Physics 211 Experiment 4 Newton s Second Law Atwood s Machine Newton s second law FNET ma can be experimentally tested with an apparatus known as an Atwood s Machine See Figure 1 Two weights of unequal mass connected by a thread are draped over a pulley as shown in the figure When released the larger mass accelerates downward and the smaller one accelerates upward Figure 1a The Atwood s Machine showing the pulley and the two masses after a run Figure 2a A schematic diagram of the apparatus shown in Figure 1 Figure 1b A close up of the pulley and one of the masses after a run Figure 2b The free body diagram for M1 Figure 2c The free body diagram for M2 Newton s Second Law applied to the larger mass M2 implies see Figure 2c FNET on M2 M2a T M2g M2a 1 Newton s Second Law applied to the smaller mass M1 implies see Figure 2b FNET on M1 M1a T M1g M1a 2 The tension T can be eliminated from equations 1 and 2 obtain M2g M1g M2a M1a 3 The magnitude of the acceleration a of the system is then a M 2 M1 g 4 M1 M 2 The numerator M2 M1 g is the net force causing the system to accelerate The denominator M2 M1 is the total mass being accelerated Equation 4 can be written a THEOR FNET M TOTAL 5 Where FNET M2 M1 g And MTOTAL M2 M1 Apparatus Pasco 750 Interface 10 spoke smart pulley Pasco ME 9387 with stereo phone plug Table clamp for pulley Two 5 gram mass holders Masses 2 x 100gm 3 x 50gm 2 x 20gm 2 x 10gm 2 x 5gm Thread 01 13 19 2 Detailed Procedure and Analysis for Atwood s Machine Experiment I Set up of computer and interface 1 Turn on the PASCO 750 interface first Verify that the indicator light is on 2 Turn on the computer and login 3 Follow the instructions on the Data Studio Information Sheet to set up the computer for the experiment 4 When you must choose the sensor choose smart pulley 5 Under measurement choose velocity Ch1 m s make sure this is the only option checked 6 Note there is no calibration for this experiment 7 Now you are ready to set up and run the experiment the velocity as a function of time will be recorded by the computer and the computer will display the results graphically for you to analyze II Setting up and Running the Experiment 1 Clamp the smart pulley to the lab table as shown in the Figure 1 and plug its stereo phone plug into channel 1 of the interface 2 Set up masses M1 95 grams and M2 105 grams as shown Use the brass masses supplied When adding to obtain the total mass be sure to include the 5 grams for each weight holder 3 Hold the system steady with M2 far from the ground and allow the system to come into equilibrium i e make sure the masses are not swinging 4 To have the computer record the data click the start button on the computer screen and release the system After M2 has fallen to the ground click the stop button which will be in the same location as the start button III Determination of the Acceleration of the Masses 1 The computer will have plotted velocity vs time for you The slope of the best fitting line to the velocity as a function of time is the experimentally determined acceleration Determine the slope of the best fitting line and record it into an excel spreadsheet This spreadsheet should also include the values of M1 and M2 2 To obtain a reliable fit only data points recorded while the masses are in free fall should be included in the fit This part of the data can be selected by clicking down on the mouse from an initial position on the graph dragging the mouse to the final position 01 13 19 3 and releasing To obtain a close up view of this part of the data click on the scale to fit icon which is located in the top left hand corner of the graph window IV Measuring acceleration for M1 M2 constant with different values of M1 and M2 1 To obtain the value for the acceleration of another system with the same total mass but with different values of M1 and M2 increase the mass of M2 and decrease the mass of M1 by a fixed amount so the mass difference is 20 30 40 and 50 g the total mass should remain at 200g i e the mass of M2 runs from 105 to 125 g in increments of 5 g and the mass of M1 runs from 95 to 75 g in increments of 5 g For each run the total mass of the system M1 M2 should be equal to 200 g 2 Follow the instructions given above for each run and record the values of the masses and the experimentally determined acceleration into the excel spreadsheet Print out one or two typical graphs to include in your laboratory report V Measuring acceleration for M2 M1 constant with different values of M1 and M2 1 Choose initial values of M2 and M1 of 45 and 35 g respectively Run the experiment analyze the velocity vs time graph and determine the acceleration Record these results into a second excel spreadsheet along with the values of M1 and M2 2 To obtain a total of five runs increase each mass by 40 g rerun the experiment and record the results The mass difference should remain the same Thus M1 will take on values of 35 75 115 155 and 195 g while M2 should have the values of 45 85 125 165 and 205 g VI Analysis of the Results 1 Theory predicts that the acceleration is given by the net force divided by the total mass see equations 4 and 5 Now you should compare your experimentally determined acceleration with the theoretical prediction To determine the theoretical prediction create three new columns in the excel spreadsheets one for the net accelerating force M2 M1 g one for the total mass M1 M2 and one for the theoretically predicted acceleration Acceleration Net accelerating force total mass 2 Create another column for the percent difference between the experimental and theoretical values of acceleration 3 Another way to compare experimental and theoretical results is to plot the net force FNET vs the experimental acceleration Equation 5 indicates that this should be a straight line with slope equal to the total mass For the results obtained in part IV with the total mass constant plot FNET versus experimental acceleration and fit the graph with a straight line 01 13 19 4 Compare the slope of the line with the actual total mass 200 kg What is the percent error Print out this graph and include it in your laboratory report 4 Theory predicts that when the net force is constant the acceleration will vary inversely with total mass see …