Lab #2
Free Fall Lab
Free Fall Lab
Determination of g and some statistics for analyzing data
Ricardo Gonzalez
Josue Luna
3-1-17
Lab Part 1
This lab experiment was conducted in order to prove that objects under free-fall will fall at the speed of gravity, 9.8 m/s^2.
Lab Part 2
Secondly, we are able to measure the percent error in our value of gravity due to uncertainty.
1. Introduction
Lab Part 1
We have a rod of 1.86 m tall with a magnet holding an object from falling 1.5 meters. At the moment the magnetism is broken, the object falls with no other forces other than gravity in the downward direction. As the object falls, the position is recorded onto a spark-sensitive tape during equal time intervals. By measuring the distance within a time interval, we are able to find the acceleration through a position time graph and velocity-time graph.
Lab Part 2
When we look at data, it is inevitable to have variation between data, as nothing is ever perfect. We can calculate the difference between our data by finding standard deviation which would give us the range in which our data fluctuates.
2. Procedure
Lab Part 1
We were handed a spark-sensitive tape that was had the distance traveled marked for each time interval. We creating an excel file and on the first column we input the time after every time interval. Notice, the frequency used to mark the distance onto the spark sensitive tape was 60 Hz, therefore, a mark was made for every 1/60th of a second. On the second column, we placed all distance measurements for each time interval on the tape. For the third column, we measured the change in distance, Delta X. Under column D, we found the Mid-Interval Time. Lastly for the final column, we measured the Mid-Interval Speed. By selecting The Mid-Interval Time and Mid-Interval Speed, columns C and D, we created a scatter graph, giving us a Velocity-Time graph. Furthermore, we created a Position-time graph by utilizing the Time and Distance columns, columns A and B.
Lab Part 2
We created a second Excel file. On this excel file we gathered all the data that will be used to find the average standard deviation. he specific data we re looking at is the value of gravity that each group experimentally found. We numbered the first column from 1-10 for each group. Under the second column we placed the corresponding experimental-value of gravity from each group and found the average. For the third column, we subtracted the average value of gravity to each individual experimental-value of gravity for each group and then took the sum. Too find the deviation, we squared each result from the difference taken and once again, we took the average. Finally, we took the square root of the deviation, giving us the average of the squared deviations.
3. Data
Lab Part 1
Lab Part 2
Secondly, we are able to measure the percent error in our value of gravity due to uncertainty.
1. Introduction
Lab Part 1
We have a rod of 1.86 m tall with a magnet holding an object from falling 1.5 meters. At the moment the magnetism is broken, the object falls with no other forces other than gravity in the downward direction. As the object falls, the position is recorded onto a spark-sensitive tape during equal time intervals. By measuring the distance within a time interval, we are able to find the acceleration through a position time graph and velocity-time graph.
Lab Part 2
When we look at data, it is inevitable to have variation between data, as nothing is ever perfect. We can calculate the difference between our data by finding standard deviation which would give us the range in which our data fluctuates.
2. Procedure
Lab Part 1
We were handed a spark-sensitive tape that was had the distance traveled marked for each time interval. We creating an excel file and on the first column we input the time after every time interval. Notice, the frequency used to mark the distance onto the spark sensitive tape was 60 Hz, therefore, a mark was made for every 1/60th of a second. On the second column, we placed all distance measurements for each time interval on the tape. For the third column, we measured the change in distance, Delta X. Under column D, we found the Mid-Interval Time. Lastly for the final column, we measured the Mid-Interval Speed. By selecting The Mid-Interval Time and Mid-Interval Speed, columns C and D, we created a scatter graph, giving us a Velocity-Time graph. Furthermore, we created a Position-time graph by utilizing the Time and Distance columns, columns A and B.
Lab Part 2
We created a second Excel file. On this excel file we gathered all the data that will be used to find the average standard deviation. he specific data we re looking at is the value of gravity that each group experimentally found. We numbered the first column from 1-10 for each group. Under the second column we placed the corresponding experimental-value of gravity from each group and found the average. For the third column, we subtracted the average value of gravity to each individual experimental-value of gravity for each group and then took the sum. Too find the deviation, we squared each result from the difference taken and once again, we took the average. Finally, we took the square root of the deviation, giving us the average of the squared deviations.
3. Data
Lab Part 1
Lab Part 2
(Please note that we used cm/s^s as opposed to m/s^s. )
4. Results
Lab Part 1
As we can see from the graphs below that we have increasing functions for our Position-Time graph and Velocity Time graph. Looking at the Position-Time graph, if we took the slope of the line, we can get the Velocity. Now if we took the derivative of the function for the Position-Time graph, we would be given the function of the Velocity-Time graph. When analyzing the Velocity-Time graph, if we took the slope of the line, we can find the acceleration. Likewise, we can also take the derivative of the Velocity-Time function which would also give us the Acceleration. I would also like to mention, if we found the area under the curve of the Velocity-Time graph, we would get the total displacement. Likewise, If we took the integral of the Velocity-Time function, we would be given the Position-time Function. Simply by looking at the function of the velocity, we can see if we took the integral, mentally in our heads without any real effort, we would get the number 9.5 m/s^s. That number is our acceleration due to gravity. Our acceleration is a constant value as we can see, there is no longer any variables in our function after taking the derivative of the Velocity function. Notably, our acceleration calculated was not exactly 980 cm/s^2 (9.8 m/s^2) as we initially believed due to errors and uncertainty.
Lab Part 2
From the results we have gathered, we can see that 1 standard deviation is equal to 1 sigma. Our 1 sigma, in this experiment is equal to 6.1 cm/s^2 therefore giving us a range of values acceptable to our calculated value of gravity. Our range is from 955.4-967.6 cm/s^2, that is that at least 68% of our data were within 1 standard deviation of our value of gravity. Secondly, going further away from our first standard deviation from our average to the range of 949.3-973.7 gives us a second standard deviation from the average, in which at least 95% of our data was within 2 standard deviations.We can see a pattern in the data gathered for the value of gravity, in such that not one group was further away from two standard deviations of our average. As we compare our average value of gravity from all group, we can see that we are still far from the value of gravity, as much as 31 cm/s^2 and as low as 6.3 cm/s^2.
5. Conclusion
Having analyzed the data, we have to conclude that there must have been another factor that was not taken in account for when conducting this experiment. I say this because as we can see, random error was a clear reason for having deviations in the calculated value of g. These deviations could have been made when measuring the distance after each time interval on the spark-sensitive tape. Uncertainty between measurements of the same distance is completely possible which is why some groups were able to within two standard deviations from the average value of gravity. A systematic error, such as air resistance could have affected the acceleration of the object as it fell. Also, the time the object took to begin falling in response to the electromagnetism disengaging could have, to a certain extent, affected the first time interval, inevitable affecting the following intervals.
The point of this lab was not only to learn how to calculate the acceleration do to gravity, assuming an ideal case where no other forces are applied to the experiment, but also to be able to use tools like Excel to do the Calculations for us. Key concepts of this lab were that not all experiments are perfect, in such that there will always be at least some variation between data. However, we are able to find an average and thus a standard deviation from our average. By finding a standard deviation, we are able to utilize a range of acceptable values within a number of deviations.
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ReplyDeleteHello Professor Wolf, This is Ricardo reminding you that i had done the wrong lab report For Monday march 12. I have completed both labs due this week but in the wrong order. Thank you, Ricardo.
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