Is it possible for a balloon to rise up with an acceleration of 1 m/s²?

[Ockonal]

Homework Statement

A balloon which has weight 10.8 kN fall down with acceleration 1 m/s². What mass we have to pull of from balloon 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 balloon 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 balloon 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?

 

[mantxi]

The balloon's mass is given by the formula P=m*g, the speed at which it's moving doesn't change its mass.

So, 10800=m*10
then m=1080kg

Using that value in your calculation gives us:

F= -m(a-g) => F= -1080*(1-10) = 9720N