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  • Level: GCSE
  • Subject: Maths
  • Word count: 2338

An Experiment to measure the gravitational field strength of the Earth and the length of a grandfather clock, which has a time period of two seconds, using a simple pendulum.

Extracts from this document...

Introduction

An Experiment to measure the gravitational field strength of the Earth

and the length of a grandfather clock, which has a time period

 of two seconds, using a simple pendulum.

Diagram

Apparatus List

Metre rule 0-1m ± 0.001m        Protractor 0-180°± 1°

Cork                                Card

Stop clock 0–60s ± 0.01s        Tape measure 0-2m ± 0.001m

Clamp                                Light inextensible string

Clamp stand                        Micrometer screw gauge

Selotape                                Weights

Setsquare

Variables Involved [constant and changing]

There are only two variables. These are the length of the string and the time period. The time period differs because the length is continually changing.

In order to ensure the experiment is carried out fairly, several factors must remain constant. These are:

  • The same method used throughout the entire experiment,
  • Timing the same number of oscillations,
  • Using the same bob,
  • Ensuring that the pendulum’s displacement from the equilibrium position is constant,
  • Using the same apparatus,
  • And maintain a certain temperature during the experiment as an increase could make the effective length different therefore affecting the time period.

Method

  • Set out the apparatus as shown in the diagrams
  • Using the metre rule, set square and/or tape measure, set the length to the required value (start with a length of 0.300m)
  • Pull back the pendulum to a certain displacement ensuring that the angle of swing is smaller than 10°
  • Count down from free and when at zero release the bob and start the timer instantaneously
  • Begin counting the oscillations when the pendulum is at its equilibrium position
  • Using the fiducial mark towards the bottom of the pendulum and observing it at eye level, count twenty oscillations and when at the twentieth, stop the timer
  • Record the value obtained
  • Repeat the process twice more until three values for the time at that specific length have been obtained for twenty oscillations
  • Re-measure the length of the pendulum using the necessary equipment to confirm there has not been a discrepancy in length
  • Change the value for the length of the pendulum using the required apparatus increasing it with increments of 0.100m and repeat the entire experiment so as to acquire three values for the time and two for the length
  • Record all readings in a table and calculate values for T2
  • Plot a graph of T2 against l
  • Find the diameter of the bob using a micrometer screw gauge and the length of the hook using a ruler

N.B. when the length exceeds 1.000m, it would be more accurate and more straightforward to use a tape measure instead of two metre rules

Intended Readings

During the experiment I shall calculate the time for twenty oscillations and will start with a length of 0.300m and finish with a length of 1.100m increasing the length with increments of 0.100m. The length will be taken firstly at the beginning and then at the end of timing the oscillations for a specific length. In addition, I shall be repeating the reading of time with the intention of acquiring three values from which to calculate an average.

Safety Considerations

To ensure the experiment is carried out safely, I will have to make sure:

  • The string is secured to the cork and the cork to the clamp,
  • The clamp stand is stable (using weights) and therefore cannot topple over causing damaging to equipment and others around,
  • The pendulum is oscillation at a reasonable pace so as not to cause an imbalance,
  • And that I am always aware of my surroundings
...read more.

Middle

The y intercept (c) is equal to:                        and will have units = s2

I predict the graph will look like the one found below:

T2 (s2)

l (m)

From the graph, I will be able to calculate the gradient:

                                                And will have units = s2m-1

And then from this, I can work out the value for the gravitational field strength and from the y intercept on the axis I can calculate a value for the end correction (x). This will help me calculate the true length L of my grandfather clock.

The value of g that I will obtain will be the value of freefall (units ms-2) but as g can also be thought of as the gravitational field strength the actual units will be Nkg-1. I therefore hope to obtain a value for the gravitational field strength equal to 9.81Nkg-1, as this is the value quoted both in the textbook and on the datasheet.

Aspects of Plan Based on Procedures

As I know the time period for the grandfather clock is 2 seconds, I can make a calculation for an approximate length of the grandfather clock’s pendulum as seen next.

T2 (s2)                                                        I intend to use my graph

as illustrated to find a value

        4                                                for the length of the

Grandfather clock.

         L         l

...read more.

Conclusion

In the variation of length there is no variation. However, when measuring time an increased amount of variation is apparent. The worst examples are tabulated below,

Av. Length (m) ±0.0001m

T1 (s) ±0.01s

T2 (s) ±0.01s

T3 (s) ±0.01s

Av. T (s) ±0.01s

± variation (s)

1

0.300

23.06

22.97

23.10

23.04

0.06

2

0.500

29.31

29.36

29.39

29.35

0.04

3

1.100

42.71

42.84

42.87

42.81

0.10

The worst percentage error in the variation of repeats is:

Comment on Suitability of Techniques Used

My techniques were suitable as they were able to verify my prediction and I found little difficulty throughout.

Reliability of Conclusions

I believe my conclusion is reliable as:

  • My points are close to the lie of best fit,
  • My value of g is close to the official value,
  • I timed twenty oscillations, therefore reducing the errors

 incurred,

  • I repeated my readings for length twice and time three times,
  • The value for the length obtained is similar to my predicted

value,

  • I used a countdown method,
  • And I began timing when the pendulum was at the centre of its

oscillation and moving fastest.

Reliability of Experiment

  • Compare calc value of L in prelim to L found how reliable?
  • % error from alt gradient high or low?
  • Compare value of g to official value % error from diff. if small % the experiment is reliable
  • Compare calculated x with measured x % diff how reliable
  • Comment on size of errors on instruments – very small. % error smaller for T than L reaction time ( fairly large but ca be discounted)

Proposals for Improvements

  • More precise equipment
  • More than one person
  • Length measurement better
...read more.

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