Mechanical problem-solving training in exam-oriented education cultivates students’ application abilities but lacks training in exploration skills. The ETA Physics Problem-Solving Method, based on the ETA Physics Cognitive Model, transforms problems into research topics. The process of solving problems is also a scientific research process, which can simultaneously train scientific cognition, scientific methods, and scientific spirit, truly achieving the unification of teaching, learning, examination, and research. This paper illustrates the advantages of the ETA Physics Cognitive Model in problem-solving by analyzing a mechanics competition problem using the ETA Physics Problem-Solving Method, laying the foundation for students to better apply ETA in scientific research, artificial intelligence, and other fields in the future.