Explanation Given: δ ( x , y , z ) = e − z ,r=2,z=4 Formula used: M = ∭ W δ ( x , y , z ) d v M x y = ∭ W z δ ( x , y , z ) d v M y z = ∭ W x δ ( x , y , z ) d v M x z = ∭ W y δ ( x , y , z ) d v x ¯ = M y z M , y ¯ = M x z M , z ¯ = M x y M Calculation: M = ∭ W δ ( x , y , z ) d A = ∫ 0 2 π ∫ 0 2 ∫ 0 4 ( e − z r d z d r d θ ) = ∫ 0 2 π ∫ 0 2 r [ e − z − 1 ] 0 4 d r d θ = ∫ 0 2 π ∫ 0 2 r [ e 0 − e − 4 ] d r d θ = − ∫ 0 2 π ∫ 0 2 ( 1 − e − 4 ) r d r d θ = ( 1 − e − 4 ) ∫ 0 2 π [ r 2 2 ] 0 2 d θ = ( 1 − e − 4 ) × 2 ∫ 0 2 π 1 d θ = 2 ( 1 − e − 4 ) [ θ ] 0 2 π = 4 π ( 1 − e − 4 ) M x y = ∭ W z δ ( x , y , z

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 16.5, Problem 28E

To determine

To find: The center of mass of a cylinder of radius 2 and height 4 and mass density $δ (x, y, z) = e^{- z}$ .where z is the height above the base.

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Chapter 16.5, Problem 27E

Chapter 16.5, Problem 29E

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Chapter 16 Solutions

Calculus - Standalone book

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The center of mass of a cylinder of radius 2 and height 4 and mass density δ ( x , y , z ) = e − z .where z is the height above the base.

Solution Summary: The author calculates the coordinates of center of mass of a cylinder of radius 2 and height 4 and mass density (x, y, and z) = 0.91.

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To find: The center of mass of a cylinder of radius 2 and height 4 and mass density $δ (x, y, z) = e^{- z}$ .where z is the height above the base.

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Chapter 16 Solutions

The center of mass of a cylinder of radius 2 and height 4 and mass density δ ( x , y , z ) = e − z .where z is the height above the base.

Solution Summary: The author calculates the coordinates of center of mass of a cylinder of radius 2 and height 4 and mass density (x, y, and z) = 0.91.

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To find: The center of mass of a cylinder of radius 2 and height 4 and mass density δ(x,y,z)=e−z.where z is the height above the base.

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Chapter 16 Solutions

To find: The center of mass of a cylinder of radius 2 and height 4 and mass density $δ (x, y, z) = e^{- z}$ .where z is the height above the base.