My Math Forum  

Go Back   My Math Forum > Science Forums > Physics

Physics Physics Forum


Thanks Tree2Thanks
  • 2 Post By romsek
Reply
 
LinkBack Thread Tools Display Modes
October 17th, 2017, 10:07 PM   #1
Senior Member
 
SenatorArmstrong's Avatar
 
Joined: Nov 2015
From: United States of America

Posts: 162
Thanks: 21

Math Focus: Calculus and Physics
Work in a force field

Consider a force field $\vec F(x,y)$. If I want to calculate the work done from $(a,b) \rightarrow (c,d)$ on the cartesian plane, and I pick two different paths for my line integral $$\oint_C \vec F \dot \,d\vec s$$

Will I always get the same work for any path taken?

I have been messing with a similar problem today and I keep getting different values for work as I try different paths between the same points in the force field. Doesn't seem right
SenatorArmstrong is offline  
 
October 17th, 2017, 11:35 PM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: Southern California, USA

Posts: 1,607
Thanks: 819

Quote:
Originally Posted by SenatorArmstrong View Post
Consider a force field $\vec F(x,y)$. If I want to calculate the work done from $(a,b) \rightarrow (c,d)$ on the cartesian plane, and I pick two different paths for my line integral $$\oint_C \vec F \dot \,d\vec s$$

Will I always get the same work for any path taken?

I have been messing with a similar problem today and I keep getting different values for work as I try different paths between the same points in the force field. Doesn't seem right
excellent question

If the force field is conservative, i.e. if it is the gradient of a scalar potential function, then the work done moving a particle through the field between two points will be independent of the path taken.

https://en.wikipedia.org/wiki/Conservative_vector_field

If the field is not conservative then the work done will vary with the path taken.
Thanks from topsquark and SenatorArmstrong
romsek is offline  
October 17th, 2017, 11:38 PM   #3
Senior Member
 
SenatorArmstrong's Avatar
 
Joined: Nov 2015
From: United States of America

Posts: 162
Thanks: 21

Math Focus: Calculus and Physics
Quote:
Originally Posted by romsek View Post
excellent question

If the force field is conservative, i.e. if it is the gradient of a scalar potential function, then the work done moving a particle through the field between two points will be independent of the path taken.

https://en.wikipedia.org/wiki/Conservative_vector_field

If the field is not conservative then the work done will vary with the path taken.
Ahh that makes perfect sense. Thanks!
SenatorArmstrong is offline  
October 27th, 2017, 07:12 AM   #4
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 2,829
Thanks: 753

That's pretty much the definition of "conservative" force field!
Country Boy is offline  
Reply

  My Math Forum > Science Forums > Physics

Tags
field, force, work



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Line integral work done by conservative field max233 Calculus 1 May 30th, 2016 01:23 AM
Hydrostatic force on a triangular tank (force on one end & work req'd to pump out)? leo255 Calculus 1 December 16th, 2014 08:48 PM
work done by variable force aaron-math Calculus 2 October 30th, 2011 12:52 PM
Moving proton, Magnetic field, velocity, force FishFace Physics 3 October 27th, 2011 07:39 AM
Vector force field help please!! yoyosuper8 Calculus 6 April 26th, 2009 09:26 PM





Copyright © 2017 My Math Forum. All rights reserved.