My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Thanks Tree1Thanks
  • 1 Post By mathman
Reply
 
LinkBack Thread Tools Display Modes
September 4th, 2017, 07:29 AM   #1
Senior Member
 
Joined: Jan 2017
From: Toronto

Posts: 209
Thanks: 3

Another Surface Integral problem...

Find the center of mass of an object that occupies the surface z = sqrt(x^2+y^2), 1 <= z <= 4 and has density z * x^2.

Official Answer: ( 0, 0, 2275/682 )

Here is my solution:

$\displaystyle
x = r cos \theta
$
$\displaystyle
y = r sin \theta
$
$\displaystyle
z = \sqrt { r^2 cos^2 \theta + r^2 sin^2 \theta } = r
$
$\displaystyle
G(\theta, r) = < r cos \theta , r sin \theta , r >
$
$\displaystyle
dG / d \theta = < -r sin \theta , r cos \theta , 0 >
$
$\displaystyle
dG / dr = < cos \theta , sin \theta , 1 >
$
$\displaystyle
| dG / d \theta ~cross~product~ dG / dr | = r * \sqrt {2}
$
$\displaystyle
General~Mass = \int_{0}^{2\pi} \int_{1}^{4} \sqrt {2} r^4 cos^2 \theta ~dS
$
$\displaystyle
Mass~along~Z~Axis = \int_{0}^{2\pi} \int_{1}^{4} \sqrt {2} r^5 cos^2 \theta ~dS
$

My answer: ( 0, 0, 3.4292131 ). My answer is wrong.... Any idea?
zollen is offline  
 
September 4th, 2017, 09:39 AM   #2
Global Moderator
 
Joined: May 2007

Posts: 6,852
Thanks: 743

I got z=3.335777126099707. This matches the right answer. Your error is in the arithmetic at the end, since I used your integrals to get the result.
Thanks from zollen

Last edited by mathman; September 4th, 2017 at 09:42 AM.
mathman is offline  
September 4th, 2017, 10:05 AM   #3
Senior Member
 
Joined: Jan 2017
From: Toronto

Posts: 209
Thanks: 3

Thanks. I think it is my arithmetic too...

Quote:
Originally Posted by mathman View Post
I got z=3.335777126099707. This matches the right answer. Your error is in the arithmetic at the end, since I used your integrals to get the result.
zollen is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
integral, problem, surface



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
application of Surface integral MMath Algebra 1 June 9th, 2016 06:08 AM
What is a surface integral? henrymerrild Calculus 2 May 1st, 2014 11:33 AM
surface integral kriko Calculus 1 August 21st, 2010 11:55 AM
Surface Integral sansar Calculus 1 May 10th, 2009 05:21 AM
Surface Integral Question... TTB3 Real Analysis 1 April 22nd, 2009 06:28 PM





Copyright © 2019 My Math Forum. All rights reserved.