Problem $(7)$ Cengel, $2011$

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 $F_b={}_{\text{a}\text{i}\text{r}}g{V}_{\text{b}\text{a}\text{l}\text{l}\text{o}\text{n}},$ will push the balloon upward. If

the balloon has a diameter of $12m$ and carries two people, $85kg$ each, $($a$)$

determine the acceleration of the balloon when it is first released. Assume the

density of air is ${}_{\text{a}\text{i}\text{r}}=1\mathrm{.}16k\frac{g}{m}3,$ and neglect the weight of the ropes and the

cage. $($b$)$ Determine the maximum amount of load, in $kg,$ the balloon can carry.