Method: - Attach a long piece of thread to the pendulum bob. Fix the top of the thread on the stand. Set the bob to oscillate and count the number of oscillation (Say 20 oscillations). Measure the length (L) of the pendulum and the period (T). Change the length of the thread and measure the new period time. Repeat this for at least 7 trials.
Data Collection: -
Table 1: - The table below shows the variation between length of the string and the time period of the oscillating pendulum
Data Processing: -
L= 0.2280 m, T1 =9.85 s, T2 =9.55 s, T3= 9.85 s
Tm = 9.85 + 9.55 + 9.85 / 3 = 9.75s
T = 9.75 / 10 = 0.975s
T2 = 0.9752 = 0.951s
Uncertainty of Tm = 0.01 + 0.01 + 0.01 = 0.03
Uncertainty of T = 0.03 / 9.75 x 0.975 = 0.003
Uncertainty of T2 = 2(0.003 / 0.975) x 0.950625 = 0.00585
Tm = 9.75s ± 0.03s
T = 0.975s ± 0.003s
T2 = 0.95100s ± 0.00585s2
g = 4π² x 0.2280 / 9.75 = 9.469ms-2
Table 2: - Shows the average values of the period and the period of one oscillation
Average value of g = 9.469 + 8.472 + 8.528 + 9.468 + 9.576 + 9.931 / 7 = 9.212ms-2
Max. Value of g = 9.931 ms-2
Min. Value of g = 8.472 ms-2
Max. Value – Mean Value = 9.931-9.212= 0.719
Mean Value – Min. Value = 9.212-8.472= 0.740
g = 9.212 ms-2 ± 0.740 ms-2
Graph 1: - Shows the relationship between T² and L
Gradient = Y2 – Y1 / X2 – X1
= 3.9100 – 0.95100 / 1.977 – 0.975
= 2.959 / 1.002
= 2.953
Conclusion and Evaluation: -
The gravitational energy that was found is 9.212 ms-2 ± 0.740 ms-2 there were many errors that could have occurred during this experiment starting with human errors. When turning on the stopwatch it might be too late or to early so we need a more complex structure that lets a stopwatch start automatically when we let the pendulum move. Also when the oscillations are finished we don’t stop them automatically, and other systematic errors like the calibration of the rules and all of this makes large sources of errors making our work not accurate
