Rube Goldberg was a cartoonist famous for creating fantastic contraptions that completed simple tasks through a complex series of reactions. The concept has become so synonymous with Goldberg that his name is a noun in itself. Popping a balloon is a great task to be completed by a Rube Goldberg.
Choose a Popping Method
Poking the balloon with a sharp object, like a tack or fork, is one option. The popping implement can be attached to a ruler or other object that will strike the balloon.
Heating the balloon will cause it to pop. For examle, a balloon placed over the lid of a flask that contains water, which is then heated, will burst.
The balloon can be dropped onto a sharp object like a tack, or onto or into something hot, such as a pot of boiling water.
Building Your Machine
Take an inventory of everything you can use in constructing your machine. There is no limit to what can go into it, so long as it can be trusted to work.
Work backward from the popping to the start. Once you know how you will pop the balloon, create your mechanism for that. Then work on forcing that to occur, and so on until you are at the start of your machine.
Draw up plans before constructing your machine.
Test your machine in segments, if they can be set off more than once. Test two to three sections at a time.
Build your device, and trigger the first mechanism to begin the popping process.