Question

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 = 2.15 N/m3 . Consider the displacement of the tool from the origin to the point x= 3.80 m , y= 3.80 m .

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= 3.80 m , y=0 and then moved parallel to the y-axis to x= 3.80 m , y= 3.80 m .