Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 14 - Fluids and Elasticity - Exercises and Problems: 52

Answer

The mass of the heaviest rock that will not sink the boat is 0.11 kg

Work Step by Step

We can find the volume of water that would be displaced by the hemisphere. $V = \frac{2}{3}\pi~r^3$ $V = \frac{2}{3}\pi~(0.040~m)^3$ $V = 1.34\times 10^{-4}~m^3$ The maximum possible buoyant force on the hemisphere is equal to the weight of water displaced by the entire volume of the hemisphere. To find the mass of the heaviest rock, we can assume that the total weight of the boat and the rock is equal to the maximum possible buoyant force. $M_{boat}~g+M_{rock}~g = \rho~V~g$ $M_{rock} = \rho~V-M_{boat}$ $M_{rock} = (1000~kg/m^3)(1.34\times 10^{-4}~m^3)-(0.021~kg)$ $M_{rock} = 0.11~kg$ The mass of the heaviest rock that will not sink the boat is 0.11 kg.
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