A cutting tool under microprocessor control has several forces acting on it. One force is F = _axy2j, a force in the negative y-direction whose magnitude depends on the position of the tool. The constant is a = 2.50 N/m3. Consider the displacement of the tool from the origin to the point x = 3.00 m, y = 3.00 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 = 3.00 m, y = 0 and then moved parallel to the y-axis to the going x = 3.00 m, y = 3.00 m. (c) Compare the work done by F along these two paths. Is F conservative or non-conservative? Explain.