Ancient siege engines like catapults and trebuchets harnessed mechanical forces like tension and gravity to fling projectiles at fortifications from a safe distance. Catapults stored tension in twisted ropes or bent wood to launch payloads, while trebuchets used counterweights on a swinging arm to fling projectiles with range and accuracy. The document suggests building simple catapult and trebuchet models to experiment with these mechanical principles in a safe manner.