Vernier Centripetal Force Apparatus - Manual (Page 7)

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Your graphs show how centripetal force varies with angular velocity. Now take
additional data with other masses and other radii.
Angular Velocity – LabQuest App with Dual-Range Force Sensor
and Vernier Photogate
Data collection with the Dual-Range Force Sensor and Vernier Photogate is
simplified because the LabQuest App automatically calculates the interpolated force.
To find the angular velocity, you must configure the photogate motion timing mode
with the angular position information, detailed below.
1. Start the LabQuest App and let it auto-ID the sensors.
2. On the Meter tab of the LabQuest App, tap Mode.
3. Tap User Defined.
4. Enter 1/10 of the angular position change for each slot, or 2π/10, as the User
Defined value. You will not need to adjust this value each time you change the
radius, since the angular velocity is independent of radius.
5. On this screen, choose the option to end the data collection with the Stop button.
6. Tap OK.
Collect data and examine the graphs. For further analysis, change one of your graphs
to display Force vs. Velocity or Force vs. Velocity 2 .
Tangential Velocity – Logger Pro 3 with Dual-Range Force
Sensor and Vernier Photogate
If desired, you can add calculations to the Logger Pro file to determine the tangential
velocity, and use that quantity instead of angular velocity for graphs. We show you
how to add these calculations in the file CFA-DFS-Photogate-tangential.cmbl. This
file is set up for Dual-Range Force Sensor and a Vernier Photogate, and provides
several calculated columns.
The first is the same interpolated force column as in the example above.
The second calculation is needed to determine tangential velocity, since the
tangential velocity of the rotating mass is a function of its radius of motion, using
v= r. The photogate is set up as before to collect motion data, and the “Tangential
Velocity” column is used to find the product of the angular velocity and the current
radius. The file contains a User Parameter called “Radius.” The student must set the
parameter to match the radius of motion for each run. Take note that if the parameter
is changed for a later run, all columns depending on this parameter will be updated.
This includes stored runs, therefore, altering the radius may upset previous
calculations, including curve fits.
After taking data as before, observe the Force-Interpolated vs. Time graph, and then
display Force-Interpolated vs. Tangential Velocity. Also create and analyze a graph
of Force-Interpolated vs. Velocity 2 .
Your graphs show how centripetal force varies with tangential velocity. Now take
additional data with other masses and other radii. The slope of the line for the
velocity 2 graph will be proportional to mass, and inversely proportional to radius, per
F=mv 2 /r.
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Tangential Velocity – LabQuest App with Dual-Range Force
Sensor and Vernier Photogate
Data collection with the Dual-Range Force Sensor and Vernier Photogate is
simplified because the LabQuest App automatically calculates the interpolated force.
To find the tangential velocity, you must configure the photogate motion timing
mode with the circumference information, detailed below.
1. Start the LabQuest App and let it auto-ID the sensors.
2. On the Meter tab of the LabQuest App, tap Mode.
3. Tap User Defined.
4. Enter 1/10 of the circumference of the mass path, or 2πr/10, as the User Defined
value. You will need to adjust this value each time you change the radius.
5. On this screen, choose the option to end the data collection with the Stop button.
6. Tap OK.
Collect data and examine the graphs. For further analysis, change one of your graphs
to display Force vs. Velocity or Force vs. Velocity 2 .
Logger Pro 3 with Wireless Dynamic Sensor System (WDSS)
Start Logger Pro software and establish a Bluetooth connection to the device as
described in the WDSS manual.
If you want to use a photogate to collect position and tangential velocity data, use
one of these Logger Pro files.
a. The file CFA-WDSS-Photogate.cmbl, which is part of the file collection on the
CFA web page.
b. The Vernier lab manual Advanced Physics with Vernier – Mechanics contains an
experiment called “12A Centripetal Acceleration” that uses the CFA to
investigation circular motion. The book also contains a Logger Pro file called
“12A Centripetal Acceleration.cmbl” that you can use. The file can be found in
the folder called “Supplemental Materials” on the CD that accompanies the book.
Collect data and change the Force-Interpolated vs. Time to display
Force-Interpolated vs. Velocity. Also create and analyze a graph of Force-
Interpolated vs. Velocity 2 .
Collect data and examine the graphs. For further analysis, change one of your graphs
to display Force vs. Angular Velocity (ω). The file contains a calculated column
called Angular Velocity 2 (ω 2 ). Create and analyze the graph of Force vs. Angular
Velocity 2 (ω 2 ).