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International Edition---engineerin...

4th Edition
Andrew Pytel And Jaan Kiusalaas
Publisher: CENGAGE L
ISBN: 9781305501607

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BuyFindarrow_forward

International Edition---engineerin...

4th Edition
Andrew Pytel And Jaan Kiusalaas
Publisher: CENGAGE L
ISBN: 9781305501607
Chapter 8, Problem 8.43P
Textbook Problem
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Use integration to find the centroidal coordinates for the volume obtained by revolving the area shown about the x-axis.

Chapter 8, Problem 8.43P, Use integration to find the centroidal coordinates for the volume obtained by revolving the area

To determine

Centroidal coordinates of the volume obtained by revolving the area about x-axis.

Explanation of Solution

Given Information:

The following plane in given,

Calculation:

Consider the following figure,

Consider the revolution of a rectangular strip about x-axis as shown in figure above.

The volume generated by the strip is, dV=πy2dx=π(h( 1 x 2 / b 2 ))2dx

Integrate the differential volume to get the total volume as,

  V=dV=π0b ( h( 1 x 2 / b 2 ) )2dxV=πh20b[1+ x 4 b 4 2 x 2 b 2 ]dxV=πh2[x+x55b42x33b2]0b

  V=πh2[b+ b 55 b 42 b 33 b 2]V=πh2[b+b52b3]V=8πbh215

By symmetry the y-coordinates of centroid is y¯=0

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Chapter 8 Solutions

International Edition---engineering Mechanics: Statics, 4th Edition
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