The purpose of this lab was to determine the value for gravity along with practicing excel skills which makes calculations easier and swifter. This was done with a free falling body, spark generating apparatus, and a spark sensitive tape.
Experiment
To start off the experiment there is a free falling body that is at the top of the spark generating apparatus held in place by a magnet, and behind the free body is a red spark sensitive tape. Once ready the current is turned on running electricity through the wire that run from the top of the apparatus to the bottom, then the professor turns off the magnet and thus releasing the free falling body. Then as the free falling body falls towards the bottom sparks are generated as it comes in contact with the wire on it's way down, which in turns leaves marks on the spark sensitive tape.
Once the experiment is done we then take the strip of paper that now has little black markings on it and measure the distance between them. This is done by making the first point zero then measuring the distance between the first point and each consecutive point after.
Once we have obtained our measurements we then enter them into excel in column B, and for column A we will use it for how much time has passed between each point on the spark sensitive tape. The time interval for column A is calculated by adding 1/60 of a second each time, because that is the rate at which a spark is generated as the free falling body fell. The displacement in column C was calculated by taking each distance measured and subtracting it with the prior distance e.g. 0 - 3.7 , 7.8-3.7 , etc.. After that is done we then find the mid-interval time by taking the values in column A and adding 1/120 if a second to them. Lastly we find the mid-interval time which is done by taking the displacement in column C and dividing it by 1/60.
The mid-interval times and speeds were then graphed together because we know that the slope of a velocity vs time graph give us acceleration (in this case gravity). From our graph it can be seen that our value for gravity would be 1040 cm/s^2
The class then all reported what each of their values of g was and the average was taken; however, our groups data was not included in the calculation because our values were too large compared to the others, thus making it an outlier. In the second column next to the reported values of g we find how far each reported value was from the average value of g we found, this was done by taking each reported value and subtracting the average from it. In the third column we found the average deviation from the mean, but this was done in two parts by first squaring the values in the second column then taking the average of those values. Then by taking the square root of the average deviation we are given the standard deviation.
The meaning of the standard deviation is that +/- from the average value of g that will give us a range in which we are confident in that the value of g fall in, that is if there are no errors in our assumption for the experiment. If we create a range by adding and subtracting the once then we are 68% sure the value of g falls within that rang, and if we do it twice we are then 95% sure that the value of g falls in that range. The reason that there is a range for the possible value of g even though there were no errors in our assumption (systematic errors). There is however random errors which caused each group to have different results;therefore, a range was created in which the possible values of g can fall in. Some of the random error in the experiment could be as the free falling body fell an air current slowed or sped it up, or that at some points the current didn't hit the paper at a uniform interval.
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