# The balloon with mass m is desending with an acceleration a where a

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by 19devender89
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is the acceleration itself no

2014-10-04T18:45:36+05:30

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If balloon is descending in vacuum, a = g.          Otherwise,

Let V be the volume of balloon.  Let ρ be the density of balloon. ρ = m/V

Let d be the density of air in the atmosphere at the location where balloon is descending.

There is a force of buoyancy upwards on balloon exerted by air in the atmosphere.

Net Force on balloon downwards = m g - d V g = (m - d V) g

Acceleration downwards of the balloon = (m - d V) g / m  = [1 - d V/m] g
a  = [ 1 - d/ρ ] g

If we want to be more precise, there is also a drag (damping) or contact force of air resistance on the balloon = b v, where v is the instant velocity of balloon.

a = g - (d/ρ) g - b v,           where v =

This is a second order differential equation. It is to be solved to get an exponentially decreasing function of time.