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: 39

Answer

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Work Step by Step

The free body diagram shows that there is a downward gravitational force and an upward buoyant force on the fully submerged scuba tank. Find the net force when the tank is full. $$F_{begin}=F_{buoyant} -mg = \rho_{seawater}V_{tank}g-(m_{tank}+m_{air})g$$ $$ = ((1025\;kg/m^3)(0.0157\;m^3)-(17.0\;kg))(9.8\;m/s^2)=-8.89\;N$$ We see that the net force is downward. Find the net force when the tank is empty. $$F_{end}=F_{buoyant} -mg = \rho_{seawater}V_{tank}g-(m_{tank}+m_{air})g$$ $$ = ((1025\;kg/m^3)(0.0157\;m^3)-(14.0\;kg))(9.8\;m/s^2)=20.5\;N$$ We see that the net force is now upward.
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