07-Sept-2016: Free Fall Lab determination of g

Lab #2 Free Fall and the determination of g

Andrew Martinez
Lab Partner: Richard Mendoza

Statement: Use the apparatus to demonstrate the motion of free falling bodies and learn how to determine acceleration through a position vs time graph and

Theory/Introduction:To analyze how to determine g based on the apparatus of a free falling object and using statistic to analyze gathered data through excel. Gravity is present in all case whether something is fall or not gravity is constantly pulling with a force of 9.8 m/s^2

Apparatus: An electrical device magnetically suspends the a wooden cylinder by its metal ring. A length of tape is vertically pulled down to match the length of the vertical device. Once the electromagnet turns off the wooden cylinder will fall which an active electric current going off every 1/60 of a second marks the position of the object at that moment. This can be used to make a time vs position graph.

Procedure: For this lab several steps had already been done that resulted with the tape having the spark marks finished. Next you open up excel to begin recording the data and using the program to find the time and distance. Once done create charts to fine the R and the chart equation.

Measured Data:
Part 1

Table 1

A Column: Time in 1/60 of second. B column: Position the rod was at when the time was recorded. C colum: Distance displacement. D column: Time recorded at 1/120 of second. E column: The velocity recorded at the mid-interval time.

Graph 1 (Table 1)

Graph 1 has a linear fit done to it with the equation shown

Graph 2 (Table 1)

Graph 2 has a polynomial fit done and the equation is given

Part 2

Table 2

A column is the listed groups data, B column is the deviation from the A column mean at A10, C column is the standard deviation or range that most fall within and is considered acceptable.

Calculated Results:
Part 1
1.

 As shown the resulting average velocity is nearly the same as the mid-interval time displaying how constant acceleration effects velocity.

2. You can get acceleration by deriving the equation provided after doing a linear fit on the velocity/time graph.

3. To get the acceleration from a position/time graph you take the second derivative of the equation provided from the polynomial fit.

Part 2
1. Most of the values of our g seemed to be constant with an R^2 value of .998.
2. The average value of g given by the group data is 9.48 m/s^2 while the accepted value is 9.8 m/s^2. This puts the difference between expected and experimental at -4% well within acceptable range.
3. The pattern between the class value seem to centered around 9.48 m/s^2 where the majority of values falling within one standard deviation.
4. Random errors that could have occurred are changes in the electric current which could have effected how often a mark was left on the tape. A systematic error could be misreading measurements on the meter stick as the marks were sometimes between measurements and assumptions had to be made.
5. The main point of part 2 of the Lab was to become familiar with Excel and learn useful programming for gathering data and analyzing it. That through analyzing the data we can find the standard deviation and means and see how accurate our results are to the actual.

Conclusion: While the calculated g for our group was 9.57 m/s^2 and the actual value is 9.8 m/s^2  the relative difference is -2.34% which is an acceptable margin. There are some inherit uncertainties such as the accuracy of the meter stick. Since the most accurate we could be was to the millimeter that leaves a .001% uncertainty. Though this should not effect the results to much.