v=sqrt[(1336.3-16.9*9.8)/(1/2*3.14*2.4^2*1.225)]

v=10.28 m/s

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