Pendulum Lab Report PDF

Preview

Summary

Physics for life sciences; pendulum lab report...

Description

Pendulum Lab Report

Title: Acceleration due to gravity, g. Abstract: In the following practical, the time required for ten oscillations of the chosen fixed-mass object (a travel sized hand sanitiser) was obtained by way of a stopwatch on a smartphone. By utilising L, the distance from the position of suspension to the object’s centre, it was possible to ascertain a value for g; this value was found to be 10.12m/s2, which correlates reasonably well to the universally agreed value of 9.81m/s2. Introduction to a Basic Theory: In this practical, a simple pendulum can be defined as consisting of a weight deemed to be the bob, which is suspended and secured to a non-elastic string of length L with negligible mass, which enables straightforward back and forth swaying. Through continual back and forth bob swings in a periodic manner, the bob is said to be oscillating. An oscillation can be deemed as the movement of the point of equilibrium to point B from point A. The pendulum’s specific swaying movements are powered by the transformation of kinetic to potential energy. This can be put down to the law of energy conservation; energy cannot be created or destroyed but only converted from one form to another. Therefore, it can be concluded from this that upon arrival at either point A or point B, the bob boasts maximum potential energy but no kinetic energy. When transitioning towards the equilibrium, the opposite is true; it boasts maximum kinetic energy but no potential. Additionally, the restoring force can be defined as the

force that reinstates the bob toward equilibrium. Upon displacement of the point mass from its position of equilibrium, its motion can be deemed periodic. The periodic motion of the bob, T, or more simply the time taken for one oscillation, can be summarised by the equation;

Additionally, from this we can derive the equation correlating the simple pendulum’s periodic time T with its length, L;

Fig. 1 - Oscillating Pendulum Motion Experimental Method: ● Fix one string end to the pendulum bob and place the opposite end at the edge of a desk, held in place between the desk and a fixed mass (in my case, two hardback notebooks). ● The diameter of the bob was measured at 0.038m, obtained using a piece of string and it was taken into account that the radius 0.019m needed to be subtracted from all other measurements for L. ● The pendulum was situated at a short suspension L and oscillation was initiated at no more than 5˚of an angle to

enable simple harmonic motion. L was recorded at varying lengths. ● The time required for 10 oscillations (T10) was noted. ● The procedure was replicated with the suspension increased gradually each time, up until minimum 9 values were obtained.

Fig. 2 - Simple Harmonic Motion

Experimental Data for Pendulum Oscillation(5˚): Mass(g)

Length(cm)

Total Swings Total Time(s)

101

20

10

8.94

101

30

10

10.73

101

40

10

12.47

101

45

10

13.46

101

50

10

14.02

101

55

10

14.42

101

60

10

15.52

101

65

10

15.94

101

70

10

16.62

101

75

10

17.08

101

80

10

17.90

101

85

10

18.10

Length(m)

Length(cm)

Time for swing (s)

T2(s2)

0.2

20

0.89

0.79

0.3

30

1.07

1.15

0.4

40

1.25

1.56

0.45

45

1.35

1.82

0.5

50

1.40

1.96

0.55

55

1.44

2.07

0.6

60

1.55

2.40

0.65

65

1.59

2.53

0.7

70

1.66

2.76

0.75

75

1.71

2.92

0.8

80

1.79

3.20

0.85

85

1.81

3.28

Experimental Data for Pendulum Oscillation(30˚):

Mass(g)

Length(cm)

Total Swings Total Time(s)

101

20

10

9.2

101

30

10

10.96

101

40

10

12.74

101

45

10

13.42

101

50

10

14.12

101

55

10

15

101

60

10

15.76

101

65

10

16.06

101

70

10

16.88

101

75

10

17.62

101

80

10

18.18

101

85

10

18.76

Length(m)

Length(cm)

Time for swing (s)

T2(s2)

0.2

20

0.92

0.85

0.3

30

1.10

1.21

0.4

40

1.27

1.61

0.45

45

1.34

1.80

0.5

50

1.41

1.99

0.55

55

1.50

2.25

0.6

60

1.60

2.56

0.65

65

1.61

2.59

0.7

70

1.69

2.86

0.75

75

1.76

3.10

0.8

80

1.82

3.31

0.85

85

1.88

3.53

Experimental Data for Pendulum Oscillation:

