Homework Help: Conservative Force

1. Apr 3, 2015

brianeyes88677

1. The problem statement, all variables and given/known data
A force F=(xy)i+(2*y^2)j，an object (mass=m) is move from (0,0) to (1,3) along y=3x , how much work does F do? Is F a conservative force?

2. Relevant equations

3. The attempt at a solution

Can I do it on the two axes?I mean ∫Fdx+∫Fdy , and because the work differ from the different road I take , F isn't a conservative force.
∫x*ydx=∫x*(3x)dx=1/3
∫2*y^2dy=36

2. Apr 3, 2015

abbas_majidi

If F be a conservative force yo can get work ∫Fdx+∫Fdy

3. Apr 3, 2015

brianeyes88677

Do I have to do ∫F⋅dr , where r=(1,3)/√10 ?

4. Apr 3, 2015

abbas_majidi

You can calculate curl of F if it will be zero F is conservative otherwise it isn't.

Path is clear and work is ∫F.dr, dr=dTI+3dtj and 0<t<1 whatever F be a conservative force or not.

5. Apr 3, 2015

abbas_majidi

Correction: 'dr=dti+3dtj'

6. Apr 3, 2015

abbas_majidi

I forgot tell you which x=t and y= 3t in above integral.