1. Free Fall Lab - determination of g (and learning a bit about Excel) and some statistics for analyzing data

      Lab conducted by Mohammed Karim (author), Lynel, and Curtis on September 5 and 7, 2016.

2. Objective - Find acceleration due to gravity without any other external force.

3. Theory/Introdcution - This lab focuses on deriving gravity and finding the propagated uncertainty and then using statistics to find if the actual acceleration due to gravity (9.81 m/s^2) is within 95% confidence of our answer.

4.  

Pic of Apparatus

This apparatus features a magnet that, upon flipping a switch, drops and experiences free fall for 1.86m. A spark hits the magnet with a frequency of 60 Hz, marking the long strip of paper on the back. After plugging in time and distance to excel,we can use a marked scatter and find the linear fit. (See Figure 1.1) We then use the equation: y=vo*t+1/2*at^2 and multiply acceleration by 2 to find gravity. 

However, not everyone came to the same conclusion. The answers from other classmates varied from 893 cm/s^2 to 985 cm/s^2. This is due to uncertainty and random factors. However, we can say that after multiple trials, the average will gravitate closer to the answer. After finding the standard deviation of the mean, we can say that the answer is within 95 percent confidence within two standard deviations of the mean. The data can be seen in Figure 1.3 . 

6. Data tables-

Figure 1.1

Figure 1.2

Figure 1.3

7. Explanation/Analysis - 

The first figure is the linear fit of the acceleration graph. The second figure is a distance/time graph which is in the form of the kinematics equation y=vo*t+1/2*at^2.  The third figure is a worked out explanation of standard deviation for gravity.

8. Conclusion - 

Not only were we able to derive acceleration due to gravity, but we were able to find propagated uncertainty and find the standard deviation to make an estimated guess on our confidence of the answer. Of course, the results may be inaccurate at the moment, but with more tests it should be much more accurate.