My Math Forum Integrate vectors along part of the circle

 Calculus Calculus Math Forum

 July 17th, 2013, 09:12 AM #1 Newbie   Joined: Jul 2013 Posts: 2 Thanks: 0 Integrate vectors along part of the circle Hello! I hope someone can help me out because I'm a little bit rusty with my math. I have the following problem: the cylindric surface is under pressure. I know that the total resultant force in "horizontal" direction needs to be "N". So, basically, I would need to integrate all the "p*cos theta" along the curve from "-theta" to "theta" if I'm not wrong. Then, when multiplied with "L" and "s" where "s" would be arc length, I would get "N". Right? But, am I doing something wrong? http://tinypic.com/r/bfqo7m/5 No img codes? Really?
July 17th, 2013, 03:54 PM   #2
Global Moderator

Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,968
Thanks: 1152

Math Focus: Elementary mathematics and beyond
Re: Integrate vectors along part of the circle

Quote:
 Originally Posted by rujan No img codes? Really?
No. Post it as an attachment.

Welcome to the forum, rujan.

July 17th, 2013, 04:15 PM   #3
Math Team

Joined: Sep 2007

Posts: 2,409
Thanks: 6

Re: Integrate vectors along part of the circle

Quote:
 Originally Posted by rujan Hello! I hope someone can help me out because I'm a little bit rusty with my math. I have the following problem: the cylindric surface is under pressure. I know that the total resultant force in "horizontal" direction needs to be "N". So, basically, I would need to integrate all the "p*cos theta" along the curve from "-theta" to "theta" if I'm not wrong. Then, when multiplied with "L" and "s" where "s" would be arc length, I would get "N". Right? But, am I doing something wrong? http://tinypic.com/r/bfqo7m/5 No img codes? Really?
Perhaps I am misunderstanding this. Are you saying that the pressure, P, is constant on the surface of the surface? If not you need to give the pressure function. If it is, then the total (vector) force is 0 because the force in one direction cancels the force in the opposite direction. The total (scalar) force is P times the total area the pressure is applied to. For the whole cylinder that is P times $2\pi rh$ where r is the radius of the cylinder and h is the height of the cylinder.

 July 17th, 2013, 08:58 PM #4 Newbie   Joined: Jul 2013 Posts: 2 Thanks: 0 Re: Integrate vectors along part of the circle Hi and thanks. Yes, the pressure is constant . It is applied on cylindrical surface as on the sketch. The force is not 0 because while p*sin theta components cancel each other, sum of p*cos theta should give N. What I need is, if I'm not wrong is double integral first integral from 0 to theta of p*cos(theta) then the along length of the surface (cylinder height) from 0 to L which is constant anyway. Correct?

 Tags circle, integrate, part, vectors

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post yeoky Algebra 4 May 3rd, 2014 01:06 AM Aska123 Algebra 9 January 29th, 2014 11:06 PM gailplush Algebra 5 August 8th, 2010 04:19 AM sir anrava Algebra 1 January 19th, 2010 11:18 AM Titan Algebra 0 March 7th, 2008 05:14 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top