An object has several forces acting on it. One force is a force in the x?-direction whose magnitude depends on the position of the object. (See problem 6.98). The constant is ??? = 2.00 N/m2. The object moves along the following path; (1) It starts at the origin and moves along the ?y?-axis to the point ?x? = 0, ?y? = 1.50 m; (2) it moves parallel to the ?x?-axis to the point ?x? = 1.50 m, ?y? = 1.50 m; (3) it moves parallel to the ?y?-axis to the point ?x? = 1.50, ?y? = 0; (4) it moves parallel to the ?x?-axis back to the origin. (a) Sketch this path in the ?xy-?plane. (b) Calculate the work done on the object by for each leg of the path and for the complete round trip. (c) Is conservative or nonconservative? Explain.
Solution 85P Step 1: (a).The object moves parallel to the force and so the dot product between the vectors is trivial.it's just the product of the vectors themselves.Therefore, the work done here is just W = (2.00 N/m 2 x 1.50 m dx) 1 * * = 3.0 N/m * 1/2 *1.50 m 0 m ) 2 = 1.5 N/m 2*25 m = 3.375 J.