A Problem from Work, Kinetic Energy, and Power

[fiddleninja]

Homework Statement

A force field in two dimensions is given by F(x,y) = y(i-hat)-x(j-hat). A second force field in two dimensions is given by F(x,y)=y(i-hat)+x(j-hat). Evaluate the work done by each force on a particle that moves from the origin to the point (x,y)=(1,1) along each of the following paths: (a) (0,0)->(1,0)->(1,1) along the axes; (b) (0,0)->(0,1)->(1,1) along the axes; (c) y=x; and (d) y= x^2. Note particularly that the first force yields values that are not all the same while the second force yields values that are the same.

Homework Equations

Relavent multidimensional integral equations: http://web.uconn.edu/~cdavid/mathrev2/node8.html

The Attempt at a Solution

I'm not exactly sure how to write the Work equations in terms of multidimensional integral equations. I think I understand the physics, but the notation is confusing me. I'm really just looking for an example of how the work equations should be written.

 

[tiny-tim]

welcome to pf!

hi fiddleninja! welcome to pf!

(btw, on this forum it's easier to use the bold icon and write eg yi - xj )

I'm not exactly sure how to write the Work equations in terms of multidimensional integral equations.

these aren't multidimensional integrals …

look at your own link, and you'll see they are path integrals (one-dimensional integrals), which should be easy …

you need to define a parameter s for each path, and do an ordinary one-dimensional integral over ds …

what do you get?

 

[fiddleninja]

Thanks, I got it.