Question

Balloon of volume 800 centimetre cube is filled with hydrogen gas of density 9 x 10 raise to power minus 5 gram per centimetre cube. If the empty balloon weighs 0. 3 gf and density of air is 1. 3 x 10 raise to power minus 3 gram per centimetre cube, calculate the lifting power of balloon

Answer 1

Volume of balloon = V = 800 cm³

Density of hydrogen gas = p_H = 9 x 10^-5 g cm^-3

Weight of empty balloon = 0.3 gf

Density of air = ρ_a = 1.3 x 10^-3 g cm^-3

Weight of hydrogen gas in balloon = Vρ_Hg

= 800 x 9 x 10^-5 x g

= 72 x 10^-3 gf

= 0.072 gf

Volume of balloon = Volume of hydrogen gas in the balloon = volume of air displaced by balloon.

Down thrust = Wt. of empty balloon + wt. of hydrogen gas in balloon

= 0.3 + 0.072 = 0.372 gf

Upthrust = Wt. of air displaced by balloon

= Vρ_ag

= 800 x 1.3 x 10^-3 x g

= 8 x 1.3 x 10^-1 x g

= 10.4 x 10^-1 x g = 1.04 gf

Lifting power of balloon = Upthrust - Down thrust

= 1.04 - 0.372 = 0.668 gf