Length of string (l) ~ 1
Time period (T)
Design
Materials Required
- Weighing Scale(±0.01g)
- Lab Stand
- Meter Stick (±0.001m)
- Stopwatch (±0.01s)
- String
- Bob (154.02g ±0.01g)
- Protractor (±1°)
Procedure
- After all the materials are acquired, set up the apparatus as below:
- Set the bob till 45 degrees mark (as precisely as possible) and then leave it.
- As soon as it is left, start the stopwatch and record the time for ten oscillations
- Repeat the steps 2 and three two more times without changing the length in order to get three trials
- Now, decrease the length of the string and repeat the steps 2, 3 and 4
- Record 8 data points with three trials each.
Data Table
The data table below shows the raw data collected which includes the decreases in the length of the string and the time trials for ten oscillations
The table below shows the values of the calculated data that includes the time period (time for one oscillation) which further gives us the acceleration due to gravity.
Data Processing
Average Time (s) = Trial 1 + Trial 2 + Trial 3
3
= 15.12 + 15.24 + 15.19
3
= 15.18 s
Uncertainty for Average = (Highest value – Lowest value)
2
= (15.24 – 15.12)
2
= ±0.06s
Time for one oscillation = Time for 10 oscillation
10
= 15.18
10
= 1.52 s
T =
g = 4π2 l
T2
= 4π2(0.535)
(1.52) 2
= 9.14 ms-2
Uncertainty of gravity:
(Uncertainty 1) + (Uncertainty 2) X 100
(Value 1) (Value 2)
0.2 + 0.001 X 100
1.52 0.535
= 9.14 ms-2 ±13.3 %
= 13.3 X 9.14
100
= ±1.21562
= 9.14 ms-2 ± 1 ms-2
Average of Gravity = 9.14 + 9.17 + 8.64 + 9.22 + 8.99 + 8.42 + 7.70 + 7.34
8
= 8.56 ms-2
Average of uncertainties = 1 + 1 + 1 + 1 + 2 + 2 + 1 + 2
8
= 1.375
= ± 1 ms-2
= 8.56 ± 1 ms-2
Percent Error = Theoretical Value – Calculated Value X 100
Theoretical Value
= 9.81 – 8.56 X 100
9.81
= 12.7 % Error
Conclusion
Overall, the experiment was carried out with minimum errors and was followed according to the given procedure. There were eight data points with three trials each. The investigation was related to the determination of one factor that affects the motion of a simple pendulum followed by the determination of the value of gravity. As it can be seen from the data table and the graph that the value for gravity was calculated to be 8.56 ms-2 ± 1 ms-2. Furthermore, the percent error was calculated to be 12.7 %.
In my experiment, the one factor that affected the motion of the simple pendulum was length of the string. As the length of the string was decreased, the time period also decreased. This is because the velocity increased as the bob had to cover less distance in the given time. Hence, this proves my hypothesis correct
Evaluation
The percent error was calculated to be 12.7 %. This shows that there were some errors/flaws in my experiment. Firstly, when the pendulum was oscillating, because of its momentum, the whole stand was shaking. This irregular movement of the stand affected the motion of the pendulum as it did not have the same amplitude throughout hence affecting the time period. Another error was that when the length of the string was decreased, the string was not cut and then fitted but was rounded to the top. This altered the values of my data as it affected the angle of release, which was supposed to be kept constant. To avoid such mistakes/flaws, the following measures should be taken.
Self Improvement
In order to avoid the above errors/flaws, a number of precaution steps can be taken. Firstly, the string should never be rounded to the top. After each data point, the string should be removed, measured to the required length using a meter stick and then cut using scissors. This avoids a big error in the experiment. Secondly, it is very important that the stand remains stationary. To do so, extra weight should be put on the bottom but it is also important that this weight is not touching any part of the pendulum.
