In this experiment, students use the GLX to derive the centripetal force equation.

• Microsoft Word version of this lab:
  (Zip file | Stuffit file)

• Xplorer GLX (PS-2002)
• Force Sensor (PS-2104)
• Discover Centripetal Force Kit (ME-9837)
• Multi-Clamp (SE-9442)
• Universal Table Clamp (ME-9376B)
• Pulley Mounting Rods (2) (SA-9242)
• Triple-Beam Balance (SE-8707)

Safety:

• Wear safety goggles.
• Make sure that no one is standing close to avoid hitting others.
• Hold the tube far away to avoid hitting self.

Part 1 Data Table: Force v. Velocity

Radius (m)	Time Between Peaks (s)	Number of Revolutions between Peaks	Spinning Mass (kg)	Average Force (N)

1. With the #10 stopper (3rd smallest) connected to the end of the string, spin the stopper in a horizontal circle of fixed radius above your head.


2. When the stopper maintains a constant speed, press the Start Button on the GLX.


3. After more that 7 revolutions, press the Stop Button on the GLX.


4. Observe your graph, if it contains 7 or more oscillations of consistent data, then continue. If not, then repeat the previous steps.


5. Press to Auto Scale.

6. Press and select the Delta Tool as in the picture above.


7. Use the arrows to select one of the peaks from the graph.


8. Press and select Swap Cursors.

9. Use the Arrow Buttons to find the time of at least 7 revolutions. Enter this value into the Data Table.


10. Count the number of revolutions. Enter this value into the Data Table.

11. Press and select Statistics. Find the average value of the Force as in the picture above. Enter this value into the Data Table.


12. Complete the Data Table by entering the value of the fixed radius.


13. Repeat steps 1-12 using the same stopper and the same radius for at least 7 other velocities.

Part 1 Analysis Table: Force v. Velocity

Average Force (N)	Velocity (m/s)

1. Enter the value of the Average Force for each trial into the Analysis Table.


2. Calculate the Velocity of the stopper for each trial. Enter the value into the Data Table.


3. Create a graph of Force v. Velocity with Velocity on the vertical axis.

Part 2 Data Table: Spinning Mass v. Velocity

Radius (m)	Time Between Peaks (s)	Number of Revolutions between Peaks	Spinning Mass (kg)	Force (N)

1. With the smallest stopper connected to the end of the string, spin the stopper in a horizontal circle of fixed radius above your head.


2. When the stopper maintains a constant speed, press the Start Button on the GLX.


3. This time, spin the stopper and simultaneously observe the graph. While maintaining the same fixed radius try to produce an average force of 5.0 N.


4. After more that 40 revolutions, press the Stop Button on the GLX.


5. Press to Auto Scale.


6. Press to toggle between the Scale and Move functions. Scale and Move to a region that appears to have an average force of 5.0 N.


7. Press and select Statistics.

8. Using the Swap Cursors function (), select a range of peaks whose values average to 5.0 N as in the picture above.


9. Enter the number of revolutions between peaks into the Data Table.

10. Press and select the Delta Tool. Enter the time between peaks into the Data Table.


11. Complete the Data Table by entering the value of the fixed radius.


12. Repeat steps 1-11 using the same force and the same radius for all the other stoppers.

Part 2 Analysis Table: Spinning Mass v. Velocity

Spinning Mass (kg)	Velocity (m/s)

1. Enter the value of the Spinning Mass for each trial into the Analysis Table.


2. Calculate the Velocity of the stopper for each trial. Enter the value into the Analysis Table.


3. Create a graph of Spinning Mass v. Velocity with Velocity on the vertical axis.

Part 3 Data Table: Radius v. Velocity

Radius (m)	Time Between Peaks (s)	Number of Revolutions between Peaks	Spinning Mass (kg)	Force (N)
.2
.3
.4
.5
.6
.7
.8

1. With the #10 stopper (3rd smallest) connected to the end of the string, spin the stopper in a horizontal circle of 0.2 meter radius above your head.


2. When the stopper maintains a constant speed, press the Start Button on the GLX.


3. Spin the stopper and simultaneously observe the graph. While maintaining the same fixed radius try to produce an average force of 5.0 N.


4. After more that 40 revolutions, press the Stop  Button on the GLX.


5. Press  to Auto Scale.


6. Press  to toggle between the Scale and Move functions. Scale and Move to a region that appears to have an average force of 5.0 N.


7. Press and select Statistics.


8. Using the Swap Cursors function (), select a range of peaks whose values average to 5.0 N.


9. Enter the number of revolutions between peaks into the Data Table.


10. Press  and select the Delta Tool. Enter the time between peaks into the Data Table.


11. Complete the Data Table by entering the value of the radius.


12. Repeat steps 1-11 using the same force and the same stopper for all the other radii.

Part 3 Analysis Table: Radius v. Velocity

Radius (kg)	Velocity (m/s)

1. Enter the value of the radius for each trial into the Analysis Table.


2. Calculate the Velocity of the stopper for each trial. Enter the value into the Analysis Table.


3. Create a graph of Radius v. Velocity with Velocity on the vertical axis.

1. Using words and a mathematical expression, describe the relationship between force and velocity in uniform circular motion.


2. Using words and a mathematical expression, describe the relationship between mass and velocity in uniform circular motion.


3. Using words and a mathematical expression, describe the relationship between radius and velocity in uniform circular motion.


4. Combine the three relationships above to create one relationship for force, mass, velocity, and radius. Solve it for force.


5. How would you convert this expression into an equation?


6. What is the constant of proportionality for this equation? Explain.


7. How could such an equation be used?





8. The figure above is an overhead view of the rotating mass. For each of the 4 points, draw the direction and relative magnitude of the force.