A cutting tool under microprocessor control has several forces acting on it. One force is F = -α xy^{2} hat{ j }, a force in the negative y-direction whose magnitude depends on the position of the tool. The constant is α = 2.25 N/m^3. Consider the displacement of the tool from the origin to the point x = 2.10 m, y = 2.10 m.
a). Calculate the work done on the tool by F if this displacement is along the straight line y=x that connects these two points.
b). Calculate the work done on the tool by F if the tool is first moved out along the x-axis to the point x = 2.10 m, y=0 and then moved parallel to the y-axis to x= 2.10 m, y= 2.10 m.