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## Homework Statement

A ballon which has weight 10.8 kN fall down with acceleration 1 m/s². What mass we have to pull of from ballon to make it(ballon) rise up with same acceleration.

## Homework Equations

P = m×g

P = m(g ± a)

F =m×a

P = 10.8 kN = 10.8×10³ N

a = 1 m/s²

g = 10 m/s²

m₀ - ? (but answer is in Newtons, so we have to find weight `P`)

## The Attempt at a Solution

The first we have to find ballon mass using weight:

P = m(g-a)

m = P / (g-a) => m = 1200 kg;

Write first Newtons law (Y axis show down):

Y: ma = mg - F

We have to find that `F`

F = -m(a-g) => F = -1200*(1-10) = 10800 N.

Fail! F = P, and it's impossible. In this case ballon should be static without any movement.

Anyway, my next idea is:

-ma = (m - m₀)×g - F

-ma *— because acceleration should change the direction to opposite (up)

We can't edit `F` but we can change mass.

With calculations I got:

m₀ = (F-ma) / g + m

BSOD

What's wrong?