Lab 8: Centripetal Acceleration vs. Angular Frequency
Chris Ceron, Amy Chung, John Choi
Purpose
To determine the relationship between centripetal force and angular speed by using an apparatus that allows for multiple fixed variable scenarios.
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| Apparatus used to find the relationship |
Theory/Introduction
For an object moving in uniform circular motion, the direction of acceleration is towards the center. The force that corresponds to this acceleration is called the centripetal force:
The sum of the forces in our lab is shown through the following free body diagram of our apparatus
Through this free body diagram, we determined the sum of the forces in both the x and y direction
omega can be represented in terms of period per each rotation:
The sum of the forces in the x direction is a linear equation from which isolate a certain variable and keep the other two constant. Gathering multiple test cases allows for us to graph the data and apply a linear fit to find the isolated variable.
Experimental Procedure
Our apparatus is composed of a wooden circular disc with a pole protruding from the center. The disc sits on top of a motor that allows for the disc to rotate in a uniform circular motion. The motor was connected to a power supply that would allow for us to change the speed of rotation. We attached a force sensor to the pole, and attached a mass to the sensor using string. At the end of the disc was a piece of tape that would pass through a photogate after each rotation. This allowed for us to find the period between each rotation.
The experiment was conducted several times, each time keeping a variable constant for a number of tries. The three variables we manipulating were mass, the radius, or omega. We would manipulate mass by changing the mass tied to the force sensor, the radius by either increasing or decreasing the length of the string that attached the mass to the force sensor, and omega by adjusting (increasing or decreasing) the power of the motor. Using all the data gathered, we could plot graphs for each variable we kept constant and apply a linear fit and find the correlation between the points plotted.
Our apparatus is composed of a wooden circular disc with a pole protruding from the center. The disc sits on top of a motor that allows for the disc to rotate in a uniform circular motion. The motor was connected to a power supply that would allow for us to change the speed of rotation. We attached a force sensor to the pole, and attached a mass to the sensor using string. At the end of the disc was a piece of tape that would pass through a photogate after each rotation. This allowed for us to find the period between each rotation.
We allowed the disc to reach a constant speed before and would use LoggerPro to record the force. The force would fluctuate as the disc rotated, so we used the mean value.
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| The graph of force vs. time |
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| The graph recorded for period of each rotation |
Data recorded through apparatus:
| trial # | rotations | time initial (s) | time final (s) | Δtime (s) | radius (cm) | mass (kg) | Average Force (N) |
| 1 | 10 | 1.428 | 14.769 | 13.341 | 22.86 | 0.2 | 1.2 |
| 2 | 10 | 1.728 | 14.879 | 13.151 | 29.21 | 0.2 | 1.47 |
| 3 | 5 | 13.36 | 20.11 | 6.75 | 34.29 | 0.2 | 1.691 |
| 4 | 10 | 1.57 | 15.6 | 14.03 | 46.99 | 0.2 | 1.981 |
| 5 | 10 | 2.42 | 17.44 | 15.02 | 59.44 | 0.2 | 2.198 |
| 6 | 10 | 2.68 | 17.02 | 14.34 | 46.99 | 0.1 | 1.052 |
| 7 | 10 | 1.451 | 14.97 | 13.519 | 46.99 | 0.05 | 0.57 |
| 8 | 10 | 2.35 | 16.46 | 14.11 | 46.99 | 0.3 | 2.801 |
| 9 | 10 | 1.24 | 11.48 | 10.24 | 46.99 | 0.3 | 5.393 |
| 10 | 10 | 1.12 | 10.75 | 9.63 | 46.99 | 0.3 | 5.94 |
| 11 | 10 | 1.46 | 10.6 | 9.14 | 46.99 | 0.3 | 6.434 |
You got data, and a cool video!
ReplyDeleteIt wants some interpretation . . .