Newton’s Second Law of Motion

Overview

The purpose of this investigation is to validate Newton’s Second Law of Motion in two situations.  In part A, a lab cart will be accelerated by means of a modified Atwood’s machine.  In part B, the cart will be accelerated by a bungee cord.  The goal is to explore the relations between force, mass, and acceleration. 
            Force data will be collected by a force sensor (which must be calibrated).  Mass data will be collected with a triple beam balance.  Acceleration data will be collected by a CBR sonic ranging device working in connection with Logger Pro 3 software running on a Windows computer. 

Part A – Modified Atwood’s Machine

In this section of the lab, a cart of constant mass is pulled 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 cart.  It is important to realize that it is the tension in the string that is causing the cart to accelerate.  This tension will be measured by a force sensor attached to the top of the cart.

Procedure

1.      Connect the CBR to DIG/SONIC 1 and the force sensor to CH 1.  Connect the LabPro to the computer using the USB cable.  Run the program Logger Pro 3 and open the file named “AP Law 2”.

2.      Attach the force sensor to the top of the cart.  Place the cart on the track.  Adjust the feet of the track so that it is level – this can be judged by rolling the cart in both directions.

3.      Attach the pulley to a ring stand  at the edge of the table and adjust the height of the pulley to match that of the “S” hook on the arm of the force sensor.

4.      At the other end of the track attach the CBR using the special bracket.

5.      You must calibrate the force sensor.  Under the Experiment menu choose Calibrate and Student Force.  Then click Calibrate Now and enter zero for Reading 1 with nothing touching the force sensor’s arm.  Then apply a known force to the sensor by attaching a string to the “S” hook, passing it over the pulley, and hanging a 500 gram mass on the end – note: you must hold the cart in place to prevent it from moving with this mass on the end of the string.  Enter the correct force value for Reading 2.  Then click Done.  Remove the 500 gram mass!

6.      Now place a 20-gram mass on the end of the string passing over the pulley.

7.      Give the cart a push toward the CBR and release such that it rolls one direction and then reverses direction under the influence of the weight at the end of the string.  Collect data for this motion.

8.      You should now be looking at graphs of position vs. time and force vs. time.  The position vs. time graph should be a smooth curve.  If not, you need to repeat the experiment – simply click on the Collect button to repeat.  You may need to adjust the direction the CBR is pointing if it is getting errant reflections (normally it works best when tilted slightly upward).

9.      Use the Page tool to view other available graphs.  You need to determine the acceleration of the cart as it rolled toward the CBR (backwards) and away from the CBR (forwards).  It is best to use the Velocity vs. Time graph.  However we also wish to determine the tension in the string for these motions.  Read on…

10.  Click on the word Velocity on the y-axis of the Velocity vs. Time graph and choose More...  and then check Force so that you can see both velocity and force data on the same graph.

11.  Now use the mouse to click and drag to highlight the part of the graph where the cart was moving backwards.  Have the computer put a linear regression on the velocity data and perform statistics on the force data.  This should give you the acceleration of the cart and the average amount of tension that acted during the same interval of time (that was highlighted).  Record this data in the table.

12.  Use the same process to find acceleration and tension for the cart moving forwards and record in the table.

13.  Complete the rest of the table by adjusting the mass on the end of the string to the values shown.

14.  Adjust the appearance of the graph to your liking  and then print ONE representative graph of this type showing the regressions and statistics for both the backwards and forwards motion.  Do not print this graph for every trial.

15.  Measure the mass of the cart with the sensor attached (the total mass that was being accelerated by the tension in the string).

 

Part B – Bungee Force

In this section of the lab the string/pulley/hanging weight system will be replaced by a piece of bungee cord.  Simply tie the cord to the “S” hook at one end and to the ring stand at the other end.

Procedure

1.      Once again you will give the cart a push so that it moves backward and then forward, this time under the influence of the bungee cord.  You may need to experiment with the strength of your push and the length of the cord to get acceptable data.

2.      Once you have collected acceptable data, go to the page that shows Force vs. Time.  Click on the word Time and change this graph to Force vs. Acceleration.  Change the graph so that it shows Point Protectors and does not Connect Points.  You should notice a linear pattern in the first quadrant of this graph, but you will also see spurious data in other places.  Read on…

3.      The program can be adjusted to collect data only while the bungee is acting.  Go to the Experiment menu and then Data Collection… Now set the Collection Length to 1 second and the Triggering to begin when the Force is increasing across 0.10 N.  In this way the computer will “wait” for the bungee to start pulling and then collect only for 1 second.

4.      Repeat the experiment and inspect the Force vs. Acceleration graph.  If there are still spurious data points then adjust the data collection length and triggering values and repeat the experiment.  Once you have a satisfactory graph go to the Experiment menu and choose Store Latest Run.

5.      Now securely attach the metal block to the cart and then repeat the above steps to add a second set of data to the same graph of Force vs. Acceleration.  Perform linear regressions on both sets of data, adjust the appearance of the graph to your liking and then print.

6.      Measure the mass of the metal block and record in the data table.

 

Analyses

1.      Use the results of Part A to construct a tension vs. acceleration graph.  Plot the independent variable (tension) on the y-axis.  Use different symbols and/or colors for the cart moving backward versus moving forward and include a key or legend.  Determine a line 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 acceleration as that measured for the cart.  Use this acceleration and the mass of the hanging weight to calculate the tension at that end of the string.  Create a table and corresponding graph of calculated tension versus measured tension for the two sets of data backwards and forwards.  Again use different symbols/colors and determine lines of best fit.

 

Questions (2 ea)

1.      Discuss whether or not your graphs confirm and/or support the types of relations described in Newton’s 2nd Law and explain how so.  Be specific in referring to your results and graphs.  Remember to address both aspects of the 2nd Law:  how acceleration is related to force and how it is related to mass.

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.  (c) What do the y-intercepts represent on this graph?  Explain.

3.      (a) Make a free body diagram for the cart moving backward.  Write the equation of motion and solve for the tension symbolically.  (b) Make a free body diagram for the cart moving forward.  Write the equation of motion and solve for the tension symbolically.  (c) Compare these symbolic equations to the lines of best fit on the tension vs. acceleration graph – what is the significance of the y-intercepts?  (d) Ideally how should the two y-intercepts compare to one another? 

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.      Consider the force vs. acceleration graph from the bungee experiment.  Calculate the percent error in each slope assuming the values on your data sheet are accurate.

6.      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!) 


Part A – Atwood’s Machine

 

 

Total Mass of Cart plus Force Sensor:

 

 

Moving Backwards

Moving Forwards

Mass on End of String (g)

Tension
(N)

Acceleration
(m/s2)

Tension
(N)

Acceleration
(m/s2)

20.0

 

 

 

 

50.0

 

 

 

 

70.0

 

 

 

 

100.0

 

 

 

 

120.0

 

 

 

 

150.0

 

 

 

 

 

 

Part B – Bungee

 

Run 1

Total Mass of Cart plus Force Sensor:

 

 

Mass of Metal Block:

 

Run 2

Total Mass of Cart, Sensor, and Metal Block:

 

 

 


 

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

q       Completed data/results table.  (8)

q       Example graph Force and Velocity vs. Time (computer generated).  (5)

q       Tension vs. Acceleration graph (student generated).  (10)

q       Calculated Tension vs. Measured Tension graph (student generated).  (10)

q       Force vs. Acceleration graph with two trials (computer generated).  (5)

q       Answers to questions.  (12)