NewtonÕs Laws and Modified AtwoodÕs Machine

Overview

The purpose of this investigation is to validate NewtonÕs Second Law of Motion and explore properties of friction and AtwoodÕs machine.  Lab equipment will be used to measure force, mass, and acceleration.  Force and acceleration data will be measured by a Wireless Dynamics Sensor System (WDSS).  Both sets of electronic data will be collected and analyzed by a LabQuest2 device.  Mass data will be determined simply with a triple beam balance. 

 

The Modified AtwoodÕs Machine

In this lab, an object of constant mass is pulled across a level surface by a weight hanging on a string that passes over a pulley.  By changing the weight at the end of the string, different amounts of force can be applied to the object.  It is important to realize that it is the tension in the string that is causing the object to accelerate.  This tension will be measured by the WDSS, which also serves as the test object.

Procedure

1.     Adjust the feet of the track so that its surface is level.

2.     Attach a piece of felt to the bottom of the WDSS to protect the device and promote a smooth and steady slide across the track.  Place the WDSS face up on the track.

3.     Attach the pulley to the end of the track and adjust the height of the pulley to match that of the hook of the force sensor.

4.     You must connect (i.e. ÒpairÓ via Bluetooth) and calibrate the force sensor.  Turn on the Wireless Dynamics Sensor System (WDSS).  Then under the Sensor menu choose WDSS SetupÉ and scan for the wireless device.  You should see the name of your sensor that is on the label on its side.  For this experiment you will use only the Force sensor and the x-axis Accelerometer – do not enable the other two acceleration sensors or the altitude sensor.

5.     Once it is connected, go to the Sensor menu choose Calibrate and WDSS Force.  Place the WDSS face up on the level track.  Then enter zero for Known Value 1 with nothing touching the force sensorÕs hook.  Then apply a known force to the sensor by attaching a string to the hook, passing it over the pulley, and hanging a 500 gram mass on the end – note: you must hold the WDSS in place to prevent it from moving with this mass on the end of the string.  Enter the correct force value for Known Value 2.  Remove the 500 gram mass after this process!

6.     Now choose Calibrate and WDSS Accelerometer (x).  With the WDSS face up at rest on the level track enter zero for Known Value 1.  Then hold the WDSS at rest with the positive x-axis pointing straight up.  Enter 9.8 m/s2 for Known Value 2.  (This works because the movable part within the accelerometer bends the same amount when pulled down by gravity as it would if it accelerated 9.8 m/s2 across the track in the positive x-direction.)

7.     Adjust the data collection parameters and make the duration of the experiment 2 seconds, collecting 100 samples per second.

8.     Now place a 50-gram mass on the end of the string passing over the pulley and connect the other end to the hook on the WDSS force sensor.

9.     Pull the WDSS away from the pulley and release it such that it slides freely away from the pulley and then reverses direction under the influence of friction and the weight at the end of the string.  Collect data for this motion – tap the Ògreen arrowÓ button lower left of the screen.

10.  You should now be looking at graphs of acceleration vs. time and force vs. time.  On each graph you should be able to identify a ÒspikeÓ that represents the tug of the person followed by a ÒplateauÓ that represents the WDSS sliding away from the pulley.  If this is not the case then simply click the green arrow Collect button to repeat the experiment until you have suitable graphs.

11.  On the force graph find the ÒplateauÓ that represents the WDSS sliding away from the pulley.  Tap and drag to select only this portion of the graph – do not include sections of the graph where the WDSS was tugged by the person or where it slid toward the pulley.  Then go to the Analyze menu and choose Statistics to get the mean force and the mean acceleration.  Record these mean values as tension and acceleration in the table. 

12.  Repeat the process to measure force and acceleration for the WDSS sliding toward the pulley.  Note:  depending on the amount of weight at the end of the string you may be able to simply release the WDSS or you may need to give the string a tug to get it started moving.

13.  Adjust the appearance of the graphs to your liking and then print ONE representative graph of each type including the analysis showing how the values in the table were determined.  Do not print graphs for every trial.  The goal here is to have a printed record showing one example of the manner by which the tension and acceleration values were determined.

14.  Change the mass on the end of the string to the values shown in the table and repeat the experiment to collect further data.  Note you should also measure the acceleration of the WDSS sliding in either direction with zero mass – i.e. disconnect the string (first row in the table).  And choose a value of mass for one final trial to complete the last row of the table.

15.  Measure the total mass of the sliding object (the WDSS and anything attached to it).  And measure the mass of the string.

 

Analyses

 

1.     Use the results to produce a tension vs. acceleration graph.  Plot the independent variable (tension) on the y-axis.  Use different symbols and/or colors for the WDSS sliding away and for the WDSS sliding toward the pulley and include a key or legend.  Determine an appropriate line or curve of best fit and its equation for each of the two sets of data.

2.     The mass at the end of string had the same amount of acceleration as that measured for the cart.  Use the acceleration and the mass of the hanging weight to calculate the tension at the Òhanging endÓ of the string.  Create a table and a corresponding graph of calculated tension (at one end of the string) versus the measured tension (at the other end) for the two sets of data – away and toward the pulley.  Again use different symbols/colors and determine a best fit for each set of data.

 

 

Modified AtwoodÕs Machine

 

 

Total mass of sliding object:

 

 

Mass of the string:

 

 

Sliding away from the pulley

Sliding toward the pulley

Mass hanging on string (g)

Tension
(N)

Acceleration
(m/s2)

Tension
(N)

Acceleration
(m/s2)

0.0

–

 

–

 

20.0

 

 

 

 

50.0

 

 

 

 

70.0

 

 

 

 

100.0

 

 

 

 

120.0

 

 

 

 

150.0

 

 

 

 

 

 

 

 

 

 

 

Questions (2 ea)

1.     (a) Make a free body diagram for the WDSS sliding away from the pulley.  Write the equation of motion and solve for the tension symbolically.  (b) Make a free body diagram for the WDSS sliding toward the pulley.  Write the equation of motion and solve for the tension symbolically. 

2.     Consider the lines of best fit for the graph of Tension vs. Acceleration.  (a) What do the slopes represent?  (i.e.  should equal what?)  Explain your answer.  (b) Assuming the values on your data sheet are accurate, calculate the percent error in the two slope values.  Show your work. 

3.     Again consider the lines of best fit for the graph of Tension vs. Acceleration.  (a) What do the y-intercepts represent (i.e. should equal what?)  Explain your answer.  (b) Ideally how should the two y-intercepts compare to one another?  And if this is not the case how can the discrepancy be explained? 

4.     (a) Show one example of how you calculated the tension in the string based on the hanging mass and its acceleration.  (b) Discuss the significance of the results shown in the calculated tension vs. measured tension graph.

5.     Discuss error in this lab.  (Things to discuss:  indications and signs of error – random and/or systematic, the probable and significant cause(s) of the error that is apparent in the results.  The goal of discussing error is to explain satisfactorily why the results of your lab are not quite exactly what was expected.  Be as specific as possible.  You will almost always have  unexpected results in an experiment.  Your task is to write a discussion that is intelligent, thoughtful, and insightful!) 

 

A complete report (50 pts):  (5 or 6 pages in this order)

q  Completed data/results table.  (10)

q  Example graphs of Force vs. Time and Velocity vs. Time, including analyses.  (10)

q  Tension vs. Acceleration graph with lines of best fit.  (10)

q  Calculated Tension vs. Measured Tension table and graph with lines of best fit.  (10)

q  Responses to questions  (10)