Teacher guide featuring 15 labs designed for Advanced Placement Physics 1.
Students use a photogate and pulley system to determine the mathematical relationship between the acceleration of an Atwood’s machine, the difference between its two masses, and the sum of those two masses.
How is the acceleration of the two masses of an Atwood’s machine affected by their difference in mass and by their total mass? Experimentally determine the mathematical relationship between the acceleration of an Atwood’s machine, the difference between its two masses, and the sum of those two masses.
The Structured version of this lab activity is divided into two parts: Part 1 – Students transfer masses from the heavier side of the Atwood’s machine to the lighter side to vary the mass difference m2 – m1 (and thus net force) while keeping the total mass m2 + m1 constant. In each trial they determine the acceleration from the slope of a plot of the speed versus time while the masses were moving freely. Plotting acceleration versus the mass difference for all Part 1 trials will result in a straight line, and from that students are expected to determine the proportional relationship. Part 2 – Students remove equal masses from both sides of the Atwood’s machine to vary the total mass m2 + m1 while keeping the mass difference m2 − m1 (and thus net force) constant and determine the resulting acceleration as in Part 1. Plotting acceleration versus the inverse total mass (1/total mass) will result in a straight line, and from that students are expected to determine the inverse proportional relationship. Students are then asked to combine the two discovered proportionalities into an equation relating the three variables, and to determine the value of the proportionality constant k, which should be found to be near the value of the free fall acceleration due to gravity g. Finally, students are asked to derive the equation for the theoretical acceleration of an Atwood’s machine and compare it to their experimentally-derived expression.
This experiment may require software and an interface for data collection.