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A2

Part of 1957 Putnam

Problems(1)

Putnam 1957 A2

Source: Putnam 1957

7/1/2022
Let a>1.a>1. A uniform wire is bent into a form coinciding with the portion of the curve y=exy=e^x for x∈[0,a]x\in [0,a], and the line segment y=eay=e^a for x∈[a−1,a].x\in [a-1,a]. The wire is then suspended from the point (a−1,ea)(a-1, e^a) and a horizontal force FF is applied to the point (0,1)(0,1) to hold the wire in coincidence with the curve and segment. Show that the force FF is directed to the right.
Putnamphysicsexponential