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Homework Help: Helium balloon floating at air/helium boundary

  1. Dec 12, 2009 #1
    While reviewing the Archimedes Principle with my AP students using ConcepTest questions from the Wilson, Buffa, Lou text I came across an answer that I believe is incorrect. The question was the second question in a series of questions about a helium filled balloon.
    The first question asked what would happen to a helium filled balloon in a jar of helium. The answer was that the balloon would sink to the bottom of the jar. OK, no problem. Then the next question says, "Now the jar is lifted off the table, but the jar remains inverted to keep the helium gas in the jar. What will happen to the balloon?" (From the choices I am assuming the lid is off the jar.)
    These were the choices:
    A) it floats at the top of the jar
    B) it floats at the bottom of the jar, but still fully inside the jar
    C) it floats below the bottom of the jar, sticking halfway out the bottom
    D) it sinks down to the surface of the table

    All of my students deduced that the helium filled balloon would still sink to the "bottom" (now the open end of the jar.) They disagreed, however, about where it would rest. I was very surprised when the answer provided was choice B. This was the explanation, "The balloon sinks in the helium gas (fluid #1), until it hits the surface of the air (fluid #2). Since the balloon floats in air, it will float on the surface of the air and therefore remain inside the jar, but at the bottom. "
    This seems very wrong to me. It will only float on the surface of the air if there is a buoyant force. How can there be a buoyant force without some displacement of air? It doesn't seem philosophically different from an air-filled balloon floating on the surface of a liquid.
    Can someone help me out here?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 12, 2009 #2
    The reason this question is confusing is because the book doesn't give you enough information to correctly choose between B and C.

    First I have to distinguish between two parts of the balloon: the helium filling the balloon and the actual structural part of the balloon--I'll call this the "plastic" part of the balloon.

    The book leaves out a crucial bit of information: whether or not the plastic has mass. If the plastic had ZERO mass, the answer would be B. However, if, like a real balloon, there was a nonzero mass to the plastic part, the balloon would sink out of the jar until it displaces a volume of air with a mass equal to the mass of the plastic. (Of course this would not necessarily be exactly HALF way out of the jar, as C suggests.)

    (Also we must assume that the plastic doesn't pressurize the baloon's helium giving it a higher density than the ambient helium.)
     
    Last edited: Dec 12, 2009
  4. Dec 12, 2009 #3

    ideasrule

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    I agree with you: the balloon must displace some air, or else it will continue to sink. A real-life balloon would probably displace a significant amount of air before it stops sinking.
     
  5. Dec 12, 2009 #4

    ideasrule

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    Jolb: I hear what you're saying about the mass, but a massless balloon wouldn't sink to the bottom of the jar in the first place.
     
  6. Dec 13, 2009 #5
    Yes, you're right. A massless balloon would just float with neutral buoyancy through the helium.
     
  7. Dec 13, 2009 #6
    Thanks for your replies. The explanation for question one of this series did confirm that the helium-filled balloon would sink in helium. What was disappointing was that their explanation was simply that it had negative buoyancy. They didn't explain why. Like you all, my students and I assumed that it was because the balloon material itself had mass. That's why we were so confused on the second question. Again, thanks for your responses.
     
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