Question

A balloon filled with helium gas has an average density of rhob = 0.27 kg/m3. The density of the air is about rhoa = 1.23 kg/m3. The volume of the balloon is Vb = 0.084 m3. The balloon is floating upward with acceleration a.

Answer 1

Answer:$34.84 m/s^2$

   

Explanation:

Given

density of balloon $\rho _{He}=0.27 kg/m^3$

density of air $\rho _a=1.23 kg/m^3$

volume of balloon $V=0.084 m^3$

If balloon is rising then

$F_b-mg=ma$

where $F_b=buoyant\ Force=\rho _a\times V\times g$

$mg=\rho _{He}\times V\times g=weight of gas$

$a=acceleration$

$\rho _a\times V\times g-\rho _{He}\times V\times g=\rho _{He}\times V\times a$

$\rho _a\times g-\rho _{He}\times g=\rho _{He}\times a$

divide by $\rho _{He}$

$\frac{\rho _a}{\rho _{He}}\times g-g=a$

$a=g(\frac{\rho _a}{\rho _{He}}-1)$

$a=g(\frac{1.23}{0.27}-1)$

$a=3.55\times 9.8$

$a=34.84 m/s^2$