Acceleration of Hot Air Balloon

[armolinasf]

Homework Statement

A hot air balloon of mass M has two forces acting on it. An upward lift force and its weight due to gravity. The balloon is initially accelerating at a rate of -g/3.

A)Find the upward lift force in terms of the initial weight Mg.

B) What fraction of the total weight must be dropped so that he accelerates at a rate of g/2, assume that the upward lifting force remains the same as in part A.

The Attempt at a Solution

F1=Ma=upward lifting force, f2=-Mg=weight

A) I figured that F1/M + F2/M = -g/3

a-g=-g/3
a=2g/3

So then the upward lifting force would be F1=(2g/3)M

B) This time F1/M + F2/M = g/2, but this time F2=-Mgk, k=the fraction of weight that must be dropped

2g/3 - gk = g/2, g will cancel

-3k=-1/2 ==> k=1/6

However, the answer in my book gives 5/9. Where am I going wrong. Thanks!

 

[jaumzaum]

You have scored the 1,

But in the 2 )
the balloon is accelerating, that means a force is acting in him. It's accelerating by a acceleration of g/2, so the force is mg/2

the lift force is the same , so it s 2Mg/3, no mg/2, the first M is the initial mass

mg/2 = 2Mg/3 - m g -> m =4/9 M, so 5/9 of the mass was destroyed