Hooke S Law
Exploring Hooke’s Law and the Constant (K):
Data Collection and Processing:
Data of the Hanging Masses and the Caused Displacement of the Spring
Mass Hanging (kg):
Displacement of Spring Including Original Length (m):
0.050
0.413
0.100
0.451
0.150
0.458
0.200
0.485
0.250
0.504
0.300
0.522
0.350
0.543
0.400
0.567
0.450
0.587
0.500
0.610
0.550
0.633
0.600
0.655
0.650
0.674
0.700
0.698
Original Length of Spring (m):
0.392
Table 2.1
Constant K: 22.5kg/ms2
*Refer to attached graph and calculations.
Conclusion and Evaluation: The value that was obtained appears to be quite accurate. There were many trials, 14, which would reduce error when calculating the slope using the trendline. There appears to not be significant random error as many of the points lay extremely close to, or on, the trendline. Systematic error appears to be almost non-existent as in the graph the trendline was drawn through the y-axis. The value of the y-intercept should be the original length of the spring. The theoretical value was 0.392m while the experimental value, on the graph, was 0.394m. These two values being very close indicate that systematic error was very minimal. The one main source of any random error would be from the meter stick that was used to measure the displacement of the spring. Using the meter stick would cause inaccurate measurements as the meter stick has a notable uncertainty. However, because the values were all very close to the trendline on the graph, it appears that this source of random error did not really affect the data significantly. A method of determining how accurate the value of “k” was could have been to compare it to a theoretical value. However there is no theoretical value as the value of “k” for each spring is different; this is a limitation.
Data Collection and Processing:
Data of the Hanging Masses and the Caused Displacement of the Spring
Mass Hanging (kg):
Displacement of Spring Including Original Length (m):
0.050
0.413
0.100
0.451
0.150
0.458
0.200
0.485
0.250
0.504
0.300
0.522
0.350
0.543
0.400
0.567
0.450
0.587
0.500
0.610
0.550
0.633
0.600
0.655
0.650
0.674
0.700
0.698
Original Length of Spring (m):
0.392
Table 2.1
Constant K: 22.5kg/ms2
*Refer to attached graph and calculations.
Conclusion and Evaluation: The value that was obtained appears to be quite accurate. There were many trials, 14, which would reduce error when calculating the slope using the trendline. There appears to not be significant random error as many of the points lay extremely close to, or on, the trendline. Systematic error appears to be almost non-existent as in the graph the trendline was drawn through the y-axis. The value of the y-intercept should be the original length of the spring. The theoretical value was 0.392m while the experimental value, on the graph, was 0.394m. These two values being very close indicate that systematic error was very minimal. The one main source of any random error would be from the meter stick that was used to measure the displacement of the spring. Using the meter stick would cause inaccurate measurements as the meter stick has a notable uncertainty. However, because the values were all very close to the trendline on the graph, it appears that this source of random error did not really affect the data significantly. A method of determining how accurate the value of “k” was could have been to compare it to a theoretical value. However there is no theoretical value as the value of “k” for each spring is different; this is a limitation.