Explorations: (To get a printable copy of this file click here.)
Exploration I.
Place a 20 g mass 5 cm from the center of the turntable. Set the turntable to run at 33 1/3 rpm and turn it on. Observe the motion of the mass. Then write your observations in your journal. Place an accelerometer on your turntable and set the turntable to run at 33 1/3 rpm.
Exploration II:
Place a second 20 g mass at 12 cm from the center of the turntable. Set the turntable to run at 33 1/3 rpm. Observe the motion of the mass and then write your observations in your journal.
Exploration III:
Place a single 20 g mass 12 cm from the center of the turntable. Set the turntable to run 16 rpm. Then switch to 33 1/3 rpm, 45 rpm and then to 78 rpm. Observe the motion of the mass and then write your observations in your journal.
Exploration IV:
1. Connect the Low-g Accelerometer to Channel 1 of the LabPro interface.
2. Use the USB cable to connect the computer to the Lab Pro.
3. Turn on the computer and start the Logger Pro program.
a) A pop-up screen to set up interface will appear. Press scan so the computer will locate the port for the LabPro.
b) From SETUP, on the top toolbar, select Sensor. Scroll down to Accelerometer-5g and click OK at the bottom of the screen.
4. To zero the Accelerometer so that it reads zero when it is horizontal:
a) Place the accelerometer on the table with the arrow level and horizontal.
b) Make sure the sensor is motionless. From Experiment on the toolbar select Zero.
5. To get ready to collect data complete the following: a) From the Data heading on the toolbar select Clear Data and scroll to the right to select Latest. b) Under "Experiment" at the top menu bar of the screen select Sampling. Adjust the Experiment Length to 90 seconds and enter "1" as the samples/second. Select OK to return to the main screen.
6. To begin the collection of data click the Collect button at the top of the toolbar. How do you know the direction of the centripetal acceleration? You will now need to understand the measurements that your Accelerometer makes. Relative to the arrow on the Accelerometer, what direction corresponds to a positive measurement? Determine how to interpret the sign of your acceleration measurements by moving the Accelerometer back and forth in a straight line. Press START to begin collecting data. Check your graph of acceleration vs. time for your motion.
Discussion IV:
1. If you are moving in a straight line, does speeding up while moving in the positive direction correspond to a positive or a negative acceleration? If you are slowing down while moving in the positive direction does this correspond to a positive or a negative acceleration? You should base your answers on the definitions of position, velocity, and acceleration. Record your answers in your Learning Log.
2. In your graph of acceleration vs. time, the Accelerometer had to first speed up in the direction of the arrow before slowing down later. Is the acceleration in the direction of the arrow read as positive or negative? Record you result in the Data Table below. Save these answers for your portfolio
Speeding up in a + direction Slowing down in a + direction Acceleration in direction of arrow Exploration V:
During this exploration you will determine the relationship between the centripetal acceleration and the angular speed by measuring the centripetal acceleration while varying the angular speed and keeping the radius constant.
1. Instructions:
a. Hook up a Low-g accelerometer to the LabPro and set up the Low-g accelerometer following the procedure outlined in Exploration I, section IV.
b. Place a turntable on a level surface and check with a level.
c. Use Velcro strips to fasten the interface to the center of a wooden disk and place the accelerometer 12 cm from the center of the wooden disk on the Velcro strip. Convert this distance from centimeters to meters and record this value as the radius in the data table.
d. Turn on the computer and start the Logger Pro program.
1) A pop-up screen to set up interface will appear. Press scan so the computer will locate the port for the LabPro.
2) From SETUP, on the top toolbar, select Sensor. Scroll down to Accelerometer-5g and click OK at the bottom of the screen.
e. Close the text box by clicking on the "X" in the upper right-hand corner of the textbox only. Click once on the graph title and change the type in the new title, "Centripetal Acceleration versus Time."
f. Make sure the arrow of the accelerometer is pointing inward toward the spindle and all loose cables are taped secured to the turntable. Place the disk on the turntable. Remember to zero your accelerometer!
g. Set the speed of the turntable to 16 rpm. (Different ranges are available depending on the turntable used)
h. Under "Experiment" at the top menu bar of the screen select Sampling. Adjust the Experiment length to 120 seconds and enter "1" as the samples/second. Select OK to return to the main screen.
i. Select "Remote" from the menu bar at the top of the screen and select "Set Up LabPro."
j. Unplug the USB plug from the LabPro.
