Lab 2 Determination of g (and learning a bit about Excel) and some statistics for analysing data.

Student: Xavier Lomeli
Partners: Matthew Ibarra, Billy Justin
Date of Lab: 31 August 2016 

Determination of g (and learning a bit about Excel) and some statistics for analyzing data.

Mission Statement:To determine whether, in the absence of all other external forces except gravity, a falling body will accelerate at 9.8 m/s^2. 

Theory: Our theory is that in a controlled environment,the value of g can be determined through free-fall mass experimentation.
Experimental Procedure: In order to determine g, we used a strip of spark paper, marked by electric chars dispensed at equal time intervals by a falling body initially held in place by electromagnets to produce the strip of spark paper showing a dotted line with the dots increasing in distance with each other. This now became our permanent record of the fall corresponding to the position of the falling mass every 1/60th of a second, and we then proceeded to measure the distances between the char dots (in cm) and type them into our Excel spreadsheet, together with other columns for time transpired, change in distances between times, mid-interval times, and mid-interval speeds. We then selected the columns for mid-interval time and speed and made a XY scatter graph with the points not connected. Finally, we installed a linear fit from which we could get the equation of the line. We repeated this procedure for the columns of time and distance.


Lists/Tables/Graphs of Collected Data with Explanation:
Below are both of my graphs, showing distance v time and mid-interval speed v mid-interval time.

Questions/Analysis
1)
2) In order to get the acceleration due to gravity from the velocity/time graph, we simply look at the slope of our fit line, which turns out to be 954 cm/s^2, which corresponds with 9.54 m/s^2, which is fairly close to the accepted value of 9.81 m/s^2.
3) In order to determine the acceleration due to gravity from the position/time graph, the second derivative of any particular point must be found. Using Excel, I identified the position function to be y = 475.91x^2 + 74.29x + 0.02 and thus the first derivative to be 951.82x + 74.29 and the second derivative to be simply 951.82. Since our units of length were centimeters, this value corresponds to 9.52 m/s^2, which is within 0.02 of the value for g we got from our velocity/time graph, and fairly close to the accepted value of 9.81 m/s^2.

Conclusion- The difference between our calculated values and the accepted value is most likely due to measurement uncertainties when we determined the distances between char marks on the spark paper and also systematic error (i.e. less-than-cutting-edge equipment). Nevertheless, our value fell well within the range of values other groups collected.