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Lecture

8.3 Physics & Engineering Applications Question #2 (Medium)

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Department
Mathematics
Course
MAT136H1
Professor
All Professors
Semester
Winter

Description
8.3 Challenging Integral Applications Physics & Engineering Applications Question #2 (Medium): Hydrostatic Force on a Submerged Vertical Plate Strategy The hydrostatic force is given by ∑ ∫ , where is the water density, the depth below the surface, the area of the thin th strip. Sample Question A vertical plate that is submerged in water has the shape shown by the diagram. Express the hydrostatic force against one side of the place by a Riemann sum as well as an integral, and then evaluate it. [a semi-circle with diameter ometer submerged meter deep] Solution Since the units are given in the Standard International metric system, ( ) As for the th rectangular strip, the area. If any th strip is chosen to be x distance from the bottom of the semi-circle, then based on Pythagorean Theorem, the width (or even length) is: √ ( ) . The distance the th strip is located beneath
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