PWV 10 Atwood's Machine

LabQuest App 10 Atwood’s Machine A classic experiment in physics is the Atwood’s machine : two masses on either side of a pulley connected by a light string. When released, the heavier mass accelerates downward while the lighter one accelerates upward at the same rate. The acceleration depends on the difference in the two masses, as well as the total mass. In this lab, you will determine the relationship between the two factors that influence the acceleration of an Atwood’s machine using a Photogate to record the machine’s motion. Figure 1 OBJECTIVES l Use a Photogate to study the acceleration of an Atwood’s machine. l Determine the relationships between the masses on an Atwood’s machine and the acceleration. Physics with Vernier ©Vernier Software & Technology 10 - 1

MATERIALS LabQuest LabQuest App Vernier Photogate with Ultra Pulley Attachment mass set string, 1.2 m long Logger Pro or graph paper (optional) PRELIMINARY QUESTIONS 1. If two objects of equal mass are suspended from either end of a string passing over a light pulley, as in Figure 1, what kind of motion do you expect to occur? Why? 2. Draw a free-body diagram of the left-side mass in Figure 1. Draw another of the right-side mass. Include all forces acting on each mass. 3. Do the two masses have the same acceleration? Why? 4. How would you expect the acceleration of an Atwood’s machine to change if you l Increase the mass on one side and decrease the mass on the other, keeping the total mass constant? l Gradually increase the mass of both sides, keeping the difference in mass constant? PROCEDURE Part I Constant Total Mass For this part of the experiment you will keep the total mass used constant, but move weights from one side to the other. The difference in masses changes. Figure 2 1. Set up the Atwood’s machine apparatus as shown in Figures 1 and 2. Note : The masses must be able to move at least 40 cm before the heavier mass strikes the floor. 2. Connect the Photogate with Ultra Pulley to a digital (DIG) port of LabQuest and choose New from the File menu. 10 - 2 Physics with Vernier Experiment 10

DATA TABLE Part I Constant Total Mass Trial m 1 (g) m 2 (g) Acceleration (m/s 2 ) m diff , m 1 – m 2 (g) m T (g) 1 2 3 4 5 Part II Constant Mass Difference Trial m 1 (g) m 2 (g) Acceleration (m/s 2 ) m diff , m 1 – m 2 (g) m T (g) 1 2 3 4 5 ANALYSIS 1. For each trial, calculate the difference between m 1 and m 2 . Enter the result in the column labeled m diff . 2. For each trial, calculate the total mass in grams. Enter the result in the column labeled m T . 3. Using LabQuest, Logger Pro , or graph paper, plot a graph of acceleration vs. m diff , using the Part I data. Based on your analysis of the graph, what is the relationship between the mass difference and the acceleration of an Atwood’s machine? 4. Similarly, plot a graph of acceleration vs. m T , using the Part II data. Based on your analysis, what is the relationship between total mass and the acceleration of an Atwood’s machine? 5. Develop a single expression for the acceleration of an Atwood’s machine, combining the results of the previous two steps in the analysis. 10 - 4 Physics with Vernier Experiment 10

Atwood’s Machine EXTENSIONS 1. Draw a free body diagram of m 1 and another free body diagram of m 2 . Using these diagrams, apply Newton’s second law to each mass. Assume that the tension is the same on each mass and that they have the same acceleration. From these two equations, find an expression for the acceleration of m 1 in terms of m 1 , m 2 , and g . Compare the expression to your result in Step 5 of Analysis. 2. For each of the experimental runs you made, calculate the expected acceleration using the expression you found with Newton’s second law of motion and the specific masses used. Compare these figures with your experimental results. Are the experimental acceleration values low or high? Why? 3. An unknown mass can be placed on one side of the Atwood’s machine. Using lab measurements and any necessary calculations, the mass of the unknown can be determined. Try it. 4. How does the force exerted upward by the pulley change as the system begins accelerating? Why? Set up an experiment to determine how this force changes. 5. How does the tension in the string change as the masses start to move? Or does it? Physics with Vernier 10 - 5