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Westchester Community College Physics 1 Lab Free Fall Purpose Find the acceleration due to gravity at height 35000-38000 m above the Earth’s surface. Procedure You will use data collected during Felix Baumgartner’s stratosphere jump. Go to https://youtu.be/raiFrxbHxV0. You will see time of fall, altitude, speed, etc. displayed. 1. Record in the first two columns of the Data Table (see the Data Sheet) total elapsed time and the corresponding altitude (in meters), from about 6 seconds to about 30 seconds after the start of the jump. Try to record data at a time interval of 1 second (or as close as you can get to 1 second). You may need to play the video at a lower speed, I would recommend 0.25. 2. Calculate βˆ†π’• and βˆ†π’š (see the Data Table). 3. Calculate 𝒗𝒂𝒗 (see the Data Table). 4. Using Excel or Google Sheets, plot 𝒗𝒂𝒗 (along the π’š-axis) vs total elapsed time 𝒕 (along the π‘₯axis). Use scatter plot. 5. Add trendline (use linear fit) and display the equation of line. Take a screenshot of the graph and include in your lab report. 6. What physical quantity is represented by the slope of the trendline? 1 Westchester Community College Physics 1 Lab 7. Calculate the acceleration due to gravity at altitude of 35 000 π‘š using: 𝑔= 𝐺𝑀𝐸 (𝑅𝐸 + β„Ž)2 where 𝐺 = 6.67 Γ— 10βˆ’11 𝑁 βˆ™ π‘š2 /π‘˜π‘”2 𝑀𝐸 = 5.98 Γ— 1024 π‘˜π‘” 𝑅𝐸 = 6.37 Γ— 106 π‘š β„Ž = 35 000 π‘š Show your work. Record the calculated value for the acceleration due to gravity on the Data Sheet. 8. Calculate the percent error. Show work. Questions 1. Why not draw the line on your graph by simply connecting two of the data points, for example the first and the last one? 2. Plot the object’s state of motion on a pair of axes which represent position (Table, column 2) and time (Table, column 1). Since a straight line is not expected here, do not infer a line and do not measure slope. What kind of curve do these points follow? Explain. 2 Westchester Community College Physics 1 Lab Data Sheet: Free Fall Data Table total elapsed time, 𝒕 (𝒔) altitude, π’š (π’Ž) βˆ†π’• = 𝒕𝒏+𝟏 βˆ’ 𝒕𝒏 (𝒔) βˆ†π’š = π’šπ’+𝟏 βˆ’ π’šπ’ (π’Ž) β€” β€” βˆ†π’š βˆ†π’• (π’Žβ„π’”) β€” 𝒗𝒂𝒗 = Equation of trendline: ____________________________________ Slope: _________________________________________________ Physical quantity the slope represents:_______________________ Acceleration due to gravity (from the graph): __________________ Acceleration due to gravity (calculated): ______________________ Percent error: ___________________________________________ 3 Westchester Community College Physics 1 Lab Free Fall Purpose Find the acceleration due to gravity at height 35000-38000 m above the Earth’s surface. Procedure You will use data collected during Felix Baumgartner’s stratosphere jump. Go to https://youtu.be/raiFrxbHxV0. You will see time of fall, altitude, speed, etc. displayed. 1. Record in the first two columns of the Data Table (see the Data Sheet) total elapsed time and the corresponding altitude (in meters), from about 6 seconds to about 30 seconds after the start of the jump. Try to record data at a time interval of 1 second (or as close as you can get to 1 second). You may need to play the video at a lower speed, I would recommend 0.25. 2. Calculate βˆ†π’• and βˆ†π’š (see the Data Table). 3. Calculate 𝒗𝒂𝒗 (see the Data Table). 4. Using Excel or Google Sheets, plot 𝒗𝒂𝒗 (along the π’š-axis) vs total elapsed time 𝒕 (along the π‘₯axis). Use scatter plot. 5. Add trendline (use linear fit) and display the equation of line. Take a screenshot of the graph and include in your lab report. 6. What physical quantity is represented by the slope of the trendline? 1 Westchester Community College Physics 1 Lab 7. Calculate the acceleration due to gravity at altitude of 35 000 π‘š using: 𝑔= where 𝐺𝑀# (𝑅# + β„Ž)$ 𝐺 = 6.67 Γ— 10%&& 𝑁 βˆ™ π‘š$ /π‘˜π‘”$ 𝑀# = 5.98 Γ— 10$’ π‘˜π‘” 𝑅# = 6.37 Γ— 10( π‘š β„Ž = 35 000 π‘š Show your work. Record the calculated value for the acceleration due to gravity on the Data Sheet. 8. Calculate the percent error. Show work. Questions 1. Why not draw the line on your graph by simply connecting two of the data points, for example the first and the last one? 2. Plot the object’s state of motion on a pair of axes which represent position (Table, column 2) and time (Table, column 1). Since a straight line is not expected here, do not infer a line and do not measure slope. What kind of curve do these points follow? Explain. 2 Westchester Community College Physics 1 Lab Data Sheet: Free Fall Data Table total elapsed time, 𝒕 (𝒔) altitude, π’š (π’Ž) βˆ†π’• = 𝒕𝒏*𝟏 βˆ’ 𝒕𝒏 (𝒔) βˆ†π’š = π’šπ’*𝟏 βˆ’ π’šπ’ (π’Ž) β€” β€” βˆ†π’š βˆ†π’• (π’Žβ„π’”) β€” 𝒗𝒂𝒗 = Equation of trendline: ____________________________________ Slope: _________________________________________________ Physical quantity the slope represents:_______________________ Acceleration due to gravity (from the graph): __________________ Acceleration due to gravity (calculated): ______________________ Percent error: ___________________________________________ 3

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