Experimental investigation of Newton's second law using a two-mass pulley system

Abstract

This study investigates Newton’s second law of motion, F = ma, through a two-mass pulley system. The experiment aimed to measure the relationship between the applied force and the resulting acceleration while considering the system's total mass. A wheeled cart (m₁) was connected to a hanging mass (m₂) by a nearly massless string over a low-friction pulley. The cart’s acceleration was measured as it traveled along a horizontal track, and both theoretical and experimental accelerations were calculated for comparison. Initially, our results did not match predictions of Newton's second law. Significant discrepancies between acceleration values were observed, which we attribute to friction between the cart and the track. When we accounted for friction by including an explicit friction term, we saw good agreement. This work demonstrates the validity of Newton’s second law within experimental uncertainty.