Question

An object is resting (x-y plane) on a frictionless surface and is subject to the following force:

F_net=Ay(cos(pi*x/B))i +Ax(sin(pi*y/B))j

where A = 1.0 N/m and B = 1.0 m. The object may move from the origin to (1.0 m, 1.0 m) by one of two paths:
Path a: Origin to (1.0m, 0.0 m), then to (1.0 m, 1.0 m)
Path b: Origin to (0.0m, 1.0 m), then to (1.0 m, 1.0 m)
If the object follows path b, the work on the object is zero.
a) Find the work done by this force on the object along path a.
Note: your answer should be fully algebraic. Only at the end you should use numbers. Also, when you use numbers, you should use units as appropriate for all numbers.
b) Is this a conservative force. Justify.

Answer 1