THE FRICTIONLESS SLIDING OF AN OBJECT ALONG A ROPE

A new method is proposed to analyze the internal force in a rope in the process of an object sliding along it without friction. A set of equations for the coupled motion is established on the basis of Newton's second law. Then, it is solved numerically by using the Runge-Kutta method, and the results are fitted through the Matlab software to obtain the formulas of motion. With the combination of the fitted formulas and the equations of motion, the internal force in the rope, as the object sliding along, is determined. Under different initial states of the object, the results, analyzed by the proposed new method, show that the internal force in the rope changes periodically in accordance with the simple harmonic motion of the object. The higher the object is released, the larger velocity and acceleration it achieves when passing through the same point on the rope, so does the internal force in the rope.