Question

Strato-lab was a 1950s project in which large balloons were used to carry astronauts in training to the Earth's stratosphere. In one flight, a balloon 38.5 m in diameter was used to lift a total payload of 580 kg. Assume the volume of the balloon was filled with helium gas of density 0.179 kg/m³. The air density was 1.20 kg/m³.

(a) What was the buoyant force acting on the Strato-lab balloon? (Enter the magnitude.)

(b) What was the net force on the Strato-lab? (Enter the magnitude.)

(c) How much more mass could the Strato-lab have carried had it ascended at a constant velocity?

Answer 1

a) Buoyant force= Fb= ρgV

where ρ= density of the surrounding air = 1.20 kg/m3, V= volume of the balloon

V=4/3 pi r³

Hence, Fb= 3,51,210 N

b) Net force,

Fnet= -(ρair- ρgas)gV-mg

Fnet     = 2,93,137 N

c) If the balloon has to maintain the constant ascent rate then, the Fb > Fg

here Fg= -mg-ρgas gV

Fg        = -58072 N

These factors are brought together in a formula of equilibrium,
LIFT = DRAG + WEIGHT

LIFT is calculated using Volume [m³] (equal volumes of lifting gas and displaced air), Density [kg/m³] of Air minus Density [kg/m³] of liftring gas, and the Acceleration of Gravity [9.8m s^-2]:

LIFT = (4pi/3)Radius³(Density_air-Density_helium)9.8m s^-2   (assumes balloon is spherical)

DRAG is calculated using Drag Coefficient, projected Area [m²]of balloon, Density of Air, and Ascent Rate

DRAG = C_d(pi)Radius²(Density_air)Ascent Rate²/2