Investigation 1 SPAN - In this activity you will investigate how the period of a simple pendulum is PDF

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In this activity you will investigate how the period of a simple pendulum is related to the length of the pendulum and measure the acceleration due to gravity. The acceleration due to gravity, 𝑎! is an important physical constant in modern science. Knowing the value accurately has enabled scientists...

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Investigation 1: Period of a Pendulum – SPAN001

Investigation 1: Period of a Pendulum Aim: One of the aims for this investigation is to find out the relationship between the pendulum length that has been used and the period of the pendulum preforming in motion. The second aim for this experiment is to find out how the different lengths of the pendulum affects the period of the pendulum. Equipment: (displayed in figure 1) 1. 2. 3. 4. 5. 6. 7. 8.

Scissors String (10cm, 30cm, 50cm, 70cm, 90cm, 100cm) Ruler (15cm) iPhone for stopwatch Protractor Pendulum – 45g metal 5/8 drill bit head for a ratchet set Scale (g) Rope/wire

Figure 1: Equipment of experiment

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Investigation 1: Period of a Pendulum – SPAN001

Figure 2: Set-up of the experiment that has been conducted

Method: 1. 2. 3. 4. 5. 6. 7. 8. 9.

Place the metal object on the scale to see how much it weighs Cut the length of string you wish to use first (10cm) Set up the equipment that is shown in figure 2 Use a protractor to measure 30o, and pull the pendulum back so that it will be at 30o Let go of the pendulum Immediately start the timer/stopwatch/iPhone Stop the timer/stopwatch/iPhone once back to centre Record results Repeat steps 2-8, 3 times for each of the different measurements

Results: Length of Trial 1 (s) Trial 2 (s) string (cm) ± 0.01cm ± 0.01cm ± 2cm 10 7.65 8.41 30 22.05 21.06 50 38.55 39.38 70 52.23 55.33 90 112.53 112.70 100 140.79 141.92 Table 1: Length of the rope and time taken

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Trial 3 (s) ± 0.01cm

Average (s) ± 0.01cm

7.90 21.70 38.50 53.44 113.38 139.38

7.99 21.60 38.81 53.67 112.87 140.70

Angle (Degrees) ± 1o 30 30 30 30 30 30

Investigation 1: Period of a Pendulum – SPAN001

Length (cm)

Length (cm) vs Average Time (s) of a pendulum 160 140 120 100 80 60 40 20 0 1

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Time (s)

Graph 1: Length vs Time of a Pendulum Uncertainty: The uncertainty for the length of the string is 2cm. This is due to the fact that the ruler only goes up by 15cm and human error may have occurred without realisation. Thus, making 2cm the uncertainty for the length of the string. The uncertainty in a period given is 1.66s. Working out is shown in Image 1.

Image 1: Uncertainty in a period given Discussion: State Uncertainties and how they were reduced? One uncertainty that was included in this experiment was the length of the string. The reasoning for the uncertainty was the use of a 15cm ruler. Each time the length of the string was measured longer than 15cm, human error could have occurred as the string may have been pulled to either increase or decrease the length. The uncertainty that was measure was ± 2 cm. This was reduced as I took off 2cm away from the length so that it can be the nearest precise/accurate measurement, however this is unlikely. Identified limitation of the period equation? 3

Investigation 1: Period of a Pendulum – SPAN001 The square root of the acceleration due to gravity is inversely proportional to the period. This means that the experiment's constraint is that we can't get a massless, inextensible, torsionfree, completely flexible fibre, thus we'll have to rely on a thin light string to achieve next to accurate measurements. Stated accuracy in the measured value of ag?

Improvements to experiment provided? One improvement that could be improved throughout this experiment is the amount of information that was given. More guidance on the topic as well as what was expected of us should have been in more detail so that we were less confused with what we needed to do. Another improvement that to this experiment is to test the period of a pendulum with different masses. This will allow us to see the difference between how different masses can also change the acceleration of a pendulum.

Conclusion: We measured g = (0.6805 ± 1.66) m/s 2 in this experiment. Because our measured periods were all statistically greater than the 2.0 that we expected from our forecast, all our measured values were systematically lower than predicted. The prediction that was considered throughout the experiment was, the longer the length of the string from the pendulum, the longer it would take for the pendulum to get back to a constant state of equilibrium. However, this was slightly difficult as measurements from the length of the string were not accurate or precise and the use of the protractor was not accurately measured from the angle in which the pendulum was released. Overall, we can see that in this experiment that we found that the relationship between the pendulum length that has been used and the period of the pendulum preforming in motion, while also finding out how the different lengths of the pendulum affects the period of the pendulum.

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