Lab 1 Freefall - Aashna Arora (1)

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Physics

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Dec 6, 2023

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Lab 1: Freefall Physics 141 Aashna Arora Introduction In this lab, we explore the motion of objects in freefall. Objects in freefall, experience constant acceleration which can be shown through the equation . In this ? − ? 0 = − 1 2 𝑔? 2 equation is the vertical displacement, g is the acceleration due to gravity and is time ? − ? 0 ? in seconds. Acceleration due to gravity on Earth is approximately . Through this 9. 81 ?/? 2 experiment we frame by frame analyze the motion of a quarter and penny falling from a height of 0.762 meters. We obtained the quarter’s position and its time in multiple instances to then graph on a scatter plot which was then linearized to find the acceleration due to gravity and then compared to an accepted value - found through determining the percent error. This will allow for us to check ourselves and see whether or not our measurements align with . 9. 81 ?/? 2 Procedure 1. In this experiment, a 20in x 30in grid lined poster board was used alongside an iPad stopwatch, a penny (2.50 g), a quarter (5.67 g), and an iPhone. 2. Prop the poster board vertically against the wall. 3. Record a video of the poster board from a head-on angle and set up the stopwatch to be within the recording. 4. Hold the quarter at the top of the poster board and release it in a way where the quarter falls down vertically and without it flipping. 5. When the recording is complete, go frame by frame and note down the height of the quarter for each time frame. Go from when the quarter is released to right before the coin hits the ground. 6. Convert the position data from inches to meters and create a data table with time as the independent variable and the position as the dependent variable. 7. Square the time data and create another data table using position data and data. Take ? 2 this data and convert it into a scatter plot. 8. Apply a linear regression to the scatter plot and record the equation of the trendline. Use the slope of the linear regression to determine the acceleration due to gravity. 9. Calculate the percent error by comparing the measured value to the accepted value. Use this equation . ??????? ????? = 100 × 𝑎???𝑎? − ??𝑎????? | | 𝑎???𝑎? 10. Repeat steps 3 through 5 but use both the quarter and the penny this time at the same 30in height.
11. Capture screenshots at the regular intervals to show the heights of the two coins are always the same regardless of time. Determine if the mass of the object affects its motion in freefall. 12. Repeat steps 3 through 5 but start the quarter at 20in. Then calculate the acceleration due to gravity using the simplified freefall equation and then ? − ? 0 = − 1 2 𝑔? 2 repeat step 9. Results Picture 1: Timestamp of frame when quarter was released.
Data Table 1: Record of the progress of the quarter down the poster board with time in seconds in relation to position (y) in meters.
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Picture 2: Both penny and quarter before being released Picture 3: Penny and quarter at same height regardless of mass
Picture 4: Penny and quarter just before they hit the ground Picture 5: The quarter being released from 20in instead of 30in
Picture 6: The frame right before the quarter released from 20in hit the ground Analysis Data Table 2: Data analyzed from Data Table 1 and used in Graph 1
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Graph 1: Scatter plot for time squared and y values with a linear regression of . ? = − 0. 236? + 4. 41 Calculation 1: Percent error of Graph 1 showing that there is a huge difference between my measurement and the actual measurement
Calculation 2: Calculating gravity with the simplified freefall equation from the introduction Calculation 3: Percent error of the quarter falling from 20 inches. It gave a huge percent error showing that there was some error made through the experiment. Conclusion From all the analysis done above, it is clear that my measurements were a little bit off. I would attribute this to human error within the experiment with deciding on distances through frames in a recorded video. This way of measurement can lead to many human errors as it is based on estimation and human eyesight which can very easily make mistakes. My percent errors of 97.6% and 540% show that some of my numbers were extremely off resulting in a very high percentage error. Alongside human error, there is also equipment error because going through a video frame by frame to estimate distances can become inaccurate as a coin dropping is a very fast experiment and it can be difficult to distinguish things in a ten second video. I believe because of these issues in gathering data, my graph and consequently my linear regression was not accurate. The linear regression had a not very steep slope which created the percent error seen in Calculations 1.
We did determine that the mass of a coin was irrelevant as we experimented with dropping a penny and a quarter at the same time from the same distance and as can be seen from Pictures 4 through 6, they were always at the same height. I believe most of my issues came from poor eyesight and estimation skills as my heights for both Activity 1 and Activity 4 were inaccurate resulting in very high percentage errors. However, I do believe I completed the purpose of this lab by exploring motion and seeing how different heights, weights and types of coins can affect the distance they go and the time they take to get there. If I were to repeat this experiment, I would try to create a more accurate way of gathering data - a method that would be more accurate and give results which align more with Earth’s gravity and do not create a percentage error that is extremely high.
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