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Physics Pendulum Practical. How does the time period vary with length and what is the value of g?

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Introduction


Design

Introduction

        In this experiment, I am going to relate the time taken for 20 oscillations with the varying lengths of string used and use this relation to find the approximate value of ‘g’ or gravity. image03.jpg

I will do this by plotting the results of the experiment on a graph and using the gradient of the graph to find ‘g’. To do this, I will be using the formula below:

image00.png

This can be rearranged to find the value of ‘g’:

image00.png

Research Question

        How does the time period vary with length and what is the value of ‘g’?

Hypothesis

        I predict that the time taken for 20 oscillations will increase as the length of the string increases as they are directly proportional. As for the value of ‘g’, I predict that it will be approximately around 9.81 m/s2 as this is the standard value of ‘g’ that is accepted all around the world today.

Variables

Controlled or Constant variables:

  • Bob
  • Mass of bob
  • String used
  • Amplitude of oscillation

Independent variables:

  • Length of string

Dependent variables:

  • Time taken for 20 oscillations
  • Value of g (supposed to be constant variable)

Manipulation of Variables

Controlled or Constant Variables:

  • Bob: We used the same bob for all trials so that all the results acquired are relevant to one bob only.
  • Mass of bob: Since we used the same bob for all trials, the mass of the bob did not change and remained constant for all trials.
  • String used: We used the same string in all trials to maintain accuracy of the data.
  • Amplitude of oscillation: We made sure that in each trial, the initial amplitude of the oscillation remained approximately 15°. This was hard to do but we tried our best in keeping it constant.

Independent variables:

  • Length of string: For the string length, we took a wide range of 40-140cm (every 10 cm) and therefore we did trials with 11 different string lengths. We used a meter ruler to measure the length of the string for each trial.

Dependent variables:

  • Time taken for 20 oscillations: We measured these using stopwatches and took 3 readings for each string length.
  • Value of ‘g’: In reality, the value of ‘g’ is supposed to remain constant (approximately 9.81 m/s2). However, since our experiment is not perfect, the value of ‘g’ derived from our calculations might differ for each trial or string length.

Apparatus:

  • Stand
  • String
  • Bob
  • Meter rule
  • Digital stopwatch
...read more.

Middle

Trial 1 (s)

Uncertainty: ±0.01s

Trial 2 (s)

Uncertainty: ±0.01s

Trial 3 (s)

Uncertainty: ±0.01s

40

25.15

25.13

25.10

50

28.81

28.77

28.78

60

31.72

31.69

31.70

70

34.22

34.21

34.26

80

36.53

36.51

36.48

90

38.66

38.68

38.71

100

40.75

40.71

40.70

110

42.60

42.64

42.63

120

44.28

44.26

44.29

130

46.26

46.23

46.25

140

47.97

48.01

47.96

        The uncertainty for the length is 0.05cm as the smallest unit on the meter was 0.1cm. Since the meter ruler is not a digital device, it is necessary to take half of the smallest unit to determine the uncertainty and so it is 0.05cm. As for the time, we used a digital stopwatch and smallest unit is 0.01s and so that becomes the uncertainty.

Processed Data

Now I will process the data and find the averages of the time. Averaging should reduce the uncertainty but I decided

...read more.

Conclusion

There are many ways in which my experiment could have been improved. I could have constructed a better set-up for the experiment which allowed me to keep the amplitude of the bob exactly the same for each trial. This could have been achieved through a clamp which holds onto and then releases the bob. To reduce human error, we could have used a light sensor which automatically starts recording the moment the bob crosses it and then stops recording after the bob has done 20 oscillations. This would give us a highly accurate reading for time as the reaction time of a human being is not being factored in.

...read more.

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