Answer to Question #220725 in Molecular Physics | Thermodynamics for Muhammad

Question

Suppose an empty balloon weighs 50 g and that it has a diameter of 1.5 m when it is helium filled. The density of air is 1.3 kg/m3, and the density of helium is 0.18 kg/m3. Calculate the maximum lifting force that the balloons can exert. 

Answer 1

Buoyant force can be defined as

$BF = V \times ∆d \times g$

V = the volume of balloon

$V = \frac{4}{3}πr^3$

∆d = the difference in densities

g = acceleration due to gravity

$BF = \frac{4}{3}π(\frac{1.5}{2})^3 \times (1.30-0.18) \times 9.8 \\ BF = 19.39 \;N$

Force in downward direction due to weight of balloon

$W = 0.050 \times 9.8 = 0.49 \;N$

Net lifting force is thus given by

$F_{net} = 19.39-0.49 = 18.90 \;N$