Lab Atwoods Machine_Final

1 Pre Lab (5%) Comments: __5___ Format (5%) 1. Lab Title and Team members name. comments: 2. Each section clearly labeled, neat & organized. _2.5___/2.5 _2.5___/2.5 Purpose (5%) 1.Proper statement of purpose __5___ Apparatus & Procedure (11 %) 1. Independent and dependent variables are clearly identified 2. Diagram drawn with all components labeled 3. Clear and brief sequence of steps followed, including an explanation of the control of variables 4. Description of data collection methods. _3___/3 _2___/2 _3___/3 _3___/3 Data (15 %) 1. Measurements organized into a neat table; 2. Values are clearly labeled, correct units; 3. Significant figures of data; 4. Quality/range/ multiple trials (when appropriate); 5. Table of generated values, labeled with units. _3___/3 _3___/3 _3___/3 _3___/3 _3___/3 Evaluation of Data (31 %) 1. Graphs: • Variables on appropriate axes (use of units); • Quality of results. 2. Interpretation of graphs and Mathematical Model: • Brief written statements of relationships shown on the graphs; • Equation of the relationship obtained from the graph; • Correct interpretation of slope and y intercept. 3. Sample of Calculations with Units and Significant Figures 4. Answer to the Analysis questions. 5. Correct units and Calculation of % error. comments: _3___/3 _3___/3 _4___/4 _4___/4 _4___/4 _4___/4 _6___/6 _3___/3 Conclusion (28% ) Quality of written explanation of relationships. The discussion must include all of the following: 1. New terms and concepts: Definitions according to the textbook; 2. Physical meaning of slope / significance of Y-intercept; 3. Conditions and derivations of general equations; 4. Reasonable explanation for divergent results; 5. Textbook correlation. (4 %) comments: TOTAL: Grade: _4___/4 _4___/4 _12___/12 _4___/4 Appendix B: Individual Lab Report Rubrics Experiment _Atwood ’ s Machine and Newton ’ s Second Law_______________ Student Name: __Luis Goicoechea___________________________________

2 40 cm INTRODUCTION: Miami-Dade College PHY2048L Newton’s Second Law; Atwood’s Machine* Purpose: The purpose of this lab is to use an Atwood’s machine to determine the relationship between acceleration and the masses using acceleration vs difference in mass and acceleration vs total mass graphs and using Newton’s Second Law of Motion for a system of objects. Figure 1 PRELIMINARY QUESTIONS: 1. If two equal masses are suspended from either end of a string passing over a light pulley (an Atwood’s machine), what kind of motion do you expect to occur? Why? If there are two equal masses hanging from either end of a string passing over a light pulley, I expect there to be no motion unless some force is introduced, as the masses would be in equilibrium so the acceleration of the system would be zero. Logger Pro

4 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 six different combinations. Part II Constant Mass Difference For this part of the experiment, you will keep the difference in mass between the two sides of the Atwood’s machine constant and increase the total mass. 9. Place a 20g and 30g total as ? 1 and ? 2 , respectively. 10. Repeat Steps 6 – 7 to collect data and determine the acceleration. Pulley Mass 1

5 11. Add 5g to each mass to increase both sides by the same amount as to keep the difference in mass 10g and increasing the total mass by 10g each time. Record the resulting mass for each combination in the data table. Repeat Steps 6 – 7 for each combination. Repeat the procedure until you get complete part II table. DATA TABLE: Part I: Total Mass Constant Trial m 1 (g) m 2 (g) Acceleration Trials ( ? / ? 2 ) Average acceleration ( ? / ? 2 ) ∆? (g) ? 𝑇 (g) 1 50 40 0.8152 0.8831 0.8506 0.8496 10 90 2 55 35 1.912 1.938 1.953 1.934 20 90 3 60 30 2.979 2.911 2.971 2.954 30 90 4 65 25 3.981 3.922 3.868 3.924 40 90 5 70 20 5.010 4.818 4.701 4.843 50 90 6 75 15 6.005 5.970 6.036 6.004 60 90 Part II: The Mass Difference Constant Trial m 1 (g) m 2 (g) Acceleration (m/s 2 ) Average acceleration ( ? / ? 2 )  m (g) m T (g) 1 30 20 1.636 1.635 1.634 1.635 10 50 2 35 25 1.357 1.349 1.359 1.355 10 60 3 40 30 1.170 1.133 1.137 1.147 10 70 4 45 35 1.015 1.018 1.004 1.012 10 80 5 50 40 0.8616 0.8714 0.8741 0.8690 10 90 6 55 45 0.8389 0.8346 0.8106 0.8280 10 100

7 ∆? = ? 1 − ? 2 = 50𝑔 − 40𝑔 = 10𝑔 3. For each trial, calculate the total mass ? 𝑇 = ? 1 + ? 2 . Enter the result in the column labeled ? 𝑇 ? 𝑇 = ? 1 + ? 2 = 30𝑔 + 20𝑔 = 50𝑔 4. Plot a graph of acceleration vs.  m, 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? The acceleration of an Atwood’s machine is directly proportional to the mass difference between the two hanging masses. We can see from the graph that the acceleration increases by 0.0996 m/s 2 for every 1 g increase in the mass difference. 𝑎 ∝ ∆m ????? = ∆? ∆? = ∆𝑎 ∆? = 0.09996 ? ? 2 1𝑔 ? − 𝑖???????? = ? 𝑥=0 = −0.06900 ?/? 2 𝑎 = 0.09996 ? ? 2 𝑔 ∆? − 0.06900 ?/? 2 5. 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?

