Physics Technology Update (4th Edition)

Published by Pearson
ISBN 10: 0-32190-308-0
ISBN 13: 978-0-32190-308-2

Chapter 15 - Fluids - Problems and Conceptual Exercises - Page 531: 23

Answer

$\mathrm{a}.$ greater $\mathrm{b}. 52 \mathrm{P}\mathrm{a}$

Work Step by Step

Pressure, P, is force F per area A: $\mathrm{P}=\mathrm{F}/\mathrm{A} \qquad $15-2 --- $\mathrm{a}.$ The water is accelerating upwards. An upward net force is acting on it. This net force is the result of the bottom of the glass pushing the water up with force greater than the water's weight. The water, in reaction (Newton's third law) pushes down on the glass with the same magnitude force. Observe 15-2. F has increased. Then, so has P. $\mathrm{b}.$ Given $\Delta \mathrm{v}$ and t, we find the acceleration. $\displaystyle \mathrm{a}=\frac{2.4\mathrm{m}/\mathrm{s}-0}{3.2\mathrm{s}}=0.75\mathrm{m}/\mathrm{s}^{2}$ The mass of the water is $\mathrm{m}=\rho \mathrm{V}=\rho(\mathrm{A}\mathrm{h})=(1000\mathrm{k}\mathrm{g}/\mathrm{m}^{3})\cdot(0.069\mathrm{m})\cdot \mathrm{A}$ $\displaystyle \Delta P=\frac{\mathrm{F}_{\mathrm{n}\mathrm{e}\mathrm{t}}}{\mathrm{A}}=\frac{\mathrm{m}\mathrm{a}}{\mathrm{A}}=\frac{(1000\mathrm{k}\mathrm{g}/\mathrm{m}^{3})\cdot(0.069\mathrm{m})\cdot \mathrm{A}\cdot(0.75\mathrm{m}/\mathrm{s}^{2})}{\mathrm{A}}$ $=(1000\mathrm{k}\mathrm{g}/\mathrm{m}^{3})(0.069\mathrm{m})(0.75\mathrm{m}/\mathrm{s}^{2})=52 \mathrm{P}\mathrm{a}$
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