28 August 2014: Freefall Lab 2

I'm sure we've all heard the famous story of a young Isaac Newton sitting beneath an apple tree contemplating the ways of the universe. All of a sudden, an apple hits him on the head. As simply as that, he is able to comprehend that the very same force that brought the apple crashing toward the ground also keeps the moon falling toward the Earth and the Earth falling toward the sun. This force is called gravity. In this lab we will be exploring this value of "g" and verifying its agreed value of 9.81 m/s^2.


Materials:
An apparatus that measures "g" by generating sparks.
A ruler
Paper
A computer with a Logger Pro or Excel System


Procedure:

The apparatus had a weight that was allowed to drop from 1.5 m high drop. When the weight is released, an electric generator sent a shock on the strip where the weight is every 1/60 of a second leaving a distinct mark. We were to use strips already made from a previous class

We then picked a mark to be our first and measured the distance of every mark that appeared after the one we had chosen. 

Then we entered our data into excel. For column A we entered time at every 1/60 of a second. Column B is in cm and is the distance of every mark; it is important to note that the mark we chose as our first is our 0. For column C, we were able to calculate, with the help of excel, the distance between each mark; that is to say that Δx= Mark(n)-Mark(n-1). For column D, we were able to calculate the time between each mark by taking the time from column A and adding 1/120. Lastly, for column E, we were able to calculate the speed between each mark by taking the delta x from column C and dividing by (1/60).

After we performed these calculations, we constructed a graph that compared the mid interval speed and the mid interval time.

We then added a trendline on excel and found that our acceleration due to gravity (g) was 9.39 m/(s^2) as seen by the slope of the graph.

Next, we gathered the acceleration due to gravity "g" that was calculated by every group and entered them into excel.

We then calculated the average from all our "g" values. As you can see the average was 9.48 m/(s^2). We also calculated the deviation from the average as well as standard deviation, deviation squared, and the average of the deviations squared.

Conclusion:

In conclusion, our results that was calculated by the slope of our graph of 9.39 m/(S^2) was much lower than the value of 9.81 m/(s^2). If we were to calculate percent error whose formula can be seen below:

We would get these results:

9.39-9.81   x   100% = -4.28%

                                               9.81

This means that our value was 4.28% lower than the theoretical value. This was most likely due to systematic error of the apparatus rubbing against the weight. Also, since these strips of paper were done in the previous class, we were not able to see if there were other sources of error in the process.