Why were american sailors willing to risk their lives on the open seas in order to trade with foreign countries?

Most American sailors did this because they needed to get money and make a living. Making/earning money or receiving needed materials back then was much harder than it is right now, and sailors and regular people were willing to go to extremes to get money to provide for themselves and possibly their families. The materials that were traded with foreign countries were also typically not available to receive in the US, so those who really needed them were willing to do whatever it took.

Hope I helped!