DNA secondary structure may prove to be a significant obstacle both for enzymes that process DNA through an orifice and for the passage of DNA through nanopores proposed for some novel sequencing schemes. A nanomechanical molecular "tape reader" is assembled by threading a nanopore over DNA and pulling it using an atomic force microscope. Its formation is confirmed by studying the force required to open hairpins under that geometry. Unfolding induced by this 0.7-nm-diameter aperture requires 40 times more force than that reported for pulling on the ends of the DNA. Kinetic analysis shows that much less strain is required to destabilize the double helix in this geometry. Consequently, much more force is required to provide the free energy needed for opening.