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Chapter 6: Q. 67 (page 557)

Find the hydrostatic force described in each of Exercises 61鈥�69.

The hydrostatic force exerted on a dam in the shape of a trapezoid whose top is 400 feet long and whose base is 250 feet long, given that the dam is holding back a body of water that reaches all 200 feet from the bottom to the top of the dam.

Short Answer

Expert verified

The hydrostatic force exerted on a dam in the shape of a trapezoid is 405,600,000.

Step by step solution

01

Step 1. Given Information.

A trapezoid top is 400 feet long and whose base is 250 feet long, given that the dam is holding back a body of water that reaches all 200 feet

02

Step 2. Find Ak,dk

Area of the trapezoidAk=(400+250)2鈭�y=325鈭�y

Depth,dk=200-yk*

The density of the water is 62.4pounds.

03

Step 3. Find the hydrostatic force.

The hydrostatic force is given by,

F=蝇Akdk=62.4(325)(200-yk*)鈭�yF=20280鈭�0200(200-y)dy=20,280[200y-y22]0200 =20,280[20,000]=405,600,000

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