Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 10 - Fluids - Problems - Page 287: 33

Answer

The child needs to use a minimum of 32 bottles in order to stay dry.

Work Step by Step

To stay dry, the buoyant force must be equal to the child's weight. We can find the volume $V$ of water that must be displaced. $F_B = M~g$ $\rho~V~g = M~g$ $V = \frac{M}{\rho}$ $V = \frac{32~kg}{1.00\times 10^3~kg/m^3}$ $V = 0.032~m^3$ We can express this volume in units of liters; $V = (0.032~m^3)(10^3~L/m^3) = 32~L$ The bottles must displace a volume of 32 liters of water. Therefore, the child needs to use a minimum of 32 bottles in order to stay dry.
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