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# Determining Gravity with a Pendulum

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Introduction

SPH141        Practical 2

Practical Experiment 2

Determining Gravity with a Pendulum

Aim

To determine the local acceleration due to gravity using Galileo pendulum technique.

Theory

Gravity is a force that acts on Earth every day. Sir Isaac Newton was first to underline the principles of gravity when an apple fell on his head (Ashbacher 2002). He stated that each particle with a mass attracts all other particles with mass with a gravitational force that is directly proportional to the product of their masses and inversely proportional to their distance of separation squared (Ashbacher 2002).

This is due to that gravity acts between objects (Ashbacher 2002), consequently causing a force of attraction which pulls the two object together, such as that an object with a mass will fall down towards earth ground. The Earth’s mass creates a gravitational force, which pulls the object down towards Earth.

This theory is also supported by Newton’s three law of motions, particularly the first law stating that, ‘an object in motion or at rest will remain in motion or at rest unless acted upon by an external fore‘. An object will remain at rest floating in the air, however since an external force, gravity, acts upon it, the object falls towards Earth.

Theoretically, the acceleration due to gravity on Earth is 9.8ms-2

Middle

Average

0.30

10.9

11.3

10.2

10.8

0.60

15.8

15.7

15.7

15.7

0.90

19.1

19.0

18.9

19.0

Resolution                Ruler – 0.1cm                Stop Watch – 0.01s

Calculations

Calculating the gravitational acceleration

T = 2π

T = 2π

g =

Calculating Gravitational Acceleration for 0.30m

10.8s per 10 pendulum swing cycle = 1.08s per pendulum swing cycle

L = 0.30m and T = 1.08s

g =

g = 10.2ms-2

Calculating Gravitational Acceleration for 0.60m

15.7s per 10 pendulum swing cycle = 1.57s per pendulum swing cycle

L = 0.60m and T = 1.08s

g =

g = 9.6ms-2

Calculating Gravitational Acceleration for 0.90m

19.0s per 10 pendulum swing cycle = 1.90s per pendulum swing cycle

L = 0.90m and T = 1.90s

g =

g = 9.8ms-2

Calculating Uncertainties for the gravitational acceleration

0.30m Pendulum

Since T = 10.8 and L = 0.30, the uncertainty for T = 10.8s ± 0.05s and L = 0.30m ± 0.05m

Highest value for the gravitation acceleration using 0.30m pendulum is;

L = 0.30m + 0.05m

= 0.35m

T = 10.8s – 0.05

=10.75s per 10 cycles

g =

where L = 0.35 and T = 1.075s per cycle

g =

g = 11.9ms-2

Lowest value for the gravitation acceleration using 0.30m pendulum is;

L = 0.30m - 0.05m

= 0.25m

T = 10.8s + 0.05

=10.85s per 10 cycles

g =

where L = 0.25 and T = 1.085s per cycle

g =

g = 8.4ms-2

0.60m Pendulum

Since T = 15.7 and L = 0.60, the uncertainty for T = 15.7s ± 0.05s and L = 0.6m ± 0.05m

Highest value for the gravitation acceleration using 0.60m pendulum is;

L = 0.60m + 0.05m

= 0.65m

T = 15.7s – 0.05

=15.65s per 10 cycles

g =

where L = 0.65 and T = 1.565s per cycle

g =

g = 10.5ms-2

Lowest value for the gravitation acceleration using 0.

Conclusion

Conclusion

The acceleration due to gravitation was determined to be 10.2ms-2, 9.6ms-2 and 9.8ms-2 for the pendulum measurements of 0.30m, 0.60m and 0.90m. This shows that the aim f the experiment was achieved through the conduction of the experiment. Though, the theoretical acceleration due to gravitation on Earth is determined to be 9.8ms-2, in which it was found that by using the 0.90m, the exact value could be calculated. However there were some errors involved such as the parallax error, but within all trials, the acceleration due to gravity of each individual was within the highest and lowest uncertainty range. An improvement was suggested in regards to the errors and that was to use a longer pendulum to reduce the pendulum cycle time. Overall the experiment was followed according to the method, and the result obtained had a percentage error less than 10%, hence the results are considered acceptable.

References

Ashbacher, C 2002, ‘Sir Isaac Newton: The Gravity of Genius’, Mathematics & Computer Education, vol. 36, no. 3, pp. 302-310, viewed 5 September, via Education Research Complete

Houston, K 2012, ‘The Simple Pendulum’, College Physics, vol. 1, no.1, pp.1-4, viewed 5 September, <http://cnx.org/content/m42243/latest/?collection=col11406/latest>

Appendix

Diagram 1.1

Experiment Set Up

This student written piece of work is one of many that can be found in our GCSE Forces and Motion section.

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