Lab partners:
Lab performed: 09/07/16
PART 1:
In this lab, we test to see if the acceleration of an object in free fall will equal the acceleration of gravity (9.8 m/s^2) if no other forces acted on it. To do this, we used an apparatus from which the object was released and a strip of spark paper that recorded the data.
Spark generator apparatus with tripod base and spark paper strip
Every 1/60th of a second, the spark generator left a dot on the spark paper. After recording a good amount of data points, we lined the spark paper up with a meter stick, and marked the position of each dot.
Dotted spark paper aligned with meter stick (positions recorded in cm)
We took this data along with some other information and entered it onto an excel sheet. Because we want to record the time in intervals of 1/60th of a second, we enter the time in cell A3 as "=A2+1/60", A2 being the initial time (0 seconds). The equal sign makes it so that what we enter into the cell becomes a function. Then, instead of doing this with every cell going down column A, we can use Excel's fill function. This will automatically fill the column with the corresponding cells (so in cell A4, "=A3+1/60" will be entered, and so on).
On the left: Excel spreadsheet with data for time, distance, delta x, mid-interval time, and mid-interval speed
To continue, we made two graphs: one of column D versus column E, and another of column A versus column B. For both graphs we chose a corresponding graph fit and displayed the equations and R-squared values.
On the top: Graph of mid-interval time v. mid-interval speed with linear fit
On the bottom: Graph of time v. distance with polynomial fit of order 2
PART 2:
In the second part of the lab, we learned how to calculate the uncertainty in our data whilst implementing our learned knowledge of excel through analysis of the class' data (from part 1). The lab manual goes over in detail how to find uncertainty, but there are two ways.
The first way is called taking the average deviation of the mean. With this method, you take the average of the absolute value of all the deviations from the mean to make the values positive. The second way, which we used for our data in this part of the lab, is to square them, average them, and then finally, take the square root.
The first way is called taking the average deviation of the mean. With this method, you take the average of the absolute value of all the deviations from the mean to make the values positive. The second way, which we used for our data in this part of the lab, is to square them, average them, and then finally, take the square root.
Formula used to analyze class data
In excel, we create three columns. The first will have the class' values of g and the average of those values, and the second will be the deviations from the mean. The third we had to construct ourselves to find the uncertainty, so we finish the formula by squaring column two's values, and finally taking the square root of the average of those values.
Excel sheet with class' g values and the final calculation of the standard deviation of the mean
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