In this work, we study several closely related problems involving chains, conveyor belts, and rockets, which are described and solved without the application of infinitesimal calculus, or even the concept of mathematical limit. On one hand, the novelty lies not in the problems themselves, but in the method used for their solution, which brings them down from more advanced courses of engineering studies to the ambit of early-stage students. On the other hand, they shed new light on old questions and give teachers the chance to discuss subtle matters on energy conservation that have led to some controversy in the recent past.