Question

Why is acceleration is the same for an object on two ends of a taut string in the analysis of dynamical systems? It's intuitive if the string is moving in a straight line, but not so if the string is curved over the side of a table or something like that. Please provide some rigorous justification if possible using Newton's. second law of motion represented by F=ma.

Answer 1

According to Newton's second law of motion, the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass. In a dynamical system with a taut string, the tension force acting on each end of the string is equal, leading to the same acceleration for the objects on both ends of the string.

Step-by-step explanation:

According to Newton's second law of motion, the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass. In a dynamical system with a taut string, the tension force acting on each end of the string is equal, leading to the same acceleration for the objects on both ends of the string.

When analyzing a dynamical system with a taut string, we consider the forces acting on each end of the string. Since the string is taut, the tension force acting on each end of the string is equal. Therefore, the net external force on each end is the same. As a result, the acceleration of the objects on both ends of the string will be the same.