31-Aug-2016:Free Fall Lab - Determination of g (and learning a bit about Excel) And Some Statistics For Analyzing Data

    Title: Free Fall Lab - Determination of g (and learning a bit about Excel) And Some Statistics For                     Analyzing Data
    Name: Qiwen Ye (Sherry)
    Lab partners names: Eugene, Chandler
    Date: 31-Aug-2016

Part 1
-- Purpose:
In this lab, we will show that an object under the influence of gravity alone accelerates at a constant rate. We will also measure this acceleration and compare with the actual value of 9.8m/s^2. We will also learn techniques of Excel and analyze data.

-- Theory/Introduction:
Free fall is the motion of a freely falling body, it is determine by gravity. If a net force acts upon a body, then that force caused the body to accelerate. If the force is constant magnitude, then the acceleration of the body will also be constant. Use sturdy column to provide a constant distance for studying free fall. When the free fall body held at the top by an electromagnet, it released and is recorded by a spark-sensitive.

-- Apparatus:
Use sturdy column provide a long 1.5m falling distance for an accurate reading. Through the spark-generator to record the fall, and the marks made at intervals on the spark-sensitive tape attached to the column give us a permanent record of the fall. We can measure the distance in the paper in order to get time and velocity.

-- Data:
Use a Excel Function to enter data.

-- Result/Graph:

Mid-Interval Time vs. Mid-Interval Speed

Time vs. Distance

-- Analysis:
The velocity in the middle of the a time is the same as the average velocity for that time interval, because for constant acceleration, any speed for interval is equal to speed at the middle of the time.
We can get the acceleration due to gravity from Velocity vs. Time, the equation of acceleration is a=(Vf-Vi)/(t2-t1). Through the equation of position and time, we can do the second derivative to get the acceleration.

-- Conclusion:
This lab proved very helpful to understand free fall. I learned that when an object falls under the influence of gravity, its velocity increases at a regular pace and the average of this pace is known as g= 9.8. We were able to prove this within an error of    % which is still good considering the equipment. I also learned that use Excel to build up table and analyze data. Overall, this was a great learning experience and an awesome lab.


Part 2 - Errors and Uncertainty
-- Purpose:
In this lab, we used Microsoft Excel to study the standard deviation. Generally, We used the last class lab's values (from free fall) and use Excel functions to fill down the data in order to find the relationship between the average deviation of the mean and the standard deviation of the mean. Also, we learned how to use the Excel functions of sum, count, average, power, square and absolute cell reference in order to analyze our data.

-- Theory/Introduction:
There are two forms of error (not including human error), random error and systematic error. Random error is scatter in date that people can not "blame" on anything particular. Systematic error comes from assumptions that people made which are not true and consistent equipment problem. The average deviation of the mean is to take the average of the absolute value of all of the deviations from the mean. We write this as:

Standard deviation of the mean is a very popular way of describing the spread of data, assuming the spreads around the average value are "random". the  People make all of the deviations positive is to square them, average the squared deviations, then take the square root. We write this as:

-- Apparatus/Experimental Procedure

Use a Mac book and open a new file in Microsoft Excel to enter the last class lab's values from each groups. Then, followed the lab guild line to set up a worksheet. 

-- Data:

Here is the data that we used from last lab's values:

Here is the guild line that how to enter the data into Excel:

-- Results/Graphs:

Here is what data look like in Excel, we entered last lab's values from cell A2 to A11. Then, we entered the formula "=average(a2:a11)" in cell A12 to get the average. We entered the formula "=a2-$a$12" in cell B2. After that, highlight the cells Ba through B11, enter the Edit menu select the option Fill Down. We can get all the deviation of the mean in each g. 

The pictures below is with the outline of 880:

This one is without 880, the number of 880 is the lowest value in those data, therefore, we removed the lowest value to calculate in order to get a more precision results.

-- Explanation of graph/Analysis:

The first picture in the results/graph shows that the average of those g is 935.9 and standard deviation of the mean is 28.2717173, it means that the propagated uncertainty in this case is 935.9+/-28.2717173. Without of 880, the average is 942.11111; the standard deviation of the mean is 21.262382, and the propagated uncertainty is 942.111111+/-21.262382. Compared to both results, we found that the second results is more close to the values that we want. 

-- Conclusion:

Our average value plug the standard deviation of the mean is close to the accepted values of g. Air assistance and offset or zero setting error may cause difference between the average value of our measurements and those of the class. Air assistance is the random error; offset or zero setting error is the systematic errors. In this lab, we practice use Excel to analyze data, and Excel is very helpful to compare the different date in different conditions.