Lab 2 Summary - Covers the \"Free Fall-Measure of \"g\" lab PDF

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Covers the "Free Fall-Measure of "g" lab...

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Free Fall-Measure of "g" Kristen Holmes

Oliver Larroque 14 September 2017

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PURPOSE: The purpose of this experiment was to learn how to calculate different gravity values and determine acceleration values due to those gravities. The experimenter also learned how to use the Capstone program in relation to the use of sensors. THEORY: Two freefall experiments were performed. The first experiment involved objects of different masses being dropped out of a window and the time was recorded with a stopwatch. The second experiment obtained much more accurate measurements since the mass of the object was the same each time and the time of the drop was measured with a sensor and measured through a computer program. The reason for having two different experiments but using the same calculations and having the same goal of finding the acceleration due to gravity is to perform an error analysis and be able to compare the results of the two different experiments. It can be clearly seen in the results that there is a great difference in each of their percent errors, which is exactly what was supposed to be seen. Acceleration:

Gravity:

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Standard Deviation of Gravity:

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Fractional Error (Deviation Percentage):

Percent Error:

Slope:

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PROCEDURE: For the first procedure the Teaching Assistant (TA) was in charge of performing the actual experiment. Each student was responsible for recording the time of the drop using a stopwatch or a phone stopwatch. After the TA said "One, Two, Three, Drop" each student started their stopwatch and stopped it as the mass that was dropped hit the ground. Then that time was recorded individually by each student. This was done six times with a variety of different masses. After each drop was performed the class pulled together their times to create a more balanced data table and to eliminate some of the error. One person from each group was also selected to measure the height of the window to provide an average distance of travel. To perform the calculations for the first experiment the average times for each trial were used to determine the average values. The average value could then be used to find the uncertainty (standard deviation of the mean). The average and uncertainty were found for the height. The average values for height and time were used to determine the average gravity. Then using the uncertainties of height and time the standard deviation of gravity formula was used to find the uncertainty of gravity. Using the uncertainty of gravity, the fractional error of gravity was calculated. Lastly, the percentage error of gravity was determined using the given accepted value (GAV) of 9.8m/2. For the second procedure, performed by the students, a set up was required for the equipment as well as the computer program. To set up the apparatus for the second experiment the steel ball was gently clamped in the release mechanism by loosening the thumb screw on the side and inserting the ball. Then to tighten it, the pin with the spring on it had to be pushed on until it was tight and the thumb screw was tightened until the ball was secure. The sensor pad was then positioned directly underneath the ball using a long ruler.

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To set up the computer program the controller box had to be connected to the Digital Channel of the PASCO 850 computer interface. Then Capstone was opened on the computer desktop. The option of two large digits was then selected. Along the left side bar the icon that says "set up hardware" was selected and showed an interface box icon. This icon was clicked on and the input was selected to select the digital channel to which the Free Fall adapter was plugged into. Then Free Fall adapter was selected and ok was clicked to finish that part of the set up. In the upper right corner there was a orange push pin, this was selected to change the digit screen. To complete the set up, the option "select measurement" was selected and set to time of fall. Now that everything was set up the actual experiment could be performed. For each of the five trials, the height of the apparatus was raised by 0.25meters, starting at 1.0meter and ending with 2.0meters. The ball was gently clamped in the release mechanism. Then the record button on the bottom left of the screen was clicked and the ball was released by loosening the thumb screw. After the ball hit the sensor pad, stop was clicked so that the time could be recorded. The previous step was then repeated two more times from the same height for a total of three trials. Then after readjusting the height, the previous steps were repeated, recording three trials for each height. The first calculation for the second procedure was done by determining the average time values for each height. Then the acceleration was found in order to find the gravity value for each height. Then the average gravity was found along with the uncertainty of the time values and the height values. These were then used to in the standard deviation of gravity calculation to determine the uncertainty of gravity. Then the uncertainty of gravity was used to find the

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fractional error. Lastly, the percentage error of gravity was determined using a given accepted value (GAV) of 9.8m/s2. The last part of this procedure was to graph height vs. time. Then height vs. time2 was graphed and the slope was calculated. For this experiment, I participated in the first part by timing the fall of the different masses, like the other students. For the second part, I was responsible for operating the computer, making sure everything was accurately set up, and ensuring that the data given to us by the computer was not affected by any outside factors and was given to my lab partners correctly.

