Question

A helium balloon has a radius of 2m. The density of helium of helium is 0.17 kg/m3 and the density of air is 1.25 kg/m3. What is the maximum mass that the balloon can lift?

Answer 1

To solve this problem we will begin by finding the force on each of the elements. For this it will be necessary to obtain the mass, which can be related to density and volume. Finally, by balancing forces it will be possible to obtain the final value of the maximum mass that can be lifted.

By Newton's second law we have,

$F = mg$

Here,

g = Gravitational acceleration

m = mass

At the same time mass can be described as,

$m_1 = \rho \times V$

$m_1 = (1.25)\times \frac{4}{3} (2)^2$

Therefore the Force 1 is,

$F = m_1 g$

$F = \frac{40\pi }{3} (9.8)$

$F = 410.501N$

Applying the same concepto but for the second mass we have,

$m_2 = \rho \times V$

$m_2 = (0.17) \times \frac{3}{4} \pi 2^2$

$m_2 = 5.697kg$

Now by equilibrium we have,

$W + mg = F$

$m = \frac{F+W}{g}$

$m = \frac{410.501-55.828}{9.8}$

$m = 36.19kg$

Therefore the maximum mass lift by balloon is $36.19kg$