Question

a) A Balloon operates at an altitude where the air density is 0.9 kg/m3. At that altitude, the balloon has a volume of 20m3; the balloon is filled with helium (helium has a density of: pHe: 0.178 kg/m3). if the weight of the balloon bag is 94N, what load can the globe withstand at this altitude?

b) A balloon filled with helium has 21m radius and the mass of the entire globe is 50kg. What extra mass can the balloon load?

Answer 1

a)

$$F_B=W=m_bg+m_{load}g,$$ $$(\rho_{air}-\rho_{He})V_bg=m_bg+m_{load}g,$$ $$m_{load}=(\rho_{air}-\rho_{He})V_b-\dfrac{W_b}{g},$$ $$m_{load}=(0.9\ \dfrac{kg}{m^3}-0.178\ \dfrac{kg}{m^3})\cdot20\ m^3-\dfrac{94\ N}{9.8\ \dfrac{m}{s^2}}=4.85\ kg.$$

b) Let's first find the buoyant force:

$$F_B=(\rho_{air}-\rho_{He})V_bg=\dfrac{4}{3}\pi r^3(\rho_{air}-\rho_{He})g.$$

Finally, we can find the extra mass:

$$m_{load}=\dfrac{4}{3}\pi r^3(\rho_{air}-\rho_{He})-m_b,$$ $$m_{load}=\dfrac{4}{3}\pi\cdot(21\ m)^3(1.225\ \dfrac{kg}{m^3}-0.179\ \dfrac{kg}{m^3})-50\ kg=40527\ kg.$$