Purpose:
This lab aims to determine a relationship between the centripetal force on an object and the speed at which it rotates.
Theory:
As an object moves in a circle, it will experience centripetal force accelerating it towards the center of its path. This force changes proportionally with the angular velocity of the object as well as its mass and path radius in the form F=mrw^2. In a system rotating parallel to the ground, the only forces acting on the rotating object will be gravity and centripetal force. Assuming friction is negligible, the measured centripetal force can be expected to behave according to our model. This means that when changing only one variable of mass, radius, or angular velocity, a graph of force vs one changing variable should produce a linear graph with slope equal to the product of the constants.
Apparatus:
- Rotating table (1)
- Wireless force sensor (1)
- Measuring tape (1)
- 100g mass (3)
- String
- Stopwatch (1)
- Adjustable power supply
Procedure:
Prepare the experimental setup as shown in the photo below. Set the power supply to one value and measure a length of string. Collect data for force and angular velocity at constant radius while varying mass at 100g intervals up to 300g. Collect data again for 3 trials while varying radius, keeping mass and power setting the same. Collect another 3 trials while varying the power supply, keeping all else constant.
Data and Graphs:
Photo of experimental setup
Photo of data collection procedure for Force
Photo of data collection procedure for angular velocity
Prepare the experimental setup as shown in the photo below. Set the power supply to one value and measure a length of string. Collect data for force and angular velocity at constant radius while varying mass at 100g intervals up to 300g. Collect data again for 3 trials while varying radius, keeping mass and power setting the same. Collect another 3 trials while varying the power supply, keeping all else constant.
Data and Graphs:
Photo of experimental setup
Photo of data collection procedure for Force
Photo of data collection procedure for angular velocity
Data table of measured and calculated values
Graphs of Force v Mass*w / Radius*w / w
Analysis:
Angular velocity was calculated based on time taken for 10 revolutions. The slope of each graph represents the constant values in each relationship. Plots of force were always taken against w^2 due to highly inconsistent angular speeds at each trial.
Conclusion:
The Force vs Mass*w^2 graph produced a slope of 0.454, near the actual radius of 0.47m. The plot of Force vs w^2 graph produced a value for m*r of 0.095kgm compared to actual m*r value of 0.078kgm. The Force vs Radius*w^2 graph produced a slope of 0.263kg with an actual mass of 0.2 kg. Of these graphs, only Force vs Mass*w^2 produced a theoretical constant that was deemed acceptable with a 3.4% error compared to predicted m*r with an error of 21.8% and predicted m with 31.6% error. The huge error in Force vs radius*w^2 may be attributed to the second data point which does not appear to follow the proportional relationship with force, having a value of 1.651N, very near the first data point of 1.659N despite a significantly changed radius. As force measurements were taken as an average over a period of time, the uneven design of the rotating tabletop likely did not contribute much to our error in measurement. It is also unlikely that the force sensor was improperly calibrated enough to produce this value. This suggests that our model may not be entirely valid for our experimental system and that an idealized assumption made during experimentation was false.
Graphs of Force v Mass*w / Radius*w / w
Analysis:
Angular velocity was calculated based on time taken for 10 revolutions. The slope of each graph represents the constant values in each relationship. Plots of force were always taken against w^2 due to highly inconsistent angular speeds at each trial.
Conclusion:
The Force vs Mass*w^2 graph produced a slope of 0.454, near the actual radius of 0.47m. The plot of Force vs w^2 graph produced a value for m*r of 0.095kgm compared to actual m*r value of 0.078kgm. The Force vs Radius*w^2 graph produced a slope of 0.263kg with an actual mass of 0.2 kg. Of these graphs, only Force vs Mass*w^2 produced a theoretical constant that was deemed acceptable with a 3.4% error compared to predicted m*r with an error of 21.8% and predicted m with 31.6% error. The huge error in Force vs radius*w^2 may be attributed to the second data point which does not appear to follow the proportional relationship with force, having a value of 1.651N, very near the first data point of 1.659N despite a significantly changed radius. As force measurements were taken as an average over a period of time, the uneven design of the rotating tabletop likely did not contribute much to our error in measurement. It is also unlikely that the force sensor was improperly calibrated enough to produce this value. This suggests that our model may not be entirely valid for our experimental system and that an idealized assumption made during experimentation was false.
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