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We have explored the electromechanical properties of DNA by using an electric field to force single hairpin molecules to translocate through a synthetic pore in a silicon nitride membrane. We observe a threshold voltage for translocation of the hairpin through the pore that depends sensitively on the diameter and the secondary structure of the DNA. The threshold for a diameter 1.5 < d < 2.3 nm is V > 1.5 V, which corresponds to the force required to stretch the stem of the hairpin, according to molecular dynamics simulations. On the other hand, for 1.0 < d < 1.5 nm, the threshold voltage collapses to V < 0.5 V because the stem unzips with a lower force than required for stretching. The data indicate that a synthetic nanopore can be used like a molecular gate to discriminate between the secondary structures in DNA.