Lab Atwood's Machine PHY1111 (1)

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Community College of Denver *

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1111

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Physics

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Dec 6, 2023

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docx

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5

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Department of Physics and 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 will accelerate 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 which influence the acceleration of an Atwood’s machine using a Photogate for measuring acceleration. OBJECTIVES: Use a photogate to study the acceleration of an Atwood’s machine. ● Determine the relationships between the masses on an Atwood’s machine and the acceleration of the system. MATERIALS: Computer utility Universal Lab Interface ● Logger Pro Vernier Photogate with Super Pulley ● 500 g of various masses Second pulley ● String Graphing utility or graph paper CCD - Physics 211 - Atwood’s Machine 1 of 7
PRELIMINARY QUESTIONS: 1. If two equal masses are suspended from either end of a string passing over the pulleys, what kind of motion do you expect to occur? Why? 2. Regarding an Atwood’s machine, how would you expect the acceleration to change if you: Move mass from one side to the other, keeping the total mass constant? ● Gradually increase the mass of both sides, but keep the difference constant? 3. Why do the two masses have the same acceleration? 4. Draw a free-body diagram of the left side mass ( m 1 ). Draw another of the right side mass ( m 2 ). Include all forces acting on each mass. PROCEDURE: Part I: Keeping the total mass (m T ) constant For this part of the experiment, you will keep the total mass (m 1 + m 2 ) constant, but move weights from one side to the other. The difference in mass changes. 1. Set up the Atwood’s machine apparatus as shown in Figure 1. 2. Connect the Photogate with Super pulley to the DG 1 Port of the Universal Lab Interface. 3. Prepare the computer for data collection by opening “10 Atwoods Machine.cmbl” from the “_Physics with Vernier” experiment files of Logger Pro. A graph of velocity vs. time will be displayed. 4. Arrange a collection of masses totaling 250 g on m 2 and a 250 g mass on m 1 . What is the acceleration of this combination? Record your values for mass and acceleration in the data table. 5. Move 5 g from m 2 to m 1 . Record the new masses in the data table. 6. Position m 1 as high up as it can go. Steady the masses so they are not swinging. Click “Collect” to begin data collection. Wait one second and CCD - Physics 211 - Atwood’s Machine 2 of 5
release the masses. Catch the falling mass before it strikes the floor or the other mass strikes the pulley. 7. Select the region of the graph where the velocity was increasing at a steady rate. Click the “Linear Fit” button, circled below, to fit the line y = mx + b to the data. Record the slope, which is the acceleration, in the data table. 8. Continue to move masses from m 2 to m 1 in 5 g increments, changing the difference between the masses, but keeping the total constant. Repeat Steps 6 - 7 for each mass combination. Repeat this step until you get at least five different combinations. Part II: Keeping the mass-difference (Δm) constant For this part of the experiment, you will keep the difference in masses between the two sides of the Atwood’s machine constant. The total mass changes. 9. Put 120 g on m 1 and 100 g on m 2 . 10. Repeat Steps 6 – 7 to collect data and determine the acceleration. 11. Add mass in 20 g increments to both sides, keeping a constant difference of 20 g for all trials. Record the resulting mass for each combination in the data table. 12. Repeat Steps 6 - 7 for each combination until you get at least five different combinations. DATA COLLECTION: Part I: Keeping the Total Mass Constant Trial m 1 (g) m 2 (g) Acceleratio n ( m/s 2 ) Δm (g) m T (g) 1 CCD - Physics 211 - Atwood’s Machine 3 of 5
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2 3 4 5 Part II: Keeping the Mass-Difference Constant Trial m 1 (g) m 2 (g) Acceleratio n ( m/s 2 ) Δm (g) m T (g) 1 2 3 4 5 ANALYSIS: 1. For each trial, calculate the difference between m1 and m2 in grams. Enter the result in the column labeled Δm. 2. For each trial, calculate the total mass in grams. 3. Using Graphical Analysis, Excel, or graph paper, plot a graph of acceleration vs. Δm , 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. Using Graphical Analysis, Excel, or graph paper, plot a graph of acceleration vs. total mass , using the Part II data. Based on your analysis of the graph, 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. 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 CCD - Physics 211 - Atwood’s Machine 4 of 5
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? CCD - Physics 211 - Atwood’s Machine 5 of 5