Is the Force Described by F = A(10ai + 3xj) Conservative?

[Ishida52134]

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.

 

[3_14159265]

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).

 

[Ishida52134]

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

 

[3_14159265]

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

 

[Ishida52134]

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]

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.

 

[Ishida52134]

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.

 

[Ishida52134]

any ideas