15685729 Simple Pendulum Lab PDF

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Sagar Sood IB Physics Yr.1 HL Block E Due: May 22, 09

Sagar Sood IB Physics Yr. 1 HL Block E Due: May 22, 09 Introduction A pendulum is a weight suspended from a pivot so it can swing freely. When a pendulum is displaced from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force will cause it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. In this experiment, the length of the string will be altered to see the affect on the time period. With the collected and calculated values, the value of acceleration due to gravity will be determined as gravity plays a vital role in the motion of the pendulum (and the only force acting). The bob has to travel more distance in the given time. As the length of the string is being changed, it is the independent variable. This would affect the time period, hence being the dependant variable. Factors like the mass of the bob (154.02g ±0.01g), angle of release (45° ±1°), the stopwatch (±0.01s) The main purpose of the experiment is to find one factor that affects the time period of a simple pendulum. In this case, the factor is length of the string. Hypothesis As the length of the string decreases, the time period also decreases. This is because, as the length of the string decreases, the bob has to travel less distance in the same time (10 oscillations). And as there is less distance to cover in the same number of oscillations, the velocity of the pendulum increases which hence decreases the time period. This means that the length of the string is inversely proportional to the time period. 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 1. After all the materials are acquired, set up the apparatus as below:

2. Set the bob till 45 degrees mark (as precisely as possible) and then leave it. 3. As soon as it is left, start the stopwatch and record the time for ten oscillations 4. Repeat the steps 2 and three two more times without changing the length in order to get three trials 5. Now, decrease the length of the string and repeat the steps 2, 3 and 4 6. 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 Length of string (m)

Time for 10 oscillations (s)

0.535 0.502 0.435 0.365 0.317 0.235 0.165 0.125 ± 0.001m

Average time (s)

Trial 1

Trial 2

Trial 3

15.12 14.69 13.84 12.62 11.89 10.59 9.19 8.41

15.24 14.53 14.32 12.44 11.90 10.43 9.12 8.09 ±0.01s

15.19 14.81 14.07 12.53 11.72 10.56 9.15 7.97

15.18 ± 0.06 14.68 ± 0.14 14.08 ± 0.39 12.53 ± 0.09 11.84 ± 0.09 10.53 ± 0.08 9.15 ± 0.03 8.16 ± 0.22 ±0.1s

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. Average Time (s) 15.18 14.68 14.08 12.53 11.84 10.53 9.15 8.16 ±0.1s

Time Period (s) 1.52 1.47 1.41 1.25 1.18 1.05 0.92 0.82 ±0.1s

Data Processing Average Time (s) = Trial 1 + Trial 2 + Trial 3 3 = 15.12 + 15.24 + 15.19 3 = 15.18 s

Acceleration due to Gravity (ms-2) 9.14 ± 1 9.17 ± 1 8.64 ± 1 9.22 ± 1 8.99 ± 2 8.42 ± 2 7.70 ± 1 7.34 ± 2 ± 1ms-2

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 Theoretical Value

X 100

= 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....