Determination of G using a simple pendulum PDF

Preview

Summary

extra...

Description

Determination of G using a simple pendulum Aim: The aim of this experiment is to confirm that the acceleration is cause by gravity (G), by measuring the span of oscillation and the length of the pendulum. Introduction: All masses are attracted to the centre of gravity Where is stable. The only variable that affects the oscillation period of a period is the length of the string. The longer the string length the longer the period of oscillation is. This is due to the pendulum having to fall farther to the centre point. This results in the equation period equal to the square root of the length. So as the length of the string decreases the period of oscillation is quicker. Another variable is acceleration of the pendulum. The maximum acceleration of the pendulum is at the poles (when being released). The lowest acceleration is at the acceleration (when pendulum is no longer falling). The only variable for the acceleration was due to gravity alone which is constant at 9.81.

Experiment equipment:

String holding the ball (change lengths)

Measuring tape to measure the string length

Pendulum ball (kept constant)

Stand to hold the pendulum in place and keep it elevated

Stop watch to time the oscillations

Figure 1

Procedure and observations 1)The pendulum was set up, as shown above in figure 1. 2)The length of the string was measured using a measuring tape from the top of the string to the middle of the metal ball. 3)The pendulum was pulled to an angle and as soon as it was released the timer was started. 3) the number of oscillations was counted and at the 25th oscillation the stop watch was stopped, and the time was recorded in seconds. 4) This was repeated for a total of 5 different lengths making sure there were 2 long, 1 middle and 2 shorter ranges in the length of the string measured (good range) 5) At each length the experiment was repeated % times to increase reliability and to get a mean value.

Observation and results Through the experiment there was a clear pattern as the length of the string was shortened. As the length of the string was reduced the period of oscillation was more quicker compared to the longer lengths of string. This was due to the ball falling down a shorter length and so the period of oscillation was shorter.

Length 0.88 (m) T ² (s) 3.3

0.68

0.48

0.28

0.18

2.6

1.9

1.1

0.3

(Period of 1 oscillation)²(s) against Length of String (m) 3.5

T ² (s)

3

2.5

S=gradient

2

Y axis divided by x axis

1.5

S= (2.6-1.1)/ (0.68-0.28)

1

S=3.75

0.5 0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Graph 1

Length of string (m)

Calculation for the values if the y axis-The T value was found by dividing the mean time (at each length) by the number of oscillation (which was 25). Then this value was squared to get T ².

Calculations Length of string (m) 0.88 0.68 0.48 0.28 0.18

Solutions for T ² 3.54 2.74 1.93 1.13 0.72

Experimental Calculation of gravity S= gradient calculated on graph 1 (from 0.68m to 0.88m) S=3.75

Theoretical value g=4pi ² x L/T ² At 0.88 meters g=10.5 At 0.68 meters g=10.3

g=10.5

Discussion These are the theoretical values that should have been obtained in the experiment. The difference is values would be due to experimental errors. Although there was a variation in amplitude that the ball was released at as we repeated the test multiple times for each length. The only variable that would affect the period of oscillation is the length. The length was kept constant, so it didn’t affect the results. However, amplitude only has no affect if the length is constant. So, the angle at which the ball is released at should stay constant for each length to not affect the results. The angle of release was not measured and so would have changed between each trail at each length. The same person could release the ball but, there would still be human error. One thing that would have affected the results would have been the reaction time in starting the stop watch as soon as the ball was released and as soon as 25 oscillations were completed. The same person could again time for the whole experiment but there is still possible human error. Another error could be from when measuring the length of the string. This is due to having to measure up to the middle point of the pendulum ball. The middle point was hard to get each time and so could have affected the results.

Conclusion Through the results obtained, shows that length does indeed have an affect on the period of oscillation of a pendulum. As you decrease the length of the string the pendulum falls over a much shorter distance, and so the oscillation period is shorter then that of a longer string length (falls over a much larger distance). This pattern found in the experimental results have a very similar pattern to that of theoretical values. There is only a slight difference in values due to possible experimental errors that would reduce the accuracy of the results. However, the difference is values is only small, which was improved by repeating the trials at each string length. However, there is a very clear pattern in the experimental results that match the theoretical calculations, showing validity of the affect of length on the period of oscillation.

References http://sciencenetlinks.com/lessons/exploring-pendulums/ https://www.teachengineering.org/lessons/view/cub_mechanics_lesson09...