Final answer:
To test the difference between torques at two fan speeds, attach an arm with a mass to the fan blade, record the time it takes to stop, and calculate torque using the angular deceleration. Repeat for both speeds and compare the results.
Step-by-step explanation:
To collect and analyze data to test the difference between the torques provided by two different speeds on a tabletop fan, you would first need to set up the fan so that it can operate at distinct, selectable speeds. Once the fan is operational, you can use the following steps:
- Secure the fan to prevent movement.
- Attach a small, lightweight arm to the fan blade, perpendicular to the blade, with a known mass at the end.
- Measure the distance from the center of the fan to the mass to calculate the radius (lever arm).
- Turn the fan on to its first speed setting, allow it to reach a stable speed, and then turn it off.
- Record how long it takes for the fan to come to a complete stop. This time measurement can be analyzed to infer torque.
- Repeat the steps for the second speed.
- Compare the time taken for the fan to stop at each speed—the longer the stopping time, the higher the initial torque.
Analyzing this data involves calculating the angular deceleration using the change in speed over the stopping time and then using the deceleration to find torque with the formula Torque = Moment of Inertia * Angular Acceleration. The moment of inertia can be calculated based on the mass and radius of the arm attached to the fan blade. By comparing the calculated torques for both speeds, the difference can be analyzed.