If everything is working correctly and you haven't found some previously unknown game breaking bug the following should be how you get through.
Spoilers:
I imagine it's not the most surprising to learn that any obstacle in the game that gives you multiple chances before seemingly killing you arbitrarily is actually dealing damage to your health. The death state of the obstacle is engaged when you interact with that obstacle and your health is dropped to 0. The second area, especially combined with the first is designed to be impossible to cross with your current health.
However the vending machine in combination with the coin on a string you should have gotten from the research area allows you to restore your health to full which should allow you to get across provided you don't take the wrong path.
Assuming everything is working correctly, you should just have to interact with the vending machine. If that doesn't work... I'll ask you to provide more explanation on exactly what you're doing that is causing this to see if there is a bug in play.
Thank you for enjoying the game.