Data Analysis:

Fig. 3 - Graph of First Attempt Data

Fig. 4 - Graph of Second Attempt Data

Fig. 5 - Graph of First Attempt Data vs Data with 30˚starting point of swing

Fig. 6 - Graph of Second Attempt Data vs Data with 30˚starting point of swing

Originating from the equation outlining the period of a simple pendulum, it is possible to acquire an equation to determine g:

Accuracy and Uncertainty: Numerous practically unavoidable errors were observed throughout the practical; ● By means of acquiring Simple Harmonic Motion of the system, it was necessary for the angle of swing to be less than 5˚. In spite of the utmost caution taken to guarantee the angular swing was minute, the estimate was made by eye and not validated by a protractor, ergo occasionally the angle could have reached 10˚or even 15˚, however the process was undertaken twice so as to acquire the most accurate findings obtainable. ● It was not consistently observable for the oscillating bob to remain in one plane. In spite of utmost attempts, the bob was not travelling in an entirely unanimous arc throughout the practical. ● L was determined by means of a ruler with markings visible in mm, therefore these measurements are deemed to have a margin of error of +/- 1mm. ● Through the course of undertaking this experiment, it was necessary to bear in mind air resistances. This can be put down to the fact that the procedure was not carried out in a vacuum; ergo, air resistance would have hampered the results acquired. ● Percentage Error= 100% x |9.5-9.80|/9.80 = 100% x 3/9.8 = 3.0612%

Final Results and Conclusions Derived from Fig. 4, an obvious linear relationship is observed between the figures obtained with a minor intercept value, displaying a clear correlation between theory and practice. Resulting from the discovery of this linear relationship, it became possible to derive g by way of the slope of the plot. As earlier stated, this was found to have a value of 10.12m/s2; this is reasonably near to and in direct correlation with the accepted value of 9.81m/s2. During the course of the Simple Pendulum Practical, I found it increasingly difficult to obtain data with required precision. In the initial trial run of the practical, I had enabled the pendulum to oscillate from sizable angles including 45˚/90˚. These angles would not provide naturally precise results on the basis that Simple Harmonic Motion was not in operation, as proven in the data from a swing with a 30˚starting point. Furthermore, while carrying out the experiment, an additional error which was detected involved the fact that insufficient lengths were taken into consideration, signifying inadequate data had been gathered. By the time I began to undertake the second attempt of the practical, I was able to comprehend what was necessary to ensure successful completion of the experiment, and to the required accuracy, excluding unavoidable sources of human error. Regarding my plots for which the starting point of the swing was 30˚, the data is almost unanimously larger in value than the data obtained with a starting angle of 5˚. Visibly from the line of best fit, there is a sizable jump in the x-coordinate figure alone, rising from 3.897 to 4.248. The line of best fit doesn’t appear as accurate from a statistical standpoint as the line

constructed from initial data collection with the 5˚starting angle. In terms of pendulum motion, providing the displacement angle is substantial, the restoring force direction is not accurately observed to be in the same direction of equilibrium position. One of the basis under which Simple Harmonic Motion depends consists of the restoring force unequivocally being navigated to the position of the equilibrium. Therefore, in the event of sizable angular displacement, this particular condition is breached. Accordingly, pendulum motion would no longer be Simple Harmonic under these conditions. Ergo, Simple Harmonic Motion can only be observed when the angular displacement is retained ideally below 5˚. In short, the value of g obtained, 10.12m/s2, was in relatively good correlation with the accepted figure of 9.81m/s2. Through undertaking this practical, I have been enlightened on not solely the practical aspect of the experiment, but possibly more importantly, why it occurs and how. I have additionally been taught the means by which to plot functions with respect to gravity and, consequently, the ability to derive the slope from the equation of a line. I have been educated on the skill of manipulating numerous equations to suit the required experimental values. In completing the experiment, I have been left with a significant feeling of accomplishment as, in the future, if so required, I am equipped with the skill of determining the acceleration due to gravity of any planet in our universe....