The objective of the Free Fall lab was to determine a constant for gravity from the marks on our strip of tape produced by the spark apparatus (shown below).
Our Professor ran the experiment as a demonstration of how the apparatus works then handed out the tapes which contained data from previously run trials. A free fall body is held in place at the top by an electromagnet and when released, falls and marks on the tape its position every 1/60th of a second. Being that there are a lot of marks on the tape from us to choose from and we only need a few, we are allowed to start from wherever we think the marks are clearest. We decided on a starting point and recorded fifteen distances from that point.
We then used Microsoft Excel to help us with our lab because it is very good to use for computing large amounts of simple calculations. We created a data table and filled in our measurements from recorded data and the equations our Professor provided for us (shown below).
We then created two graphs; one based on our measurements on the tape (X) vs time and another with mid-interval time vs mid-interval speed. To make our X vs Time graph, we selected our values from the time and distance columns respectively and chose a polynomial fit for the trend line type (graph seen below).
We then created a graph based off our values for our mid-interval speed and mid-interval time to show that acceleration is constant through out the experiment. We then looked at the slope of our mid-interval speed and mid-interval time graph to get the slope which was what our data calculated acceleration due to gravity to be. The number we got was 930.46 cm/s. We know that the well established gravitational acceleration constant for earth is 9.81 m/s. We have an error of 5.20% below the established value. We could have also gotten the acceleration from our position vs time graph equation of the line. There we see that it is a second order polynomial equation. Comparing this with our kinematic equations for constant acceleration, ∆x=(v0)t+(1/2)at^2, we see parallels between the two giving us 1/2a = 472.54 or a=945.08. The error for this number is much smaller at 3.66% below the established value.
In the next part of the lab, we wanted to see just how good the spark apparatus was for acquiring data. Each group presented their acquired value for g and we entered then into our own Excel spreadsheets (seen below). We found the class average for the g value to be 956.03 cm/s^2. Using this, we found how much our individual values deviated from the class average. Unfortunately there were negative values so we squared the deviations, took the average of the squared deviations and then took the square root of the average deviation squared to give us 20.12 which is our average deviation of the mean.
In conclusion, the spark apparatus is not a very good tool for obtaining data. With values as high as 992 cm/s^2 and as low as 926.20 cm/s^2 the spread of values is kinda big. Our class average for g values is 2.55% below the accepted value for g at 9.81 m/s^2 which is just alright. What might account for the difference between the class average g value and our g value is the uncertainty which came up from measuring with a meter stick. The uncertainty in the measurements wasn't too big at 1 millimeter and we checked the measurements amongst our lab group. For the individual group g values to be so different must come from the data produced by the spark apparatus. I realize from hindsight of this lab that the big ideas here are that the equipment you use to obtain data and take measurements is very important to your findings. Also, that taking multiple experiments is necessary to get more reliable and accurate values. Finally I learned that knowing how to compute error is necessary for determining just how good your findings are and if you should present them to future employers.
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