Determining the value of gravity due to acceleration from simple pendulum motion
Raw data:
Data processing:
Average time: (Trial 1 + Trial 2 + Trial 3)/3 eg: (40.77+41.00+41.07)/3 = 40.95
Uncertainty of average: [(Highest value)-(lowest value)]/2 eg: [(41.07)-(40.77)]/2 = +/-0.15 s
Time period: Average time for 20 oscillations/20 eg: 40.95/20 = 2.05
Acceleration due to gravity: ( 4 π2 l)/t2 eg: ( 4 π2*1)/2.052 = 9.394 = 9.40 ms-2
Uncertainty of gravity: [(Uncertainty of length/ value of length)+(Uncertainty of time period/value of time period)]*100 eg: ( 0.1/1)+(0.01/2.05)*100 =9.40 ms-2 +/- 14%
Therfore, (14/100)*9.40 =+/- 1.316
So, g = 9.40 +/- 1 ms-2
Average gravity: (9.40+9.52+9.30+9.52)/4 = 9.44 ms-2 +/- 4.5 ms-2
Percent error compared to theoretical value:
[(Theoretical value- calculated ...
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Uncertainty of average: [(Highest value)-(lowest value)]/2 eg: [(41.07)-(40.77)]/2 = +/-0.15 s
Time period: Average time for 20 oscillations/20 eg: 40.95/20 = 2.05
Acceleration due to gravity: ( 4 π2 l)/t2 eg: ( 4 π2*1)/2.052 = 9.394 = 9.40 ms-2
Uncertainty of gravity: [(Uncertainty of length/ value of length)+(Uncertainty of time period/value of time period)]*100 eg: ( 0.1/1)+(0.01/2.05)*100 =9.40 ms-2 +/- 14%
Therfore, (14/100)*9.40 =+/- 1.316
So, g = 9.40 +/- 1 ms-2
Average gravity: (9.40+9.52+9.30+9.52)/4 = 9.44 ms-2 +/- 4.5 ms-2
Percent error compared to theoretical value:
[(Theoretical value- calculated value)/ theoretical value)]*100
=[(9.81-9.44)/9.81]*100 = 3.8%
Conclusion:
Overall, the experiment seemed to be effective, yielding a reliable result. The aim was to determine the value of gravity by a simple pendulum, in which the string was altered each time. As the length of the string decreased, the time period also decreased. This is because as the string was cut smaller, the ball bearing had to cover less distance in order to complete one cycle in a given time period.
Evaluation:
We can see by comparing our result to the theoretical value, that the experiment can be considered successful. A 3.8% error suggests that there is still room for improvement, however we managed to end up with a value that is therfore reliable and accurate to a certain degree when compared to the theoretical 9.81 ms-2. The uncertainties built up during the experiment would still not compensate for the slight difference between the theoretical value and ours, so therefore we must take into account random errors and systematic errors. Such are errors that resulted from the string instead of being cut to the exact length with a loop which would have been used to attach the string to the stand, it was only rounded ot the top. This might have affected the acceleration of the pendulum when swinging to one side.
Graphs:
*Graph number 2: The period of a simple pendulum is directly proportional to the square root of length of the pendulum, thus we get a more or less straight line.
