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5 Pages

### lab write up 1

Course: BIO 205, Fall 2011
School: SUNY Stony Brook
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Word Count: 715

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Roel 6/7/2011 6/8/2011 lab Christopher #1 The Pendulum and Error Analysis Purpose In this lab a metal ball was attached to a length of string from a fixed position. Time intervals and the length of string the pendulum was attached to, were used to calculate gravity. Absolute and relative error analysis equations were also used to account for human error. Materials The materials used in this experiment...

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Roel 6/7/2011 6/8/2011 lab Christopher #1 The Pendulum and Error Analysis Purpose In this lab a metal ball was attached to a length of string from a fixed position. Time intervals and the length of string the pendulum was attached to, were used to calculate gravity. Absolute and relative error analysis equations were also used to account for human error. Materials The materials used in this experiment consisted of; a metal holder attached to a table, a length of string, a steel ball, a protractor, a ruler and a timer. To being the procedure, a length of string was measured to 50cm and then remeasured 5 times to calculate the possible error analysis that the string was off by. Then the ball was released from 3 different angles (15, 30 and 80) and let swing for a time of 10 periods (1 period is a back and forth swing) which was called 10T. 10T was then divided by 10 to come up with the time it took for the pendulum to swing and return to its starting. The error for T was then calculated using .2 seconds as a response time. Then the angle of 15 was held constant with the length of the pendulum being increased after every 10T interval. The length of the pendulum was measured 5x which gave us a relative error for the measurement. Relative errors for the timing of 10T was also calculated. Using this as well as (relative error), graphs were constructed to represent the relationship between values. Observations Measurement # L of pendulum 1 50cm 2 50cm 3 49cm 4 49cm 5 50.5cm angle 10T 15 13.8s 30 13.9s 80 15.7s L 20cm 40cm 60cm 80cm 100cm 10T 9.0s 12.3s 15.2s 17.5s 19.4s Summary and Calculations Based on the slightly varying lengths for the pendulum in the first table of observations. The relative error of the length was able to be calculated: L calculated by: For the angles 15, 30 and 80 it was possible to calculate a single T period from the original 10T segment that was recorded. From there, relative error was able to be calculated taking into account human reaction time. angle 1 0T 15 13.8s 30 13.9s 80 15.7s T T 1.38 .028 1.39 .028 1.57 .028 T calculated by: T calculated part by: For III absolute error of the length, period T, T, T^2, T^2, L^2 and L^2 were all calculated. L 20cm 40cm 60cm 80cm 100cm L .19cm .24cm .1cm .3cm .15 10T 9.0s 12.3s 15.2s 17.5s 19.4s T .9s 1.23s 1.52s 1.75s 1.94s T .028s .028s .028s .028s .028s T^2 .81s^2 1.51s^2 2.31s^2 3.06s^2 3.76s^2 T^2 .05s .069s .085s .098s .109s L^2 400cm^2 1600cm^2 3600cm^2 6400cm^2 10000cm^2 L^2 7.6cm 19.2cm 12cm 28cm 30cm L calculated by: T calculated by: T calculated by: T^2 calculated by: L^2 calculated by: L^2 calculated by: Based on these numbers, graphs were then plotted using these numbers to represent the relationship between these values. Graph 1, M calculated by: Error in slope calculated by: Graph 2, M calculated by: Graph 3, M calculated by: G calculated by: Error in G calculated by: Questions: 1. The period T does vary with the angle , although the periods for 15 and 30 do overlap, making them equal. 2. An angle of 15 was used as opposed to 30 or 80 because it had the smallest period and it was thought that it would demonstrate a more linear relationship with the increasing length. This will allow us to find a more accurate value of G. 3. The errors for L and T in parts I and III were absolute errors. 4. Equation 8 represents a relative error. 5. Relative errors are plotted on the graphs. 6. The graph best represented by a straight line is the graph: L=k(T^2) 7. The graph of L=k(T^2) will give us the most accurate slope as well as the most accurate reading for gravity. 8. K(2^2)=g 9. g= 10.29 m/s^2 .095 m/s^2 Conclusion: Looking over the lab I was very confused about the equation in question 8. I derived a different formula to calculate G and got a somewhat close answer of g=10.29m/s^2 .095m/s^2. While I know this is not a perfect value, it is much closer than what I got when given the equation in question 8. While at times I was confused during this experiment I think it turned out surprisingly well despite the sloppiness as well as human error factors that played in when using the stop watch to calculate time and when releasing the pendulum at a certain angle.
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