Conceptual Physics (12th Edition)

Published by Addison-Wesley
ISBN 10: 0321909100
ISBN 13: 978-0-32190-910-7

Chapter 14 - Think and Solve: 41


He wants the balloon to lift 20 kg, or to have a buoyant force of (20 kg)(g) = 200 N. The buoyant force is the weight of the displaced air, so 200 N = (balloon volume)(weight density of air). On page 271, the latter number is given as $12 \frac{N}{m^{3}}$. Solve for the volume of the balloon, $\frac{200 N}{12 N/m^{3}} = 17 m^{3}$. Note: for this calculation to work out with the numbers provided in the question, the mass of the helium should be neglected. Helium has a mass density of 0.1786 $\frac{kg}{m^3}$, and if the helium is taken into account, a balloon volume of about $20 m^{3}$ would be required.

Work Step by Step

This is discussed on page 271.
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