Data processing
Mass
The I.S. unit for mass is kg. I had to transform the measurement of the hanging mass from g to kg. For example, 50g to 0.050 kg
Time
In the data collection, time to complete 10 rotation periods is taken instead of 1 rotation because 1 rotation period is too short to be measured with a stopwatch accurately. In this investigation, it is aimed to find the relationship between the hanging mass and 1 rotation period. To transform the data to 1 rotation period, all time taken for 10 rotations has to be divided by 10. However, since the stopwatch can only measure to the nearest 0.01s, the divided number is still taken to the nearest 0.01s and not 0.001s.
For example, average time taken for to rotation 1 period when hanging mass is 0.050 kg = 7.42/10=0.74 s to the nearest 0.01s.
Processed Data
From the graph, the best fit is does not pass through the origin and it is more like a negative curve. This may suggest a positive linear relationship between and the hanging mass M.
Time
In order to have a linear graph, I have to plot against the hanging mass. The average time taken for 1 period of each mass have to be processed to .
For example, the rotation period when mass is 0.050 kg, is 0.74s. Then
Final Data
The random uncertainty of can be found be using formula
Eg. Uncertainty of when hanging mass is 0.050kg
,
Maximum gradient =
Minimum gradient = s-2kg-1
Best-fit gradient = (21.04 + 16.88) / 2 = 18.96 s-2kg-1 ± 2.08 s-2kg-1
Conclusion:
The second graph shows a positive linear graph between and the hanging mass, which suggest a negative relationship between mass and the rotation period. This means that as the hanging mass increase, the time for 1 rotation period decrease in a decreasing rate when the tension of the string and the mass of stopper remain constant. Since the weight of hanging mass should be equal to the tension of the string, I can also conclude that as the tension of the string or the length of the string increases, the rotation period will decrease as well.
In this experiment, the centripetal for is the horizontal component of the string. Since the weight of the hanging masses is equal to the tension T of the string, ∴ F=Mgcosθ and r=Lcosθ. Substituting r=Lcosθ to equation . Substituting F=Mgcosθ to the RHS of equation and r=Lcosθ, to the LHS. ➔ . Therefore, the theoretical gradient of the graph should be gradient = , which is well within the uncertainty of the graph.
Evaluation:
Systematic uncertainty
From the T-2-mass graph, the best-fit line and the uncertainty range do not pass through the origin. This suggests that there may be a systematic uncertainty shifting the best-fit line to the left.
In this experiment, it is assumed that there is no friction of any kind acting on the swing of the object. However, in practical situation, there is air resistance and friction between the string and the upper edge of the tube. This may cause the rotation period to be short than the theoretical period.
For improvement, a sand paper can be used to smoothen the edge of the plastic tube to reduce friction between the tube and the string.
Random uncertainty
There are many random uncertainties in this experiment.
First of all, it is not possible to unsure that the rotation of the swing being 100% horizontal to the ground and the swing of the ball is always tilted to one side. When the stopper reaches to the higher part of the circular loop, part of the weight of the stopper will be added to the centripetal force. Centripetal force is not even throughout the circular motion of the stopper and may cause random uncertainty. For improvement, a straight horizontal line can be draw on the nearby wall as an indicator for the person to unsure that the swing is nearest to horizontal.
The length of the string may differ between each trial. The string is marked to unsure that the length of the string in the circular motion remains constant. However, during the swing, the force applied to the circular motion by the human body is inconsistent and the length of the string may changes accordingly during the swing. When the force applied to the circular motion by the human body altered, the person would readjust his/her force until the string return to the desirable length. This random uncertainty can be improved by increasing the rotation period when measuring the time so that the uncertainty can be cancelled out. Measuring more rotation period can also lower the percentage error.
The timing process of the rotation period causes a major random uncertainty in this experiment. Since there isn’t a certain point indicating the start and end of a rotation, timing the rotation period involve estimation of the starting/ending point of the rotation and may cause uncertainty.
Reaction time when using the stopwatch also causes uncertainty. A person cannot start or stop the stopwatch exactly at the point where rotation starts. The reaction time can be kept constant by having the same person as the timer throughout the experiment. However, in most cases, the reaction time starting and stopping the stopwatch may not always be equal and cannot fully cancel each other out. The percentage uncertainty can be reduced by timing more rotation period to reduce the significance of the reaction time on the data.
