1. (measuing gravity pendulum) 18-10-11

8/3/2019 1. (Measuing Gravity Pendulum) 18-10-11

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Charles Xu

Measuring gravity using period of pendulum Practical Report

Aim

To attempt to measure the acceleration due to gravity using the motion of a pendulum.

Hypothesis

Using the period of a pendulums swing and the measurement of a length of string, I will be able to find a value for

acceleration due to gravity that is close to the current accepted value of 9.8ms-2

.

Equipment

y A 50g mass or a large nut that weighs around 50g

y About 1.2m length of string

y A ruler or tape measure

y Protractor

y A watch with a second hand or a stop watch

y A table or raised flat platform

y Retort stand

y Bosshead

y Clamp

Method

1) Set up as seen in diagram

2) Adjust the length of pendulum to 1m. Record as precisely as possible.

3) Set the pendulum swinging by gently pulling it back(no more than 30° either side of vertical). Starting at extreme

of the motion, time 10 full periods(1 full period is movement away from start then back to original postion).

4) Divide this time by ten and record this time.

5) Repeat this another 2 times

6) Calculate a value for g using the formula, ;

Where T = period(s),

l = length of string from pivot point to bottom of mass(m)

g = acceleration due to gravity(ms-2)

7) Repeat this process 3 more times, shortening the string by 5cm each time.

8) Finish by calculating an average value for g, based on all trials.

Bosshead & Clamp

Retort Stand String

Mass

Table



Charles Xu

Results

Trial # Pendulum length(m) Period(s) g(ms-2

)

1 1.000 2.000 9.8670

2 1.000 1.966 10.214

3 1.000 1.987 9.9992

4 0.950 1.897 10.422

5 0.950 1.940 9.9651

6 0.950 1.957 9.7927

7 0.895 1.887 9.9230

8 0.895 1.902 9.7670

9 0.895 1.876 10.039

10 0.852 1.840 9.9349

11 0.852 1.852 9.8066

12 0.852 1.857 9.7538

Average = = 9.957



Charles Xu

Discussion

The physical properties of a pendulum are that when it swings with a small angle, its period depends only upon the

length of the string and the value of acceleration due to gravity. This is demonstrated in the equation

where T is the period of the pendulums swing in seconds, l is the length of the pendulum in metres and g is the

acceleration due to gravity. This equation can be rearranged in order to equate a value for gravity by finding out the

period of a pendulum swing at certain lengths; . By using these results I was able to carry out the

experiment and determine values for the acceleration due to gravity.

Initially, a table of results was used with 3 repetitions of timing at a certain length and then at subsequent lengths of

0.05 in difference starting from 1m to 0.85m. These results were averaged and I came up with a result of the

acceleration due to gravity to be 9.957ms-2

. These results obtained from the average of all trials in the table had

elements of reliability as there were several repetitions to the experiment and an average was determined in order to

limit the effects that outliers would have on the result. The values of the acceleration due to gravity of each trial were

relatively close to the acknowledged value of 9.8ms-2

, within .

In the second instance, I used a graph using some results and determined a l ine of best fit. The independent variable in

this experiment is the length of the pendulum in metres on the x-axis. The dependent variable is the period in seconds,however this must be squared in order to obtain a line is the form y=mx. This can be explained by manipulating the

original equation . Where and and given that the gradient m, is

this simply gives

as the gradient m, in s2m

-1. Using this information, the equation can be further manipulated for g, so that

since

. Using the value of the gradient obtained from the line of best fit on the graph, this is another method to

determine acceleration due to gravity.

These results have a high degree of validity as they gave results in close proximity to 9.8ms-2

and the experiment itself is

very easy to complete and repeat. However, there are several errors that may have had an effect on the reliability of the

results. The results are expected to be closer to the accepted value of acceleration due to gravity and this may be

accounted through improper measurements of the length of the pendulum or the duration of the period. This is largelyhuman error as reaction time for the time recorder or the eye level of the person measuring the length could increase or

decrease the measurements. This could be corrected by using electronic timers. There is also the possibility that the

experiment was set up in a way that the pivot was not correctly centred or the length was not being measured properly

from the pivot to the base of the pendulum. In addition, an angle of less than 30° either side of the vertical must be used

otherwise the reliability of the results may lessen as it is the optimum angle for the experiment to work. When recording

and calculating results, there may be errors in calculations on the part of the people performing the experiment.All of

these errors can cause outliers and when taking an average, the more results used the more reliable it is as it lessens the

effect of the outliers. This may require a larger sample size whereas drawing a graph and determining the line of best fit

in order to calculate gravity does not require as much and may give an even more reliable result, this is due to the fact

that drawing a line of best fit is a way in which outliers can be ignored and therefore have little to no impact of the final

result.

The individual results had many variations and decrease the accuracy and reliability. By averaging the results of different

trials, a more reliable result is determined since the degree to which outliers effect the results is decreased. The most

accurate of methods to obtain a result was graphing to find a line of best fit and calculate acceleration due to gravity by

finding the gradient of the line. The real change in the acceleration due to gravity that I calculated was from 9.957ms-2

using an average to 9.953ms-2

using the line of best fit. This is a more accurate result, closer to 9.8ms-2

, and a more

reliable result as it critically limits the effects of outliers.



Charles Xu

Conclusion

In conclusion, I was able to determine acceleration due to gravity with just the length and period of a pendulums swing

which was close to the general value of 9.8ms-2

through the use of manipulation of a formula. The resultant value for

acceleration due to gravity was able to be more reliably measured using a line of best fit to eliminate outliers and the

experiment was valid due to its appropriate result.

1. (measuing gravity pendulum) 18-10-11

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