Question

1.) A balloon with 20 ft diameter is filled with Helium at STP (assume spheryical shape volume is negliable) how massive can payload/lifitng capacity of balloon be? 2.) Same size balloon is filled with hot air this time. What must the internal temp be to lift the same mass as in part one? 3.) Increase the size of the balloon from part 2. What must the radius of the balloon be to lift the mass from parts 1 and 2, with internal temperature of 373.15 k?

that is all information, need help!

Answer 1

1 )

given

d = 20 ft

r = d/2

= 10 ft = 3.048 m

volume is V = 4 r³ / 3

= 4 x 3.14 x 3.048³ / 3

V = 118.553 m³

mass = volume x density

m = V x _He

_He = 0.164 kg/m³

m = 118.553 x 0.164

m = 19.442 kg

the buoyant force

F_b = m g + M g

V _air g = ( m + M ) g

V _air = ( m + M )

118.553 x 1.275 = 19.442 + M

M = (118.553 x 1.275) - 19.442

M = 131.76 kg

so the load / lifting capacity of balloon of mass is M = 131.76 kg