Putnam 1957 A2

Let $a>1.$ A uniform wire is bent into a form coinciding with the portion of the curve $y=e^x$ for $x\in [0,a]$ , and the line segment $y=e^a$ for $x\in [a-1,a].$ The wire is then suspended from the point $(a-1, e^a)$ and a horizontal force $F$ is applied to the point $(0,1)$ to hold the wire in coincidence with the curve and segment. Show that the force $F$ is directed to the right.