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A balloon weighing 'W' newton descends with an acceleration of 'a'. If weight 'w' is removed from the balloon, the balloon has upward acceleration of 'a'. Show w=2aW/(a+g) g is acceleration due to gravity.

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any luck y2o2?
Well, i'm trying..but i really like it :D
Don't worry , it'll be solved

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Other answers:

ok! waiting!
are you sure there is nothing about the mass ?!
yeah sure, mass isnt mentioned anywhere.
how about we eliminate mass after forming 2 equations?
nah, that gives W=2gw/a+g
The balloon has two forces acting on it. Gravity and the upward force form the gas in the balloon. Call the second \( F_b \). The first, \( F_g = -mg \) where \( m \) is the mass of the balloon. We're using the convention that upwards is positive and downward is negative. Hence \( F_b > 0 \) and \( F_g < 0 \). The net force acting on the balloon is \[ F_{net} = F_g(m_{initial}) + F_b \] We're told that that initially the balloon is descending. Hence \[ F_{net} = ma_{initial} \] where \( a_{initial} < 0 \).
The weight \( W \) is the gravitational force, hence \( W = mg \). We're told that a weight of \( w \) is removed from the balloon. Hence the new weight of the balloon is \[ -F_g = W' = W - w = mg - w \] Hence the net force acting on the balloon now is \[ F_{net}' = F_g' + F_b = -(mg - w) + F_b = w + (-mg + F_b) = w + F_net \ \ \ ---(1)\] and we're told that now the balloon is now accelerating upward with the same magnitude of acceleration. Write \( -a = a_{initial} \). Therefore \( a \) is a positive quantity. Then we have \[ F_{net} = -ma \ \ \ ---(2) \] and \[ F_{net}' = ma \ \ \ --- (3) \] Now use the three equations--(1), (2) and (3)--to show the result you're looking for.
Equation one got chopped off. It is \[ F_{net}' = w + F_{net} \ \ \ -- (1) \]
Actually, you'll need the more general form of equation (1) \[ F_{net}' = w - mg + F_b \] Anyway. Play around with those for a bit.
I solved it.............Finally
While going down, \[W - F_{air} = \frac{W}{g}a\] After removal of mass w. \[F_{air}-(W-w) = \frac{W-w}{g}a\] Solve these now, eliminate \(F_{air}\).
After removal of weight* w.
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Got it! Thanks y202, JamesJ, Ishan94 for you time and help. Much appreciated!!!
This was asked in the exam i am giving tomorrow, i hope they ask a similar one tomorrow :P

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