I don't bother with locking my luggage anymore. The locks you bought can be used since they are TSA approved, if your bag needs a full search they won't have to rip the zipper off the bag to do so. If it does go through a full search, you will be left with a nice little note from TSA when you get your bag on the other side.

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When you get to the end of your rope, tie a knot and swing.