Randall D. Knight — Interactions and Potential Energy: Problem 65

An object moving in the $xy$-plane is subjected to the force $\vec{F} = (2xy \hat{i} + x^2 \hat{j}) \text{ N}$, where $x$ and $y$ are in m. a. The particle moves from the origin to the point with coordinates $(a, b)$ by moving first along the $x$-axis to $(a, 0)$, then parallel to the $y$-axis. How much work does the force do? b. The particle moves from the origin to the point with coordinates $(a, b)$ by moving first along the $y$-axis to $(0, b)$, then parallel to the $x$-axis. How much work does the force do? c. Is this a conservative force?