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Inquiry: Critical Velocity

Purpose: To determine the relationships between critical velocity, mass and radius of an object moving in a vertical plane.


Critical velocity is the lowest velocity at which an object rotating in a vertical plane maintains a circular path. In this experiment it is the velocity at which a mass will just remain in the carriage when the carriage is at the highest point in the plane. Launch Data Studio and select the Smart Pulley Rotational mode. Enter the spoke angle of 30 degrees. Under Setup checkmark only the rotational velocity box in rad/s. To calculate the actual velocity we will need to always take the rotational velocity times the radius.

Mass Radius Velocity
0.090 kg 0.50 m
0.120 kg 0.50 m
0.130 kg 0.50 m
0.130 kg 0.40 m
0.130 kg 0.30 m
0.130 kg 0.25 m

Inquiry Questions:

  1. Using the last four data rows make a graph of velocity squared versus radius.

  2. Calculate the slope of the graph and compare it to gravity with % error.

  3. What would be the critical velocity of a roller coaster at the top of an 12.7 meter radius loop in mph. (1 mph = 0.447 m/s)