Consider the force given by vec$(F)(y)=F_0{e}^{-ay}$hat$(j)$ where a and $F_0$ are real, positive constants.

a$.$ Please find the work done by this force on an object moving over the paths, $AB$ and ACB as shown below. Is the work done on each path the same or different?

b$.$ Is this force conservative? Why or why not?

c$.$ Can one define a potential energy corresponding to this force? Why or why not? If so$,$ find an expression for the potential energy corresponding to this force.

Problem $3$

d$.$ If vec$(F)(y)$ is the only force acting on an object, what is the work done as this object moves from point, $A,$ to point, $B$ over each path? How should these answers compare? Why?