Lab 3

Jackson Summers and Jonathon Fairchild October 20, 2023 Simple Pendulum and Conservation of Energy Lab Introduction Purpose: The purpose of this lab is to create and use a pendulum to measure and investigate the effect of the pendulum's amplitude on its period of oscillation; determine maximum angular velocity; and carry out an analysis of conservation of energy. This will be completed by using Logger Pro and its Pendulum and rotary motion sensor. Equipment:  Pendulum and rotary motion sensor (Vernier CI 6625)  LabQuest Mini Interface  Laptop computer running Logger Pro software.  Meter stick, pan (or digital) balance/scale. Equations: T = 2 √ 2 L g ∗ S ∅ We use this equation to find the predicted and measured periods during the trials where we vary the amplitude Procedure: Image 1-1: Image 1-2 Shows the pendulum in motion. Shows the setup of the pendulum and the Length of the pendulum.

Image 1-3: Drawing of a simple pendulum where it was released at point P. Also notes the LabQuest Mini Interface, and Laptop Computer running Logger Pro. 1) Measure the mass of the nut and verify the confidence of the measurement by taking multiple readings on multiple scales. The average mass of the nut was 16.56 grams. 2) Assemble the pendulum by cutting a string of about 1.4 meters. Then tie a knot to keep the nut on the string. 3) Measure the length of the pendulum from the center of mass of the nut to the point of revolution. This should be around 0.6 meters to 0.7 meters. 4) Connect Sensor to computer running logger pro via the LabQuest mini and ensure the connection is registered. 5) Record data by having one person release the mass from a chosen amplitude, while the other starts the recording process on the computer and ensure that the mass only swings on the desired axis, preventing twisting and drifting. 6) Measure the data first at the angular displacement of 30 0 . 7) Repeat the data recording process 5 times at different amplitudes between 10 and 60 o , excluding 30 0 . Data Collection: Trial # Release Angle Amplitud e Period from Equation 1-1 Period from Logger Pro Percent Error 1 10 0.22 rad 1.5315 s 1.5000 s 2.10% 2 20 0.40 rad 1.5403 s 1.5333 s 0.46% 3 25 .50 rad 1.5470 s 1.5333 s 0.89% 4 30 .58 rad 1.5543 s 1.5666 s 0.79% 5 35 .66 rad 1.5650 s 1.5666 s 0.10% 6 40 .81 rad 1.5765 s 1.6000 s 1.47% 7 50 .94 rad 1.6046 s 1.6333 s 1.76% Table 1-1 Logger Pro LabQuest Mini Interface

Figure 1-1 The figure above shows the angle and time graph as well as the velocity and time graph when the angular displacement started at 10 0 . In this data collection amplitude and the period can be calculated. This may not be entirely accurate as data is taken every .0333 seconds.

Figure 1-2 The figure above shows the angle and time graph as well as the velocity and time graph when the angular displacement started at 10 0 . In this data collection amplitude and the period can be calculated. This may not be entirely accurate as data is taken every .0333 seconds.

The following is the measured amplitude maximums and minimums when the pendulum has an angular displacement of 25 o : Angular Amplitude Max 1 0.02 Angular Amplitude Min 1 -1.03 Max 2 0.02 Min 2 -1.01 Max 3 0 Min 3 -0.99 Max 4 -0.02 Min 4 -0.98 Max 5 -0.02 Min 5 -0.98 Max 6 -0.03 Min 6 -0.98 Max 7 -0.03 Min 7 -0.96 Max 8 -0.05 Min 8 -0.96 Max 9 -0.05 Min 9 -0.94 Max 10 -0.05 Min 10 -0.94 Table 2-1