Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 15 - Fluids and Elasticity - Exercises and Problems: 12

Answer

The 2.0-cm-diameter piston must be pushed down 3.2 meters.

Work Step by Step

Since the liquid is incompressible, the magnitude of the volume change $V_S$ in the small cylinder must be equal to the volume change $V_L$ in the large cylinder. Therefore; $V_S = V_L$ $\pi~R_1^2~h_1 = \pi~R_2^2~h_2$ $h_1 = \frac{R_2^2~h_2}{R_1^2}$ $h_1 = \frac{(0.040~m)^2~(0.20~m)}{(0.010~m)^2}$ $h_1 = 3.2~m$ The 2.0-cm-diameter piston must be pushed down 3.2 meters.
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