Alexander Reyes
Lab Partners: Mike Flores & Mike
Date Performed: 9/7/16
Purpose: To observe and approve that a falling body will accelerate at 9.8m/s^2 with only gravity acting as a force.
Theory/Introduction: g value of a free falling body must be determined by graphing a velocity vs time graph and a position vs time graph. In this specific case a spark generator with a free falling body would be studied in order to conclude if the falling body accelerated at 9.8 m/s^2.
Apparatus/Experimental Procedure:A spark generator free fall apparatus was used within the experiment. The generator had a column with a 1.5 meter falling distance, and the free-fall body was held at the top by an electromagnet. When the electromagnet was released, the fall was accurately recorded by a spark generator. Markings were engraved on the piece of tape that was attached to the generator in order to record the fall.The distance between each marking on the tape was measured using a meter stick. Pictures of apparatus and tape from spark generator are provided below.After obtaining all information, a velocity vs time graph and position vs time graph were plotted.
Table of Measured Data:
Below is the data that was needed in order to plot each graph. Time data started from 0 sec, and 1/60th of a second was added continuously. The distance column shows the distance between each marking in centimeters on the spark generator tape.
Position vs Time Graph: In order to obtain the acceleration from the position vs time graph the second derivative must be taken from the equation. After calculating the second derivative the value for g= 9.2m/s^2. Calculation of derivative can be found below. Experimental value is slightly off from the accepted value of 9.8 m/s^2
Velocity vs Time Graph: In order to obtain the acceleration from the velocity vs time graph the first derivative must be taken from the equation. After calculating the derivative the value for g= 9.2 m/s^2. Experimental value is slightly off from the accepted value of 9.8m/s^2
Errors & Uncertainty: Below is an excel spreadsheet which determined the standard deviation of the mean of the class. Every group within the class got a value for g in the 900 mark. The average value of 942.1 is slightly off from the accepted value of 980, but is still close enough to give a good average.
Conclusion:
A spark generator apparatus was used to calculate the acceleration (g value) of a free falling object. Once data was gathered from the apparatus tape an excel spreadsheet was created along with two graphs, a position vs time and velocity vs time graph. The acceleration of the free body object was determined by taking the second derivative of the position vs time graph equation and first derivative of the velocity vs time graph. Experimental acceleration found for the free falling object was 9.2 m/s^2. Another excel spreadsheet was created in order to find the class mean and standard deviation. Sources of uncertainty or error could have occurred when measuring the markings on the spark generator tape that was obtained. Also, the tape could of been placed incorrectly into spark generator.
Apparatus/Experimental Procedure:A spark generator free fall apparatus was used within the experiment. The generator had a column with a 1.5 meter falling distance, and the free-fall body was held at the top by an electromagnet. When the electromagnet was released, the fall was accurately recorded by a spark generator. Markings were engraved on the piece of tape that was attached to the generator in order to record the fall.The distance between each marking on the tape was measured using a meter stick. Pictures of apparatus and tape from spark generator are provided below.After obtaining all information, a velocity vs time graph and position vs time graph were plotted.
Table of Measured Data:
Below is the data that was needed in order to plot each graph. Time data started from 0 sec, and 1/60th of a second was added continuously. The distance column shows the distance between each marking in centimeters on the spark generator tape.
Position vs Time Graph: In order to obtain the acceleration from the position vs time graph the second derivative must be taken from the equation. After calculating the second derivative the value for g= 9.2m/s^2. Calculation of derivative can be found below. Experimental value is slightly off from the accepted value of 9.8 m/s^2
Velocity vs Time Graph: In order to obtain the acceleration from the velocity vs time graph the first derivative must be taken from the equation. After calculating the derivative the value for g= 9.2 m/s^2. Experimental value is slightly off from the accepted value of 9.8m/s^2
Errors & Uncertainty: Below is an excel spreadsheet which determined the standard deviation of the mean of the class. Every group within the class got a value for g in the 900 mark. The average value of 942.1 is slightly off from the accepted value of 980, but is still close enough to give a good average.
Conclusion:
A spark generator apparatus was used to calculate the acceleration (g value) of a free falling object. Once data was gathered from the apparatus tape an excel spreadsheet was created along with two graphs, a position vs time and velocity vs time graph. The acceleration of the free body object was determined by taking the second derivative of the position vs time graph equation and first derivative of the velocity vs time graph. Experimental acceleration found for the free falling object was 9.2 m/s^2. Another excel spreadsheet was created in order to find the class mean and standard deviation. Sources of uncertainty or error could have occurred when measuring the markings on the spark generator tape that was obtained. Also, the tape could of been placed incorrectly into spark generator.
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