4 Plota graph of acceleration ve total mass, using the Part Il data. Based on your analysis of the graph, what is the relationahip betwoen total mass and the neceleration 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. Drawa free body diagram of m and another free body dingram of m. 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, in terms of m, m, and g. Compare the expression to your result in Step S 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? PSRE ROCPING TO Mass Contant Trial m, (a) m2 (g) Acceleration (m/s") Am my (ka) (kg) 1. 80 75 0.2509 0.05 O. 015 O.155 0.155 O. IS5 2 85 70 0.8421 1.427 3 65 O.025 0.035 0.045 90 4 15 60 2.275 O.155 55 a.632 0.155 Part II: Keeping The Mass Difference Constant Trial Acceleration Am (g) (9) (m/s) (kg) (kg) 1. 120 l00 0.8OC4 0,02 0.220 2 140 O. 260 0.6883 O.S907 O SI84 O. 4611 120 O.02 3. 160 140 0.02 O. 300 160 0.340 4 180 O.02 5. o. 380 200 O.03 ANALYSIS - For each trial, calculate the difference between m, and m; in kilograms. Enter the result in th column labeled Am. For each trial, calculate the total mass in kilograms. Using Logger Pro, plot a graph of acceleration vs. Am, 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? 6