Suppose there is a conservative force with potential energy function U(x, y) =−ax − bx2 + 3cy3, where a, b, and c are positive constants, throughout the entire x-yplane. Find the associated force F~ (x, y). Consider a bead of mass m that is free tomove along a frictionless wire that is fixed to the x axis. If the bead is released fromrest at the origin, in which direction will it start to move? How fast will it be travelingafter it moves a distance L?

Suppose there is a conservative force with potential energy function U(x, y) =−ax − bx2 + 3cy3, where a, b, and c are positive constants, throughout the entire x-yplane. Find the associated force F~ (x, y). Consider a bead of mass m that is free tomove along a frictionless wire that is fixed to the x axis. If the bead is released fromrest at the origin, in which direction will it start to move? How fast will it be travelingafter it moves a distance L?