Two blocks connected by a string with variable tension: A dynamic case

TL;DR

This paper investigates the dynamic behavior of two blocks connected by a string over a pulley, combining theoretical modeling with experimental validation to analyze the vertical displacement over time.

Contribution

It provides a detailed dynamic analysis of a two-block system with variable tension, including deriving motion equations and validating them experimentally using modern data acquisition and analysis tools.

Findings

Theoretical and experimental results agree within approximately 3.61% to 10.14%.

The vertical displacement y(t) can be modeled by a sixth-degree polynomial.

The system's motion was successfully simulated using Mathematica.

Abstract

In this paper, the dynamic case of a system made up of two blocks connected by a string over a smooth pulley is revisited. One mass lies on a horizontal surface without friction, and the other mass has a vertical displacement. The motion equation is obtained and its solution is determined using the Mathematica package. Also, an experimental montage for this system is made and experimental data for the vertical position $y$ in function of the time $t$ are obtained using a Data Acquisition System and the Tracker video analysis. The relation $y$ vs $t$ can be represented by a polynomial of degree six. An average relative error of 3.61 (10.14) % is obtained between the theoretical results acquired with Mathematica and the data taken from the Tracker (Data Acquisition System).