Chapter 11, Problem 087 Multiple-Concept Example 11 reviews the concepts that ar

Question

Chapter 11, Problem 087 Multiple-Concept Example 11 reviews the concepts that are important in this problem. What is the radius of a hydrogen-filled balloon that would carry a load of 7910 N (in addition to the weight of the hydrogen) when the density of air is 1.29 kg/m3, and the density of hydrogen is 0.0899 kg/m3? Number Units The number of significant digits is set to 3; the tolerance is +/-3% By accessing this Question Assistance, you will learn white you earn points based on the Point Potential Policy set by your instructor. Points available only if you or less.

Explanation / Answer

The weight of the load Fg = 7910 N

The density of air ?air = 1.29 kg/m3

The density of hydrogen ?H = 0.0899 kg/m3

From Bernoulli's theorem

    V?air g = mg + Fg

    V?airg = V?Hg + Fg

   V(?air- ?H) g = Fg

Then the volume of the balloon is

     V = Fg / (?air - ?H) g

        = (7910 N) / [(1.29 kg/m3 - 0.0899 kg/m3)(9.8 m/s2)]

       = 672.62m3

_________________________________________________________

The volume of the ballon is

         V = (4/3)?r3

Therefore the radius of the balloon is
              r = [3V/4?]1/3

                 = [(3)(672.62m3)/(4?)]1/3

                 = 4.435 m

                 = 4.43 m

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