Purpose: The objective of this lab is to verify that a body in free fall will accelerate at a rate of 9.8 m/s^2.
Materials:
The apparatus shown above is a spark generator attached to a 1.5 m column. At the top of the column is a mass held by an electromagnet and when dropped, the spark generator records the fall/position of the mass every 1/60th of a second onto spark sensitive tape.
Above is the spark sensitive tape secured next to a meter stick. On the tape there will be a series of dots which correspond to the position of the free falling mass.
Procedure: To save materials, a demonstration of how the apparatus works was done and spark tapes were handed out from a previous class that had run the experiment. After the spark tape was secured next to a meter stick, we lined up the 0 cm mark with one of the dots on the tape, set this dot as our origin, and measured the distance of each dot that appeared after. With this data, we used excel to create five different columns in order to generate graphs that would display our values of acceleration based on the marked positions of the spark tape. We then gathered our class data as a whole, and calculated the average acceleration.
Data Tables/Graphs:
Column A - Time every 1/60th of a second.
Column B - Distance of every dot after the origin in cm.
Column C - Change in position between each dot ∆x.
Column D - Time for the middle of each 1/60th of a second interval. (A2+1/120)
Column E - Mid interval speed. (∆x/(1/60)
By selecting columns D and E in excel we were able to generate a graph that compared mid-interval speed vs. mid-interval time. This was done by using an XY scatter graph, adding a trendline, and displaying the trendlines equation along with its R^2 value. Based on our results, the slope of the equation showed the acceleration due to gravity was 932.7 cm/s^2 or 9.32 m/s^2.
Another graph can be generated by selecting columns A and B (Distance vs. Time). By taking the derivative of the equations slope, we get 2(476.224)x, which equates to 952.4 cm/s^2 or 9.52 m/s^2. This graph is slightly more accurate because we have an R^2 value equal 1.
By gathering every groups acceleration value, we were able to calculate the class average and standard deviation, which turned out to be 952 cm/s^2 or 9.52 m/s^2 and 31.88.
Our % error as a class equated to [(9.52-9.81)/(9.81)] x 100 = 2.96%. A pattern we saw was that most of the values for g were slightly lower when compared to the theoretical value, but our class average value compared very well with the accepted value, being only a mere 3% error. Oddly, our groups value for g was the same as the class average value for g. As far as % error goes, it can be accounted for due to systematic errors such as friction from the mass against the column while in free fall.
Summary: Overall, the lab was a success. As a class, we were able to verify that a body in free fall will accelerate at about a rate of 9.8m/s^2. Along with the spark tape/spark apparatus, we used excel to generate two different graphs and examined the slope of each graphs trendline to determine a sufficient value for acceleration due to gravity. We had a % error less than 5 % which is very reasonable.
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