## Related questions with answers

Balloons are often filled with helium gas because it weighs only about one-seventh of what air weighs under identical conditions. The buoyancy force, which can be expressed as $F_b=\rho_{\text {airg }} V_{\text {balloon }}$, will push the balloon upward. If the balloon has a diameter of $12 \mathrm{~m}$ and carries two people, $70 \mathrm{~kg}$ each, find the acceleration of the balloon when it is first released. Assume the density of air is $\rho=1.16 \mathrm{~kg} / \mathrm{m}^3$, and neglect the weight of the ropes and the cage.

Solution

VerifiedFirst we need to find the volume of a balloon that in shape of a ball.

$\begin{align*} &V = \frac{4 \cdot \pi \cdot r^3}{3}\\ &V = \frac{4 \cdot \pi \cdot 6^3}{3}\\ &V = 904.32 \text{ m}^3\\ \end{align*}$

The mass of the balloon is defined by the density of helium $\rho_h$ and the volume of the balloon (helium is 1/7 lighter than air).

$\begin{align*} &\rho_h = \frac{m_h}{V}\\ &m_h = \rho_h \cdot V\\ &m_h = \frac{1}{7} \cdot 1.16 \cdot 904.32\\ &m_h = 149.85 \text{ kg}\\ \end{align*}$

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