Question

A balloon is descending with a constant acceleration $a$, less than the acceleration due to gravity $g$. The weight of the balloon, with its basket and contents, is $w$. What weight $w$, should be released so that the balloon will begin to accelerate upward with constant acceleration $a$? Neglect air resistance.

Answer 1

Balloon descends with acceleration $a$.

$\frac{w}{g}\cdot a=w\cdot F$

Balloon ascends with acceleration $a$.

$\frac{w^{{}^{\prime }}}{g}a=F-w^{{}^{\prime }}$

$\Rightarrow \frac{a}{g}(w+w^{{}^{\prime }})=w-w^{{}^{\prime }}$.

$\Rightarrow aw+a{w}^{{}^{\prime }}=gw-g{w}^{{}^{\prime }}$.

$\Rightarrow w^{{}^{\prime }}(a+g)=w(g-a)$.

$w^{{}^{\prime }}=w\frac{(g-a)}{(g+a)}$.