Chapter 7, Problem 7.75P

CALC A cutting tool under microprocessor control has several forces acting on it. One force is $\stackrel{\to }{F}$ = −αxy²ĵ, a force in the negative y-direction whose magnitude depends on the position of the tool. For α = 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 $\stackrel{\to }{F}$ 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 point (x = 3.00 m, y = 3.00 m). (c) Compare the work done by $\stackrel{\to }{F}$ along these two paths. Is $\stackrel{\to }{F}$ conservative or nonconservative? Explain.