Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson
ISBN 10: 0321993721
ISBN 13: 978-0-32199-372-4

Chapter 15 - Exercises and Problems - Page 280: 50


The proof is below.

Work Step by Step

We know that when the balloon is floating, it is necessary for the buoyancy force to at least equal to the force of gravity on the balloon (and the air in it). Thus, we find: $ \rho_a Vg = (m_g+M)g \\ \rho_a V = m_g + M$ We know that the volume is equal to $\frac{m_g}{\rho_g}$. This gives: $\rho_a \frac{m_g}{\rho_g}= m_g + M$ Simplifying gives: $m_g = \frac{\rho_g M}{\rho_a-\rho_g}$
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