Chapter 8.3, Problem 19E

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Chapter
Section

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

# A metal plate was found submerged vertically in seawater, which has density 64 lb/ft3. Measurements of the width of the plate were taken at the indicated depths. Use Simpson’s Rule to estimate the force of the water against the plate.

To determine

To estimate: The force of the water against the plate using Simpson’s Rule.

Explanation

Given:

The density of water is Î´=64â€‰lb/ft3.

The depth and width of the plate as shown in Table 1:

The number of subintervals as n=7.

Calculation:

The width of the plate is measured at equal interval of depth. Hence, the subinterval width (Î”x) is 0.4.

Calculate the force of the water against the plate using Simpsonâ€™s Rule:

F=Î”xÎ´3[x1w1(x1)+4x2w2(x2)+2x3w3(x3)+4x4w4(x4)+2x5w5(x5)+4x6w6(x6)+x7w7(x7)] (1)

Substitute 0.4 for Î”x, 7.0 for x1, 7.4 for x2, 7.8 for x3, 8.2 for x4, 8.6 for x5, 9.0 for x6, and 9.4 for x7 in Equation (1).

F=0.4Î´3[7.0w1(7.0)+4Ã—7.4w2(7.4)+2Ã—7.8w3(7.8)+4Ã—8.2w4(8.2)+2Ã—8.6w5(8.6)+4Ã—9.0w6(9.0)+9.4w7(9.4)]=0

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