Current high-performance applications are typically implemented on large-scale general-purpose distributed or multiprocessing systems often based on commodity microprocessors. Field-Programmable Gate Arrays (FPGAs) have now reached a level of sophistication that they too could be used for such applications. In this paper we explore the feasibility of using FPGAs to implement large-scale application-specific computations by way of a case study that implements a novel molecular dynamics system. The system has been designed such that it is scalable and parallelizable. On the Transmogrifier 3 (TM3), the system performs calculations on an 8,192 particle system in 37 seconds at 26 MHz. This implementation shows that by scaling to more modern parts running at 100 MHz, a speedup of over 20 x can be achieved compared to a state-of-the-art microprocessor. This can also be achieved at less cost, using less power and taking less space than a standard microprocessor-based system, while maintaining the computational precision required.