8 From the graph we can see that the average acceleration of an Atwood’s machine is inversely proportional to the total mass of the two objects hanging. Since the acceleration is inversely proportional to the total mass, we can linearize the graph by making the x-axis 1/total mass. With this we can see that the acceleration is directly proportional to 1/total mass. 𝑎 ∝ 1/? 𝑇

10 When the two masses are not moving, the system is in equilibrium and the net force is zero, this means that the tension will equal the force of gravity. Once the objects are accelerating, the net force will be equal to mass times acceleration, so the tension will equal the mass times acceleration plus/minus the mass times gravitational acceleration. EXTENSIONS: 1. Draw a free body diagram of m 1 and another free body diagram of m 2 . T 2 T 1 T 1 =T 2 F g1 =m 1 g F g2 =m 2 g 2. Use the diagrams and Newton’s 2 nd Law to determine the acceleration of the system, start by writing the equation of motion for each mass. Use that the value of the acceleration for both objects is the same and so are the tensions at each end of the string, then solve for the acceleration of system in terms of m 1 , m 2 , and g . Compare the expression to your result in Step 6 of Analysis. ∑ 𝐹 1 = ? 1 𝑎 −𝑇 + ? 1 𝑔 = ? 1 𝑎 → 𝑇 = −? 1 𝑔 + ? 1 𝑎 ∑ 𝐹 2 = ? 2 𝑎 → 𝑇 − ? 2 𝑔 = −? 2 𝑎 → −? 1 𝑔 + ? 1 𝑎 − ? 2 𝑔 = −? 2 𝑎 ? 1 𝑔 − ? 2 𝑔 = ? 2 𝑎 + ? 1 𝑎 → ? 1 − ? 2 ? 1 + ? 2 ∗ 𝑔 = 𝑎 The expressions are the same. 3. For four of your experimental runs (two and two), 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? Table 1 Trial 1:

11 50𝑔 − 40𝑔 50𝑔 + 40𝑔 ∗ 9.81 ? ? 2 = 1.09 ? ? 2 Table 1 Trial 2: 55𝑔 − 35𝑔 55𝑔 + 35𝑔 ∗ 9.81 ? ? 2 = 2.18 ? ? 2 Table 2 Trial 1: 30𝑔 − 20𝑔 30𝑔 + 20𝑔 ∗ 9.81 ? ? 2 = 1.96 ? ? 2 Table 2 Trial 2: 35𝑔 − 25𝑔 35𝑔 + 25𝑔 ∗ 9.81 ? ? 2 = 1.64 ? ? 2 The experimental acceleration values are lower than the calculated values. This discrepancy can be explained by the fact that when we are calculating the values we are assuming that the pulley is completely frictionless, the string connecting the masses is assumed to be massless and we are not taking into consideration air resistance slowing down the masses. CONCLUSION : 1. Definitions: acceleration, force, tension, force of gravity, statements for Newton’s Laws Acceleration: the rate of change of velocity with time. Force: an interaction between two objects or between an object and its environment Tension: the pulling force exerted by a stretched rope or cord on an object to which it’s attached. Force of gravity: force exerted on an object by the pull of the earth. Newton’s 1 st Law: An object acted on by no net external force has a constant velocity (which may be zero) and zero acceleration. (Chapter 4.2 Pg. 104) Newton’s 2 nd Law: If a net external force acts on an object, the object accelerates. The direction of acceleration is the same as the direction of the net external force. The mass of the object times the acceleration vector of the object equals the net external force vector. (Chapter 4.3 Pg. 109) Newton’s 3 rd Law: If object A exerts a force on object B (an “action”), then object B exerts a force on object A (a “reaction”). These two forces have the same magnitude but are opposite in direction. These two forces act on different objects. (Chapter 4.5 Pg. 116)

13 collided which could also account for a higher error percentage. 5. Textbook correlation. Chapter 2.3 Pg.41 Chapter 4.1 Pg.101 Chapter 4.4 Pg.114 Chapter 4.2 Pg. 104 Chapter 4.3 Pg. 109 Chapter 4.5 Pg. 116 Chapter 4 Summary Pg.121 Note: This lab was developed by Dr. Jorge Gibert, Physics Professor at Wolfson Campus.