Is the Given Force Field Conservative?

Click For Summary

Homework Help Overview

The discussion revolves around determining whether a given force field, defined as F = 2xcos2yi - (x2+1)sin2yj, is conservative. Participants are exploring the conditions under which a force field is considered conservative, particularly focusing on the curl of the force field.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to verify the conservativeness of the force field using the curl and expresses doubt about the correctness of the book's assertion. They calculate the curl and question whether the resulting terms cancel out. Other participants discuss the expansion of trigonometric functions and their relevance to the problem.

Discussion Status

The discussion is ongoing, with some participants providing insights into trigonometric identities that may influence the original poster's calculations. There is a mix of interpretations regarding the expansion of trigonometric functions and their implications for the problem.

Contextual Notes

Participants are addressing potential misunderstandings related to trigonometric identities and their application in verifying the conservativeness of the force field. There is an indication of differing levels of familiarity with trigonometry among participants.

leroyjenkens
Messages
621
Reaction score
49

Homework Statement



Verify the following force field is conservative.
F = 2xcos2yi - (x2+1)sin2yj

Homework Equations



∇xF=0

The Attempt at a Solution


I'm pretty sure this is just a mistake in the book, but according to my calculations, this isn't a conservative force.
I used the determinant method to do the curl of F to find -2xsin(2y) + 4xsinycosy. Unless those two terms cancel each other to equal 0, then the force isn't conservative and there's a mistake in the book.

What do you think? Thanks.
 
Physics news on Phys.org
You should brush up your HS trigonometry before doing anymore maths/physics. How do you expand sin 2y ?
 
Oh.
Is there a way to expand sin2y manually, or is it just one of those things you have to memorize?
 
Trigonometry generally appeals to memory even though some proofs can be visual. sin (x+y) = ? then take x=y.
 
[tex]\sin(2y) = 2\sin y \cos y[/tex] for any angle [itex]y[/itex]. So yes, the terms cancel out and the force is conservative.
 

Similar threads

  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
9K
  • · Replies 18 ·
Replies
18
Views
5K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 40 ·
2
Replies
40
Views
5K
  • · Replies 10 ·
Replies
10
Views
3K