Thus the acceleration of free fall (g) will be given by the equation below
g = 4π2__
gradient
My variables are length of pendulum (l), time for oscillations (T), height from which pendulum is displaced and number of oscillations. My dependent variable is the time T for the oscillations as it depends on the pendulum length which is the independent
variable. The number of oscillations and the height from which the pendulum is displaced are my constant and will not change.
The apparatus I use in the experiment are as follows:
- Pendulum bob
- Meter rule
- Stopwatch
- Stand and clamp
Method
After obtaining the above apparatus I started my investigation by hanging the pendulum bob on a clamp as shown below, such that its length is 0.95m and set it into motion. I then measured the time for 10 complete oscillations and record my results. I repeated the above procedure with varying lengths of the pendulum bob of 0.9, 0.85, 0.80, 0.75, 0.70 and 0.65 m
Data collection and processing
After doing the above process I entered my data in the raw data table below.
Raw data
I then plotted a graph of time2 against length using the values shown in the table above using graphing software. The uncertainty for the length and time are relatively small hence I will ignore them in my graph.
Graph of time squared (T2/s) against length of pendulum (l/m)
I then proceeded to find the gradient of my graph as follows
Gradient (a) = ∆y
∆x
= 3.89 – 2.73
0.95 - 0.65
= 3.87
I proceeded to find the find the value of acceleration of free fall as follows, using the equation.
g = 4π2__
gradient
g = 4π2__
3.87
g =10.21 ms-1
However as the straight line-graph does not pass through the origin, I obtained the y-intercept of the graph using the graphing software to be 0.18. If this is taken into account then the new value for acceleration of free fall will be more accurate as it has been corrected for the systematic error that resulted in the entire line shifting upwards. Thus the new value of acceleration of free fall will be:
10.21 - 0.18 = 10.03 ms-1
Conclusion and evaluation
The method used was sufficient enough to give an percentage discrepancy of 4.01 % as shown below, the value being positive means it was higher than the actual value of acceleration of free fall of 9.81 ms-; this gives an accuracy of 96.2% as shown below
Percentage discrepancy = 10.21 – 9.81 x 100 = 4.01 %
9.81
95.99 = 4.01 - 100 = ccuracya gePercenta
However when corrected for the systematic error that led to all the data being skewed, and as result not passing through the origin, the value of free fall determined was only 2.24% higher than the actual value and improves the accuracy to 97.76% as shown below.
Percentage discrepancy = 10.03 – 9.81 x 100 = 2.24 %
9.81
% 97.76 = 2.24 - 100 = ccuracya gePercenta
In my experiment I expected the time of the oscillations to decrease as the pendulum length is decreased, my data supported this. As I drew a graph for the data it showed that the change of time for the oscillations as the pendulum length is reduced, is proportional. Thus I was effectively able to calculate the value of free fall of acceleration using the gradient of the graph drawn.
My largest problem was the small scatter of data on the graph and the data being skewed to one side of the graph due to a systematic error. This may have been caused by my reaction time in starting and stopping the stop watch, another reason for this could be that the string of the pendulum may have extended when the pendulum was in motion, also the stand holding the pendulum could be dangling from side to side as the pendulum oscillates. Therefore I would suggest the following ways to improve the data that will obtain better results.
- I would like to carry out the procedure of timing the oscillation at different pendulum lengths, for a greater number of times so as to obtain more data whose average I can use in the calculations to obtain a more accurate answer.
- I would also like to time a greater number of complete oscillations when the pendulum bob is set in motion so as to reduce errors that may have arisen due to my reaction time.
- I would also like to carry out the procedure again with a different set of apparatus, so as to eliminate the systematic error that arose in this experiment.
- Finally I would recommend that a heavy mass be placed on the stand holding the pendulum bob, so that it does not dangle when the pendulum bob oscillates thus leading to a more accurate answer.
