Work - Line Integral Homework: Calculating Work along C1 & C2 Curve

[portuguese]

Homework Statement

I have exam tomorrow and there's a problem I don't know how to do.

Consider the curve C1 (x=-y^2+3y) and C2 (x=0), both defined for y$\in$[0,3].
Calculate the work done by F(x,y)=(x,y^2) along the curve C=C1UC2 (retrograde direction).

Homework Equations

The Attempt at a Solution

The solution given is 0. I really don't know how to get it. Thanks!

 

[jedishrfu]

When you traverse the curve do you wind up at your staring point? if so then the work is zero by definition, right?

 

[algebrat]

When you traverse the curve do you wind up at your staring point? if so then the work is zero by definition, right?

This is not true in general. (If you have a conservative force then it is true; this force happens to be conservative, but how would you show that?)

You could parametrize the two separate trajectories as some r(t)=(x(t),y(t))

Then use ∫f(r(t))*r'(t)dt on each curve.

 

[portuguese]

How do I do it for C2? I think this is the biggest problem for me.

 

[vela]

You need to show your work before you can receive help here.

 

[algebrat]

How do I do it for C2? I think this is the biggest problem for me.

Hint: Organize your work, write C2:, and then write notes for that region, like r(t)=(0,y(t)), F(x,y)=F(0,y)=... You'll have to decide on the rest of the parametrization for r(t) is, that is, what do you think y(t) should be. Decide on a and b in t=a...b. Et cetera; good luck!

 

[HallsofIvy]

When you traverse the curve do you wind up at your staring point? if so then the work is zero by definition, right?

This is not true in general. (If you have a conservative force then it is true; this force happens to be conservative, but how would you show that?)

As algebrat suggests, following on what jedishrfu said (hopefully jedishrfu had already noted, but forgot to say, that the force is conservative) the simplest way to do that is show that the force is conservative. portugese, do you know how to do that?