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 - General Problems - Page 289: 86

Answer

72 people.

Work Step by Step

The volume of water that is displaced when people start getting their feet wet is the full volume of the raft $V_{raft}=12V_{log}=12\pi r_{log}^2L_{log}$. The buoyant force equals the weight of the water displaced by the full volume of the logs. $$F_b=V_{raft}\rho_{water}g$$ This equals the weight of the raft plus N passengers. $$W_{total}= V_{raft}\rho_{wood}g+Nm_{person}= V_{raft}0.60\rho_{water}g+Nm_{person}$$ $$N=\frac{V_{raft}g \rho_{water}(1-0.60)}{m_{person}}=72.97$$ When 73 people are on the raft, their feet will be wet. 72 people can manage to keep their feet dry.
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