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Acceleration of Hot Air Balloon

  1. Jul 4, 2011 #1
    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!
     
  2. jcsd
  3. Jul 4, 2011 #2
    You have scored the 1,

    But in the 2 )
    the baloon 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
     
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