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04d Atwood's MachineRVS-Revised 1
Atwood’s Machine
Introduction In this lab we will investigate the application of Newton’s Second Law to a simple physical system known as Atwood’s Machine. Under the right circumstances it is possible to use this machine to measure accelerations very accurately. The purpose of this lab is to use Atwood’s Machine for making a determination of “g”, the acceleration due to gravity.
Equipment Needed Clamp, swivel 90° Weight Hanger, 50g(2) Mass Set, Gram Ringstand, 120cm String (1.5m)
Computer with Data Pro Software Photogate Smart Pulley LabPro Interface
Theory Our version of Atwood’s Machine consists of two masses suspended over a pulley as shown in the figures above and below. If the two masses are equal in value, then the system will be in equilibrium and no motion will take place. If the two masses are close to each other in value, then the acceleration of the masses will be small, and can be accurately measured. This makes
Atwood’s Machine a technologically useful device for the determination of the acceleration due to gravity. The acceleration of the two masses is given by
a mm mm g 1 2
1 2
= −. (Equation 1)
You will derive this formula from the application of Newton’s 2nd^ Law to the Atwood Machine and include your derivation as part of your lab report. Masses can be measured very accurately, and if we can measure the acceleration accurately as well, then Atwood’s Machine can be used to give an accurate value for g. Our measured values of these accelerations will be used to calculate an estimate of “g”.
Figure 1 Atwood’s Machine
Procedure Motivated by the discussion above, we need to measure the acceleration of the masses. We will utilize a device known as a smart pulley to measure these accelerations. For now, we can think of the smart pulley as a device that measures the speed of the string as it rides on the rotating pulley. Later in the semester, we will investigate its operation in more detail.
1. Set up Feed a 1.5m length of string through the smart pulley. There should be small loops tied in both ends of the string. Hang a weight hanger on a loop at each end of the string. Clamp the smart pulley so that the masses hang over the end of the table and can move freely without hitting table.
- Preliminary Observations (Predict the results of the following experiment.)
Experimental Procedure - Constant System Mass Place 50g on one of the weight hangers and 52g on the other. The 50g side should contain at least four (4) 1g masses. Click on the Collect button to start the data collection and then release the masses. Make sure that the masses do not swing during the experiment. Click on the Stop button to end the data collection. To optimize the graphs for easier viewing click on the “A” (Auto-Size) button at the top of the screen. Although Distance, Velocity and Acceleration graphs are displayed we will be using the velocity graph to determine the acceleration of the masses.
- Click on the velocity graph and drag a box around the relevant velocity data. This will be the straightest part of the positively sloping graph. Avoid the first few points and stop selecting points before the graph starts to turn down.
- Choose the Linear Fit button along the top of the screen. This will calculate the slope of the linear fit line to the velocity data. This slope is the experimental value of the acceleration of the masses.
- Record the value of the slope in the data table along with the value both masses.
Include Slope Uncertainty Data : With the cursor over the Linear Fit data box Apple: Hold down the Control key and press enter or click on the data box with the mouse. Windows PC: Right Click on the data box This will bring up a Pop-Up box – select the “Linear Fit Options” choice. Another Pop-Up box will appear – put a check in the box next to “Show Uncertainties.” Click OK. The original Linear Fit data box will now display the Slope and the Y- Intercepts and their respective uncertainties. Record the slope uncertainty in your data table.
Repeat the experiment and analysis four more times, each time moving an additional 1g mass from the lighter side to the heavier side. There should be a total of 5 data sets when you are done.
Figure 2 Experimental Set-up
Data Analysis Use MS Excel to perform the following analysis.
1. Construct a graph of a (Vertical axis)vs. ( (^ ))
1 2
1 2 m m
m m
− (^). (Horizontal axis). The measured
acceleration “a” should be plotted on the y-axis and the mass difference ratio should be plotted on the x-axis Based on your theory given in equation (1), what would you expect the slope and y intercept of this graph to be? Include the best-fit line on your graph. Print a copy of your graph.
2. Find the standard error estimate for the slope of the best-fit line of a vs. ( (^ ))
1 2
1 2 m m
m m
- Record your best-fit slope and y intercept along with the standard error estimates in the data table. If you are using Excel then you will need to use the LINEST Worksheet function to calculate the uncertainties in the slope. Start by selecting a 2-column by 2 –row area of cells on the spreadsheet. Then, under the Inset menu item select the Function option – or – click on the “ fx ”
Report Format This lab will require a full write-up from each student individually. You should follow the format specified in the handout Format for Formal Lab Reports. You should include the derivation of the acceleration for the Atwood’s Machine, including relevant sketches and free body diagrams in the Introduction section of the report. Your report should include your graph and cleaned up data tables. Your preliminary observations should be attached as an appendix. In other words, staple your lab hand out to the back of your write up.
Data Table
m 1 (kg) m 2 (kg)
ABS(m 1 -m 2 )/ (m 1 +m 2 )
ameas (m/s^2 )
ameas Uncertainty (m/s^2 )
Slope ________________________ ± Uncertainy ______________________
*% Uncertainty = Uncertainty 100/Slope _________________
