3 Sep 2014: Determination of gravity and learning some features of Excel

Purpose: The purpose of this lab is to get as close as possible of the real value of gravity "g" as well as leaning a little more of the capabilities of Excel when computing data.

This apparatus is called spark generator, which is a electromagnet with power supply that give us some data to conclude our project. It provides us marks on a spark-sensitive tape at specific intervals so that we have records of those points, which are the distances of the object dropped as it reaches the ground.

With the data of the distances given by the apparatus, we are going to use a ruler to calculate each distance from the origin. Each mark has a time interval of 1/60 of a second, and as we all known, those distances are going to increase as it reaches the ground because gravity is acting on it. Then we calculated the distance between each point, the mid-interval time for each point with the formula: (time)+1/120, and the mid-interval speed with the formula (distance between each point)/(1/60). We compute all this data in Microsoft Excel, creating a table, and with that we created two graphs: one for Mid-interval speed vs. mid-interval time and one for distance vs. time. The slope of the graph Mid-interval speed vs. mid-interval time gave us an approximation of what is gravity.

 This table is our collection of data, each column has a title of what those numbers mean.

 This graph is the distance vs. time, its was originated with the data from columns A and B from the first picture.

This is the graph of Mid-Interval Speed vs Mid-Interval time, originated from columns C and D from the first picture. The slope of the graph is the approximated acceleration of gravity.

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This table is the collection of data from all groups in our class, our group number is #7. From this table, we could compare our results to the other groups.

Summary

First, we used the spark generator apparatus to collect the data needed for us to calculate each distance point. From that, we went to the computer and typed a table with our data plus the formulas given in the lab sheet. We were able to generate a two graph with our data information, one containing distance vs. time and another one containing mid-interval speed vs. mid-interval time. From those graphs, we found their slopes to reach an approximation of acceleration due to gravity. Then, we compared our results with other groups to see if our data was accurate.

Questions

1) For constant acceleration, the velocity in the middle of a time interval is the same as the average velocity for that interval because the both will become a function of time, and the time will be the same.

2) The acceleration due to gravity can be obtained from our velocity/time graph because it will be the slope of that graph.

3)To find the acceleration due to gravity of our position/time graph, we find the slope and multiply by 2.

Our results were a little off when compared to the real value of gravity = 9.81 m/s^2. We got 9.49 m/s^2 which was not far from it, but not so close. Some reasons for that could be systematic errors that interfered in our conclusions and also human errors, which are errors that happen from us being human beings; that is, when we calculated each distance point, they might be a little off. Another reason could be air resistance when the experiment was executed, leading to errors that affected our final result in finding the acceleration of gravity.

Difference between expected and experimental values

Relative difference:  (9.49-9.81)*100/9.81 =  -3.27%

Absolute difference: 9.49-9.81= -.32 m/s^2