Circular Motion - DOC

							Alabama Science in Motion                 2-Dimensional Motion: Uniform Circular Motion


                  Uniform Horizontal Circular Motion
Equipment:

Item                           QTY            Item                          QTY
GLX                            1              Mass Set                      1
Rubber Stoppers                assorted       Sticky Tape                   1
String and Tube                1              Measuring Tape                1


Safety Tips: Goggles are recommended and should be provided by the school. Make
sure that all masses are securely attached to the string. Start and stop the rubber
stopper carefully as demonstrated.

Procedure: (Answer all italicized questions on the student data sheet.)
In the following exercise you will determine the speed of the stopper in horizontal
circular motion while varying the radius of the orbit. In addition, your teacher may ask
different groups to work with stoppers of different masses. This will enable you to
consider what happens to the orbit of the space lab as it is being constructed in space.

You will use the GLX as a stopwatch as well as a
graphing tool.

1.     Obtain a 1.50m piece of string and feed it
       through the hollow tube.

2.     Record the mass of the stopper in the data
       table and then attach the stopper to one end of
       the string and a hanger to the other end.
       Note: loops at each end of the string may help
       when attaching the stopper and hanger
       securely. Make sure the stopper and hanger (mass) are secure before you attempt
       to swing the stopper.

3.     Use the measuring tape and the data table as a reference to set the radius from the
       center of the stopper to the hollow tube at the desired length. Place a piece of
       tape or a paperclip approximately two centimeters below the tube as a visual
       reference for maintaining the correct radius while swinging the stopper. To keep
       the radius constant, keep the reference marker at approximately two centimeters
       below the tube.

4.     Hang 200 grams of mass on the hanger. Record this value in the data table.

5.     To open the stopwatch screen, turn on the GLX and wait for the home screen to
       load. From the Home screen, navigate over to the Stopwatch icon and press the
       check button. If possible connect the GLX to the power adapter and an outlet.

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Alabama Science in Motion                   2-Dimensional Motion: Uniform Circular Motion


6.       Make sure everyone has their goggles on.

7.       Begin to whirl the stopper, adjusting the speed and motion until
         the stopper is moving in a horizontal circle at a constant speed
         indicated by keeping the reference marker in the correct
         position. Be sure the reference point (paperclip or tape) does
         not move up and down, and does not touch the bottom of the
         tube.

8.       When the orbit is steady, time the stopper for 10 revolutions.
         Make sure you begin the timer at the count of 0 and not 1 revolution. Record
         the time for each run in the data table.

9.       Repeat this trial for total of three runs. HINT: DON’T stop spinning until you
         time all three runs. It is easier to keep the system spinning than to stop and start
         again. If you must stop to make changes, make sure you re-check your radius and
         reference before each run. If one time is not consistent with the others, repeat that
         run.

Q1. What effect does changing the radius of the stopper’s orbit have on the speed of
the stopper?

10.      Make the required change to the radius and repeat steps 3 through 9.

Analysis:

1. For each trial, find the average time for 10 revolutions. Use this average to
   determine the period, T (time) for one revolution.
2. Using each pair of values for radius (r) and period, calculate v and v2.

      Note: v = 2πr/T

3. Using the GLX, enter the data for radius, velocity and velocity squared for each trial.

      a. Turn on the GLX or press the Home key to return to the main menu.
      b. Once the Home Screen appears, open Data Files by pressing the check/select
         button.
      c. Use the arrow keys to navigate up and over to the Flash drive. Navigate down to
         highlight the file Uniform Circular Motion and press F1 (open). Note that the
         screen flashes and shows that the file is now open.
      d. Press the Home key to return to the main menu.
      e. Press F2 (Table) to view the data table for Uniform Circular Motion. The table
         shows one column for radius, a second for velocity in m/s and another for velocity
         squared in m2/s2.




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Alabama Science in Motion                 2-Dimensional Motion: Uniform Circular Motion


   f. Press F2 (Edit Cell) to enter your measurements into the table. Special Note:
      With each data point, make sure you press the check (select) button to enter the
      data point before continuing.

