Quick question regarding work?

  • #1
139
0

Homework Statement


A force in the xy plane is given by F = A(10ai + 3xj), where A and a are constants, F is in newtons and x is in meters. Suppose that the force acts on a particle as it moves from an initial position x = 4m, y = 1m to a final position x = 4m, y = 4m. Show that this force is not conservative by computing the work done by the force for at least two different paths.


Homework Equations


W = integral of f dx


The Attempt at a Solution


I basically integrated and got W = A(10axi + 3/2 x^2j)
I'm not sure how to exactly calculate the work done across the paths though.

thanks.
 

Answers and Replies

  • #2
A force is non conservative if taking different routes leads to a conflict in potential between start/end points.

Try this question by calculating the work done by moving the particle directly from (4,1) to (4,4). Now move it in a different motion, no complex path is required. For example move it from (4,1) to (x2,y2) then from there to (4,4).
 
  • #3
139
0
yeah I forgot how to compute the work from one point to another point.
 
  • #4
Work is equivalent to the dot product of Force and Distance.
 
  • #5
139
0
yeah I know you have to integrate the force vector across the displacement since it varies with displacement. I don't know how exactly you do that across the points. Do you have to do line integrals or something?
 
  • #6
jtbell
Mentor
15,719
3,850
Yes, you have to do line integrals. From the statement of the problem, you need to choose two different paths and do a line integral along each of them.
 
  • #7
139
0
thanks. how exactly do you compute the line integral again?
We didn't get up to it yet, we're only doing double integrals in multi.
 
  • #8
139
0
any ideas
 

Related Threads on Quick question regarding work?

Replies
1
Views
363
  • Last Post
Replies
4
Views
610
Replies
2
Views
2K
Replies
6
Views
1K
Replies
1
Views
1K
  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
22
Views
2K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
8
Views
1K
Top