*Uncertainty value of the length of the string is from the smallest division of the instrument since 0.001m length of mark by the marker was used on the string to indicate where the length of the spring was supposed to be kept at when the stopper was spinning.
* (Average Time uncertainty) = ((Max Time)-(Min Time))/2 = (3.2-2.8)/2 = 0.2s.
*Time uncertainty was estimated to be ±0.1s since it was thought to be reasonable to estimate the human stopwatch accuracy up to 0.1 second difference.
Table 2 (Length vs. T and T2 and their uncertainties):
*T value = (Average time took for the stopper to revolve 10 times)/10 = 2.9/10 = 0.29s
*T Uncertainty = (Average Time Uncertainty)/10 = 0.2/10 = 0.02s
*T2 Uncertainty = (T2 Value)x([Percentage T Uncertainty]x2) = 0.09x([0.02/0.29]x2) = 0.01s2
Graph 1:
Table 3 (Slope and its uncertainty):
Finding the mass of the stopper:
Conclusion:
According to Graph 1, the best-fit line goes through most of the error bars and almost passes through the origin. This trend supports the theory that the length of the string is directly proportional to the squared value of the time period. The final calculation of the mass of the stopper is 0.012±0.002 kg.
However, the measured value of the mass of the stopper was 0.0175±0.0001kg, and the value does not fit into the uncertainty range of the calculated mass of the stopper. The large percentage error of 31% shows that there have been some weaknesses in the data.
One of the weaknesses in the data was that some error bars were large. From Table 1, the corresponding time values for length 0.350m and 0.450m were very far apart from each other, almost a one second difference. When the stopper was stopped spinning, the part of the string at the upper end of the tube was observed to be chipped away thread by thread, showing that there had been a frictional force that caused the abrasion of the string. Then, the cause of huge difference in time measurement could have been because there was a static friction between the string and the upper end of the tube, which would hold the string at the exact length but also would be added to or subtracted from the centripetal force, enabling the stopper to spin at different speeds at the same length. If this theory is applied, then it would mean that the stopper was spun at slower and slower rates than usual in this experiment, resulting in the less steep slope of the data points.
One of the ways to improve this weakness would be to add more trials in each lengths of the string. Since the measurements of the time would differ greatly, it would be best to take more trials to get the best average possible. Another way to improve the weakness would be to have a tube that has a very low friction constant and that has a round shape at the end to reduce the friction that will narrow the speed range of the stopper at a certain length.