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# Objective To find the acceleration due to gravity by means of a simple pendulum.

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Introduction

 School: HKTA Tang Hin Memorial Secondary School Class: 6C Name: Ho Siu Ting        (  19  ) Subject: AL Practical Physics Date: 19 th December 2010 Mark:

G4 Acceleration if free fall by means of a simple pendulum

### Objective

To find the acceleration due to gravity by means of a simple pendulum.

### Theory

Simple harmonic motion is the repetitive back-and-forth movement through a central, or equilibrium, position in which the maximum displacement on one side is equal to the maximum displacement on the other. The acceleration of a particle is directly proportional to its displacement from the equilibrium position but always opposite to its displacement from the equilibrium position. ( a = -  )

A pendulum can display the simple harmonic motion. A simple pendulum consists merely of a bob (weight) suspended from a fixed point by a rod or string of length (L). The mass of the rod or string is assumed to be so much less than the suspended mass that it can be ignored. If the suspended mass is displaced to the left or right, while the rod or string is kept taut, and then released, the mass will swing freely back and forth under the gravity’s influence.

Restoring force F = - mg  F = ma

- mg  = ma

a = -g  (provided that  is small)

a = -gθ = -g(x/l)(∵ θ

Middle

•  = 2  Find the  for each experiment by using the above formula:

 Effective length  L/m 1.251 1.127 1.027 0.927 0.827 0.1 0.11 0.11 0.12 0.13

Average value of  :  =  = 0.114

The value of g with precision is ( 9.52  0.11 ) ms-2

Compare:

The standard value of g = 9.81 ms-2

The values gained from the graph g’ = 9.52 ms-2

The percentage error =  X100  =  X100  =  X100  = 2.96  The experiment result of is 2.96  smaller than the expected value 9.81 ms-2

It is quite accurate as the experiment value does not deviate a lot from the expected value.

Discussion

1. Random Error

There are some limitations in the experiment due to instrumental limit (reading error) which cannot be reduced by repeating the experiment.

• Percentage error due to scale uncertainty

The percentage error due to the limitation of measuring length:  x 100  Find the percentage error of each measurement by using the above formula:

 Effective length  L/m 1.251 1.127 1.027 0.927 0.827 Percentage error  0.16 0.18 0.19 0.22 0.24

Average value of the percentage error due to this limitation:

=  = 0.198  Conclusion

Using this method to carry out the experiment can prevent some human error caused by the original. It would not consist of the error of reaction time. And also, the data can be obtained by the function of software. It prevents lots of calculating error of human. The valued obtained is much accurate than the original one.

1. If the experiment is performed with the pendulum suspended from an inaccessible point, e.g. the ceiling (i.e. you cannot measure the length of the pendulum), suggest a modification to the experiment to find the value of g.

Ans: It is an alternative method to find the acceleration due to gravity with the help of ticker-tape timer (The length of the string is not necessarily known.)

The separation (x) between the dots printed by the ticker-tape timer, the time for each of the position can help find the instantaneous velocity of the corresponding time by working out the slope of x-t graph plotted. Plot a suitable v-t graph. Again at suitable points on the v-t graph, find the acceleration by working out the slopes. Period of the oscillation can be found.

The acceleration due to gravity is found.

Conclusion

By means of a simple pendulum, the acceleration of free fall was found to be ( 9.52  0.11 ) ms-2 which is 2.96% smaller than the expected value 9.81 ms-2

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