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: 25

Answer

A force of 1110 N would be needed to push the ball completely under the water.

Work Step by Step

We can find the volume of the beach ball as: $V = \frac{4}{3}\pi~r^3$ $V = \frac{4}{3}\pi~(0.30~m)^3$ $V = 0.113~m^3$ Since the beach ball is very light, we can ignore the weight of the beach ball. The force $F$ we need to apply will be equal to the buoyant force $F_B$ on the ball. The buoyant force is equal to the weight of the water that is displaced by the ball's volume. $F = F_B$ $F = \rho~V~g$ $F = (1000~kg/m^3)(0.113~m^3)(9.80~m/s^2)$ $F = 1110~N$ A force of 1110 N would be needed to push the ball completely under the water.
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