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Archimedes's Principle

  1. Jul 28, 2005 #1
    i don't see how this question give enough information to answer it..

    "A lighter than air balloon and its load of passengers and ballast are floating stationary above the Earth. Ballast is the weight that van be dropped over board to make the balloon rise. The radius of the balloon is 6.25m. Assuming the density of air to be 1.29kg/m^3, determine the weight that must be dropped overboard to make the balloon rise 105m in 15 secs."

    so far i've determined the balloon has to rise at a rate of 7m/s to reach 105m in 15seconds. I was then going to use the Buoyancy formula to figure out how much force is pushing up on the balloon, but i don't understand how to do that because i don't have the volume of the balloon..
     
  2. jcsd
  3. Jul 28, 2005 #2
    You know the radius of the balloon <=> you know the volume.
     
  4. Jul 28, 2005 #3
    you can find the volume of the balloon from the radius of the balloon.

    ...and isn't the balloon going to accelerate once you change its mass? the buoyant force is going to stay the same, as the density of air is going to be the same, and the volume of the balloon will be the same. but the weight of the whole rig has just decreased, so the buoyant force will be greater than the weight, causing a nonzero net force upward, which will cause an acceleration upward.
     
  5. Jul 28, 2005 #4
    i still don't understand how to caluculate how much weight i need to get rid of to make the balloon rise at a specific rate...
     
  6. Jul 28, 2005 #5

    Doc Al

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    Staff: Mentor

    What you need to find is the acceleration of the balloon, not the average speed. Then find the net force that would provide that acceleration.
     
  7. Jul 28, 2005 #6
    You know the distance to be traveled and the time it must travel that distance. you begin at v=0. So 105 m = .5 a (15 s)^2

    Find your acceleration and you can work from there to find the force needed to make the balloon rise at the rate you need it too.
     
  8. Jul 28, 2005 #7
    how am i suppose to relate acceleration to force?
     
  9. Jul 28, 2005 #8

    HallsofIvy

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    Staff Emeritus
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    If you do not know F= ma then you shouldn't be attempting this problem!
     
  10. Jul 28, 2005 #9
    harsh but...yeah, pretty true.

    i suspect that this is toward the end of a physics 1 course without calc...

    you should really know newton's second law by now.

    you did free body diagrams earlier, right? ...drawing those will help with this problem and... all sorts of others.

    you'll need two pictures: one when the balloon was in equilibrium (and take into account the individual forces acting on it) and another when the balloon starts having a net force acting on it (recall what i put in my earlier post).

    then using the definition of buoyant force and such, you should be able to get the answer.

    keep in mind that the mass of the balloon (and the stuff attached to it) changed, which caused it to acclerate upwards!
     
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