2. You are now ready to collect centripetal acceleration data at four different angular speeds. Data collection will not begin until you press the start/stop button on the interface. You will press stop to end data collection unless the time has already expired and the interface shuts down on its own.
a. Start the turntable and press the start/stop button on the interface to begin data collection. Wait 20 seconds.
b. Increase the speed to 33 1/3 rpm and wait 20 seconds.
c. Increase the speed to 45 rpm and wait 20 seconds.
d. Increase the speed to 78 rpm and wait 20 seconds.
e. Turn off the turntable and press the start/stop button to end data collection.
3. You are now ready to retrieve your data from the LabPro.
a. Reconnect the USB plug to the LabPro.
b. Select "Remote" from the menu bar at the top of the screen and select Retrieve Data from LabPro. The data table and graph should display the data you collected.
4. Next, you will analyze your data to determine the mean centripetal acceleration for each angular speed.
a. Under "Analyze" on the menu bar at the top of the screen select Examine.
b. Click and drag on the area of the graph corresponding to 16 rpm. Under "Analyze" select Statistics. A pop-up menu will display the average centripetal acceleration. Record your information in the table provided.
c. Repeat the procedure in 4b for the areas of the graph corresponding to 331/3 rpm, 45 rpm, and 78 rpm.
5. The angular speeds in revolutions per minute need to be converted to radians per second. (Use the following conversion factors: 2p radians = 1 revolution and 1 minute = 60 seconds) Record your values in the data table.
6. Use Graphical Analysis, Excel, or a graphing calculator to plot a graph of centripetal acceleration versus angular speed squared. Calculate the slope. Print a copy of the graph you obtained.
Data:
Radius (m) Discussion V:
1. What kind of relationship exists between the centripetal acceleration and the square of the angular speed in radians per second?
2. What are the units of the slope?
3. What quantity does the slope represent?
4. Does the value of the slope correspond to any measurement in this exploration?
Exploration VI:
During this exploration you will determine the relationship between the centripetal acceleration and the radius by measuring the centripetal acceleration while varying the radius and keeping the angular speed constant.
1. Directions:
a. Hook up a Low-g accelerometer to the LabPro and set up the Low-g accelerometer following the procedure outlined in Exploration I, Section IV.
b. Place a turntable on a level surface and check with a level.
c. Use Velcro strips to fasten the interface to the center of a wooden disk and place the accelerometer 6 cm from the center of the wooden disk on the Velcro strip. Convert this distance from centimeters to meters and record this value as the radius in the data table.
d. Turn on the computer and start the Logger Pro program.
1) A pop-up screen to set up interface will appear. Press scan so the computer will locate the port for the LabPro.
2) From SETUP, on the top toolbar, select Sensor. Scroll down to Accelerometer-5g and click OK at the bottom of the screen.
3) Close the text box by clicking on the "X" in the upper right-hand corner of the textbox only. Click once on the graph title and change the type in the new title, "Centripetal Acceleration versus Time."
e. Make sure the arrow of the accelerometer is pointing inward toward the spindle and all loose cables are secured to the turntable. Place the disk on the turntable. Remember to zero your accelerometer! To zero the Accelerometer (so that it reads zero when it is horizontal):
1) Place the accelerometer on the table with the arrow level and horizontal.
2) Make sure the sensor is motionless. From " Experiment" on the toolbar select Zero.
2. Set the turntable to the angular speed you are going to use. (16 rpm, 33 1/3 rpm, 45 rpm, or 78 rpm.)
3. Convert the angular speed from rpm to rad/s using the following conversion factors: 2p radians = 1 revolution and 1 minute = 60 seconds. Record this value in the data table.
4. Under "Experiment" at the top menu bar of the screen select Sampling. Adjust the Experiment length to 30 seconds and enter "1" as the samples/second. Select OK to return to the main screen.
5. Select "Remote" from the menu bar at the top of the screen and select "Set Up LabPro." Unplug the USB plug from the LabPro.
6. Press "Start/Stop" on the LabPro to start data collection. Wait 5 seconds. Turn on the turntable and wait at least 25 seconds turn off the turntable. If the LabPro has not timed out press stop to quit data collection.
