Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Set up the integral that should be used to find the total force on the window. Use the bottom of the pool as the origin​ (0,0), with the​ y-axis passing through the left side of the window. Use increasing limits of integration

### Calculating the Force on a Window in a Diving Pool

A diving pool that is 5 meters deep and full of water has a viewing window on one of its vertical walls. Find the force on a window that is a square, 0.75 meters on a side, with the lower edge of the window 1.5 meters from the bottom of the pool. Use 1000 kg/m³ for the density of water and 9.8 m/s² for the acceleration due to gravity.

#### Finding the Width Function

Find the width function \( w(y) \) for each value of \( y \) on the face of the window.

\[ w(y) = 0.75 \]

(Use integers or decimals for any numbers in the equation.)

#### Setting Up the Integral

Set up the integral that should be used to find the total force on the window. Use the bottom of the pool as the origin (0,0), with the y-axis passing through the left side of the window. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice.

---

Make sure to apply the necessary physical principles for calculating the force on a submerged surface. Consider the pressure distribution along the depth of the window and how it translates to the total force.
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Transcribed Image Text:### Calculating the Force on a Window in a Diving Pool A diving pool that is 5 meters deep and full of water has a viewing window on one of its vertical walls. Find the force on a window that is a square, 0.75 meters on a side, with the lower edge of the window 1.5 meters from the bottom of the pool. Use 1000 kg/m³ for the density of water and 9.8 m/s² for the acceleration due to gravity. #### Finding the Width Function Find the width function \( w(y) \) for each value of \( y \) on the face of the window. \[ w(y) = 0.75 \] (Use integers or decimals for any numbers in the equation.) #### Setting Up the Integral Set up the integral that should be used to find the total force on the window. Use the bottom of the pool as the origin (0,0), with the y-axis passing through the left side of the window. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice. --- Make sure to apply the necessary physical principles for calculating the force on a submerged surface. Consider the pressure distribution along the depth of the window and how it translates to the total force.
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