This is the type of apparatus used in the second procedure. http://www.batesville.k12.in.us/physics/APPhyNet/lab/experiments/kinematics/time_of_fall.htm DATA: See attached data sheets. ANALYSIS: See attached work.

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CONCLUSION: The reason for this experiment was to perform two procedures that measured the same values and provided us with the same data; then compare them on their precision and accuracy. The first procedure was expected to have a slightly higher standard deviation and a much higher percent error, which ultimately it did. The reason for this assumption is because standard deviation and percent error represent two things, precision and accuracy. When discussing precision (standard deviation), the closeness of each measurement to each other is what was trying to be determined. When trying to determine accuracy (percent error) the closeness of the data to each other is not important, instead the result needs to be compared to an known value. This is why percent error is used because the known value to which the results are compared would be the given accepted value (GAV) for this formula. To assume that procedure one would not have a drastically different standard deviation compared to procedure two, despite procedure two having many more controlled components, is because the measurements are being compared to one another. The masses are dropped from nearly the same height each time, and the other variable (the mass) is different for each object. This would result in a range of different times and ultimately a range of different calculated gravities. So there will be a fairly large standard deviation since the measurements are not close to each other since they have different masses. However, the reason why procedure two would not have a substantially lower standard deviation is because this procedure also had a variable that changed, but for this case it was the height and not the mass of the object. The results from this procedure would not be very similar to one another since the ball was dropped from a different height each time. Although it is expected for procedure two to have a slightly smaller standard deviation since much of the process was a lot more controlled such as the height measurements and the time of free fall.

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Percent error between the two procedures, however, should be drastically different. This can be assumed simply by the fact that when compared to a given accepted value (GAV) such as gravity, calculations done with measurements that were recorded during a procedure with uncontrolled components, there will be a large amount of error. Errors in this first procedure most likely came from inconsistency or inaccurate reaction time from each student when recording the time it took for the mass to hit the ground. There was also error in the height measurements, since each mass was dropped out of the window from the TA it is likely that he could have raised his arm slightly higher or slightly lower for each one. When the height was measured by a few selected students these measurements were also susceptible to error since the measuring tape could have been held higher or lower each time, the measuring tape could have been held at an angle, or the measuring tape could have not been fully extended to the ground. Some of these errors were eliminated due to the fact that multiple trials were performed, however, this did not eliminate the majority. Simply put, having a high amount of uncontrolled factors that produce error, there will be a large percentage error meaning there is very little accuracy. For procedure two, the percent error should not be very large at all. There should only be a small amount of error in this procedure. These errors could result from inaccurately measuring the height from which the ball was dropped, or incorrectly setting up the computer program which measures the time of the drop. Therefore, there should be a much higher amount of accuracy in this procedure. All of these statements about precision and accuracy assumptions are proven to be correct in the data calculations that were done for this experiment and are attached to this document. The last thing to discuss is the graphs that were drawn in correlation to the data calculations preformed for the second procedure. There are two graphs (attached to document),

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the first is a height vs. time graph, and the second is a height vs. time2 graph. The first graph (height vs. time) resembles a straight line. This is an accurate representation of the data collected and accurately explains what is happening in the procedure. It is expected for the time of the drop to increase as the height of the drop increases. The longer the ball has to fall, the longer it takes to hit the sensor. To prove that the graph is correct, the equation y=1(gt2)/2 can be used to check the graph. Although, this equation would also show that if multiple more values were obtained eventually the graph would start to curve, still increasing but at a much slower rate. For the second graph (height vs. time2) the line was very similar to the first graph and was accurately represented by the formula as well. These graphs are expected to look very similar, since they are representing the same data and the only thing that has change is the x-axis representing a squared unit. Finding the acceleration of this graph, provides the slope of the line as well. Acceleration and slope are equal to each other, representing change in position/change in time....