7. You are now ready to retrieve your data from the LabPro.
a. Reconnect the USB plug to the LabPro.
b. Select "Remote" from the menu bar at the top of the screen and select "Retrieve Data from LabPro." The data table and graph should display the data you collected.
8. Next, you will analyze your data to determine the mean centripetal acceleration for each angular speed.
a. Under "Analyze" on the menu bar at the top of the screen select Examine.
b. Click and drag on the area of the graph corresponding to the 6 cm. radius. Under "Analyze" select "Statistics". A pop-up menu will display the average centripetal acceleration. Record your information in the table provided.
c. Repeat the same experimental procedure changing the radii to 8cm, 10 cm, and 12 cm.
Data Table:
Angular Speed (rpm) = Angular Speed (rad/s) = Radius(m) Centripetal acceleration(m/s2) Analysis:
Plot and print a graph of centripetal acceleration versus radius using Graphical Analysis, Excel, or a graphing calculator. Calculate the slope of the graph with units and record it on your graph. (Remember that a radian is dimensionless)
Discussion VI:
1. What kind of relationship did you find between centripetal acceleration and the radius?
2. Does the slope correspond to any quantity in this experiment? How about the square root of the slope?
Exploration VII:
During this exploration you will determine the relationship between the centripetal acceleration and the mass by measuring the centripetal acceleration while varying the mass and keeping the angular speed and radius constant.
1.
a. Hook up a Low-g accelerometer to the LabPro and set up the Low-g accelerometer following the procedure outlined in Exploration I, Section IV.
b. Place a turntable on a level surface and check with a level.
c. Use Velcro strips to fasten the interface to the center of a wooden disk and place the accelerometer 8 cm from the center of the wooden disk on the Velcro strip.
d. Turn on the computer and start the Logger Pro program.
1) A pop-up screen to set up interface will appear. Press scan so the computer will locate the port for the LabPro.
2) From "Setup", on the top toolbar, select Sensor. Scroll down to Accelerometer-5g and click OK at the bottom of the screen.
3) Close the text box by clicking on the "X" in the upper right-hand corner of the textbox only. Click once on the graph title and change the type in the new title, "Centripetal Acceleration versus Time."
e. Make sure the arrow of the accelerometer is pointing inward toward the spindle and all loose cables are taped down. Place the disk on the turntable. Remember to zero your accelerometer! To zero the Accelerometer so that it reads zero when it is horizontal:
1) Place the accelerometer on the table with the arrow level and horizontal.
2) Make sure the sensor is motionless. From " Experiment" on the toolbar select Zero.
2. Set the turntable to the angular speed you are going to use. (16 rpm, 33 1/3 rpm, 45 rpm, or 78 rpm.)
3. Convert the angular speed from rpm to rad/s using the following conversion factors: 2p radians = 1 revolution and 1 minute = 60 seconds. Record this value in the data table.
4. Place a 20 g mass on top of the accelerometer.
5. Under "Experiment" at the top menu bar of the screen select Sampling. Adjust the Experiment length to 30 seconds and enter "1" as the samples/second. Select OK to return to the main screen.
6. Select "Remote" from the menu bar at the top of the screen and select "Set Up LabPro." Unplug the USB plug from the LabPro.
7. Press "Start/Stop" on the LabPro to start data collection. Wait 5 seconds. Turn on the turntable and wait at least 25 seconds turn off the turntable. If the LabPro has not timed out, press stop to quit data collection.
8. You are now ready to retrieve your data from the LabPro.
a. Reconnect the USB plug to the LabPro.
b. Select "Remote" from the menu bar at the top of the screen and select "Retrieve Data from LabPro." The data table and graph should display the data you collected.
9. Next, you will analyze your data to determine the mean centripetal acceleration for each mass sample.
a. Under "Analyze" on the menu bar at the top of the screen select Examine.
b. Click and drag on the area of the graph corresponding to the 20 g data. Under "Analyze" select "Statistics". A pop-up menu will display the average centripetal acceleration. Record your information in the table provided.
c. Repeat the same experimental procedure changing the mass to 30 g, 40 g, and 60 g.
Data Table:
Angular Speed (rpm) = Radius(m) = Mass(g) Centripetal acceleration(m/s2) Analysis:
Plot and print a graph of centripetal acceleration versus mass using Graphical Analysis, Excel, or a graphing calculator.
DiscussionVII:
1. What kind of relationship did you find between centripetal acceleration and the mass? Justify your answer.
