Explanation Assume the spring obeys the Hooke’s law. Write the Hooke’s law. Δ F = k Δ x (I) Here, Δ F is the increase in force required to compress the spring by additional amount Δ x , k is the spring constant. Write the equation for Δ F . Δ F = F − F 0 (II) Here, F is the new force and F 0 is the initial force. Put equation (II) in equation (I). F − F 0 = k Δ x (III Write the equation for pressure. P = F A Here, P is the pressure and A is the area over which the force acts. Rewrite the above equation for F . F = P A Apply the above equation in equation (II). F − F 0 = ( P − P 0 ) A Here, P is the gauge pressure at the bottom of the liquid and P 0 is the pressure at the surface of the liquid. Put equation (II) in the above equation. k Δ x = ( P − P 0 ) A (IV) Write the equation for the gauge pressure at a depth. P = P 0 + ρ g h Here, ρ is the density of the fluid, g is the acceleration due to gravity and h is the depth from the surface of the fluid. Rearrange the above equation. P − P 0 = ρ g h Put the above equation in equation (IV) and rewrite it for h

Principles of Physics: A Calculus-Based Text, Hybrid (with Enhanced WebAssign Printed Access Card)

5th Edition

ISBN: 9781305586871

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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Variation of pressure

From the equation of pressure, pressure is directly proportional to the applied force.

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Chapter 15, Problem 5P

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The change in depth of the that causes the piston to move in by 0.750 cm.

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Chapter 15, Problem 4P

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Principles of Physics: A Calculus-Based Text, Hybrid (with Enhanced WebAssign Printed Access Card)

Ch. 15.1 - Suppose you are standing directly behind someone...Ch. 15.2 - Prob. 15.2QQ Ch. 15.4 - An apple is held completely submerged just below...Ch. 15.4 - Prob. 15.4QQ Ch. 15.6 - Prob. 15.5QQ Ch. 15.7 - You observe two helium balloons floating next to...Ch. 15 - A wooden block floats in water, and a steel object...Ch. 15 - Prob. 2OQ Ch. 15 - Prob. 3OQ Ch. 15 - Prob. 4OQ

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The change in depth of the that causes the piston to move in by 0.750 cm .

Solution Summary: The author explains how the spring obeys the Hooke's law. Write the equation for Delta F.

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The change in depth of the that causes the piston to move in by 0.750 cm.

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Chapter 15 Solutions