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Lecture

# 8.3 Physics & Engineering Applications Question #3 (Medium)

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School
University of Toronto St. George
Department
Mathematics
Course
MAT136H1
Professor
all
Semester
Winter

Description
8.3 Challenging Integral Applications Physics & Engineering Applications Question #3 (Medium): Hydrostatic Force on a Partially 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 partially 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 upside down trapezoid with top side of and bottom side of , height h with emerged in water] Solution The units are given in variables, thereforeis kept as it is. If x is distance from the top of the trapezoid upto where the th strip is located, then from ∑ ∫ , the depth emerged in water from the surface is
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