Sparker Free Fall Lab and Standard Deviation of Data

Purpose: The purpose of the lab was to see if gravity was actually 9.8 m/s^2 ignoring all other external forces. It also served as a way to use Excel as a means of recording and displaying data effectively.

We used a machine called a sparker generator which records the location of an object in free fall on very thin sparker paper in order for us to observe the location of where the object is at specific time intervals. An object is first held on top of the electromagent and then released and at that moment the sparker generator creates an imprint on the sparker paper with accuracy in order for us to calculate acceleration.

Purpose: In order for us to get the data in order to get gravity as close to as 9.8 m/s^2, we have to use the sparker generator with sparker tape to measure the distance between the markings it will generate for us. After having dropped the object, the sparker tape will have imprints . These imprints are used to measure the distance the object dropped. We then grabbed a ruler in order to measure how far apart the imprints were from each other. This gave us the displacement of the object which will be used to calculate the velocity of the object as well as the acceleration which turns out to be gravity. 

Data & Calculations: After having found the values, we put them into an excel spreadsheet (all calculations were done in Excel). Knowing that the sparker generator creates imprints every 1/60 of a second, the distances between points are going to gradually increase since the acceleration of gravity is taking effect. We then calculated the mid-interval time between each imprint or point using the formula (time) + 1/20 s, the mid-interval speed between each point by using the formula (distance between each point) / (1/60 s).

This table represents the relationship between distance and time using a quadratic fit because in order for there to be acceleration, there needs to be an exponential change in distance. We were able to get such a result because as the object drops, the distance changes due to the acceleration of gravity.

This other data table shows the relationship between the mid-interval speed and the mid-interval time. It allows us to see that the speed of the falling object has a slope which means that there is an existing acceleration. We used a linear fit because change in speed is gradually increasing which shows us that there is an existing acceleration.

This other data table is the standard deviation of the whole class' results in order to compare how close we came to the constant of gravity as a whole. The result was about 955.3 cm/s^2 which is pretty close. Our result was 949.3 cm/s^2 which is number 7 on the graph.

Summary: This lab was successful because even though we did not get the actual 9.8 m/s^2 we were really close. We did find a pattern within our data points and they do make sense because in order for there to be acceleration, the correlation of distance has to quadratic and the correlation of speed has to be linear. Our result was 9.49 m/s^2 which was -0.31 m/s^2. The error percentage was approximately -3.16 % which in fact is relatively not too far off. We did not get these results because we have to consider the fact that we are humans so our data collection is not the most accurate. Another factor that prevented us from getting that result was air resistance and the machine that recorded the object falling is not going to be 100% accurate because no machine is perfect either. Overall, after collecting the data from the sparker generator and using it with Excel to find the acceleration of gravity we can say that this lab allowed us to see measure how fast objects fall by finding the constant of gravity.