1. The problem statement, all variables and given/known data A force F has components F sub x = axy-by^2, F sub y= -axy+bx^2 where a= 2N/m^2 & b=4N/m^2 Calculate the work done on an object of mass 4kg if it is moved on a closed path from (x,y) values of (0,1) to (4,1), to (4,3) to (0,3) and back to (0,1). all coordinates are in metres. The path between points is always a straight line. 2. Relevant equations deltaK=F.dr 3. The attempt at a solution Looking at the forces components, the force can be expressed as F=F sub x + F sub y=(axy-by^2)+(-axy+bx^2)=bx^2-by^2 Considering 4 separate motions, we can treat them as 2 dimensional problems, so delta K = F.dr=F.dx where delta K sub 1+ delta K sub 2+ delta K sub 3 + delta K sub 4 = delta K sub total. In each motion, since 1 component (x or y) will remain constant, leaving me with 4 line integrals of a quadratic with the constant term determined on which motion I am dealing with. IE: A horizontal motion from (0,1) to (4,1) has no change in y, so y=1 for the duration of the motion. Conversely, when dealing with a vertical motion, the x value remains constant, again leaving me with a line integral of a quadratic where say in the motion (4,1) to (4,3), x remains constant where x=4. Is this the proper approach? Am I able to treat the 2 components as a single force? Further, I notice here that the mass is not included in my calculations. I can justify not needing this since the change in kinetic energy describes the work done, I do not have a component of time, and do not require any information about velocity or acceleration, thus although it is very nice that the object is 4kg, there is no need to use this in any computations. Without showing all of my work, I determined the work performed to be equal to 256J. I have handed this problem in for last weeks problem set, and have a similar problem on my new problem set this week. If truly needed I can reproduce my calculations, but as mentioned they have been handed in already, and I am simply looking for reassurance I have managed the problem appropriately. Thank you for your help in advance.