# Quick question regarding work?

## 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.

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).

yeah I forgot how to compute the work from one point to another point.

Work is equivalent to the dot product of Force and Distance.

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?

jtbell
Mentor
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.

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.

any ideas