A cutting tool under microprocessor control has several forces acting on it. One force is F⃗ =−αxy2j^, a force in the negative y-direction whose magnitude depends on the position of the tool. The constant is α = 2.70N/m3 . Consider the displacement of the tool from the origin to the point x= 2.95m , y= 2.95m .
Calculate the work done on the tool by F⃗ if this displacement is along the straight line y=x that connects these two points.
Calculate the work done on the tool by F⃗ if the tool is first moved out along the x-axis to the point x= 2.95m , y=0 and then moved parallel to the y-axis to x= 2.95m , y= 2.95m .
The Attempt at a Solution
So I was simply trying to use the W=force*distance, and I tried to use the vector equation for force by plugging in the coordinate that it would end up at and then for distance I used the distance from the origin to the point (2.95, 2.95) for the first part, and then I broke Part B into two parts, calculating work from origin to (2.95, 0) and then work from there to (2.95, 2.95).
It didn't work, and it is due by 11:59 PM. I am really confused. (Please, if you use calculus in your replies, please explain in detail. My calculus is very weak right now...)