(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A hot air ballon 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.

3. 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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Acceleration of Hot Air Balloon

**Physics Forums | Science Articles, Homework Help, Discussion**