Note: to correct a typo while entering data in a cell, use the back/edit key found below the
Home key. If you need to navigate to a previously entered cell, press the ESC key. A
dashed text box will appear. Use the arrow keys to navigate to the desired cell. Click F2
(Edit Cell) to edit content or F3 (Edit) to delete the cell.

Graphing and the Curve Fit:

   1. Once your data is entered, press the Home key to return to the main menu.
   2. From the Home screen, press F1 (Graph) to view the graph of your data. The
      graph should now display velocity vs. radius.
   3. Press Auto Scale (F1) to center the data in the graph display.

Q2. Question #1 was asked before you developed a graph displaying the appropriate
information. Now that you have a graph, use your graph to support your answer to
Question #1 or to justify a change in your opinion regarding this question. Explain.

   4. From the graph window, select Tools (F3).
   5. Select Linear fit from the menu. The Slope and Y intercept will be displayed
      below the graph and a line will also be placed in the display.

   You should notice that the data does not look very linear. So you should try changing
   the graph to show (v2 vs. r).

       1. From the Graph window, press the check/select key. The y-axis data
          (velocity) should be highlighted.
       2. Press check/select again to see the options for the y-axis data. A menu should
          appear including v2. Select v2 for the y-axis. Now your graph should show
          radius on the x-axis and v2 for the y-axis. The data should look linear at this
          point.
       3. Record the value of the slope and y-intercept from the curve fit statistics.
       4. (If instructed by your teacher to print your graph, continue with #4 and #5.
          Otherwise, go to #6.) Save your file (Home Screen, Data Files, Save)
       5. Connect to a printer and print your graph. (Home Screen, F1-Graph, F4,
          Print, F-1 again to begin printing).
       6. When you are finished, delete the file. (Home Screen, Data Files, Delete).




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Alabama Science in Motion                2-Dimensional Motion: Uniform Circular Motion


               Student Data Sheet
Name_________________________           Partner’s Name(s)________________________

Period________________________          Date__________________


Data:


         mh (kg) =                   Ms (kg) =                Fc(N) = mhg =

                                                                           Period –T
                                  Time for 10 Rev (s)
        Radius (m)                                                            (s)
                      Run 1         Run 2        Run 3       Average
           .300
           .400
           .500
           .600
           .700
           .800




Radius (m)            V (m/s)          V2 (m/s) 2        Fc = Msv2/r (N)   Percent
                       2πr/T                                               Difference
        .300
        .400
        .500
        .600
        .700
        .800

Questions:

1. What effect does changing the radius of the stopper’s orbit have on the speed of the
stopper?




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Alabama Science in Motion                 2-Dimensional Motion: Uniform Circular Motion


2. Question #1 was asked before you developed a graph displaying the appropriate
information. Now that you have a graph, use your graph to support your answer to
Question #1 or to justify a change in your opinion regarding this question. Explain.




3. Sketch a Free Body Diagram of the Fc setup as shown with procedure # 7. Label all
critical components: objects, forces, radius, etc.




4. Describe how adjustments in the stopper’s mass would affect the stopper’s velocity
given the same Fc. Use algebra to justify your answer.




5. Now relate the mass of the space lab to the mass of the stopper. What will happen to
the orbit of the lab as it grows due to construction? How can you correct the orbit
without losing mass?




6. Calculate the centripetal force on the stopper using the relationship Fc = Msv2/r.




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Alabama Science in Motion                 2-Dimensional Motion: Uniform Circular Motion


7. Calculate the centripetal force on the stopper using the relationship Fc = mhg.




8. Calculate the percent difference between these two methods for Fc.




Advanced Analysis:

   1. As you increase the mass on the hanger, you increase the Tension in the string.
      What must happen to v (or v2) of the stopper as you increase the mass added to the
      hanger? Assume the radius and mass of the stopper remain constant.




   2. Set the equation for Newton’s Law of Gravitation equal to the equation for
      Centripetal Force. Now, using algebra, re-arrange this equality to derive
      Kepler’s Third Law, T2 = α r3




   3. The moon is moving away from the earth at a rate of approximately 3.8 cm per
      year. What does this suggest about the moon’s linear speed in orbit? (If you want
      to learn more, see http://nineplanets.org/luna.html).




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