• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  10. 10
    10
  11. 11
    11
  12. 12
    12

Determining Gravity with a Pendulum

Extracts from this document...

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

...read more.

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.

...read more.

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

...read more.

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

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Forces and Motion essays

  1. Marked by a teacher

    The Simple Pendulum Experiment

    4 star(s)

    length, then I can find the acceleration of gravity by taking the gradient of this line to be m in the above equation () L (cm) T2 (s2) (3 s.f.) 80 3.53 90 3.90 100 4.33 110 4.78 120 5.06 130 5.24 140 5.62 150 6.00 T2 = time for one oscillation2 (s2)

  2. Determination of the acceleration due to gravity using a simple pendulum.

    could be affected by human error in recording or calculation of the results. Also drawing a T2 graph illustrates that the graph is exponential as it produces a straight line. This also shows that length is directly proportional to T2.

  1. Period of Oscillation of a Simple Pendulum

    The graph must not be misinterpreted, as the graph goes up, this indicates that the pendulum is slowing down. The pendulum is not speeding up. I must now theorise as to why the pendulum slows down instead of staying at the same speed throughout.

  2. Determining the acceleration due to gravity by using simple pendulum.

    Measure the length (L) of the pendulum, from its point of attachment to the centre of the pendulum bob. 3) Pull the pendulum aside and release tit so that it starts swinging, using a stopwatch, begin timing at an extreme of the pendulums motion and time twenty full swings

  1. In this experiment I aim to find out how the force and mass affect ...

    � How many results I will take � What range of variables I will experiment with Safety With this straightforward experiment there is not much that needs to be taken into consideration. No harmful substances are being used, neither are flames, solvents, atomic-reactors or insurance salesmen so all-in-all a relatively safe experiment.

  2. Measuring Acceleration due to Gravity using a simple Pendulum.

    References Advanced physics by M. Nelkon & M. Dethereidge "S.H.M. is acceleration is directly proportional to displacement and directed (acts towards) a fixed point." Evaluation From my graph I have realised that I only have 2 anomalous results, these results are at the points: length = 0.900 and 1.000 These anomalous results have occurred because of the errors.

  1. Investigating the period of a simple pendulum and measuring acceleration due to gravity.

    too many risks and it can be carried out in classroom conditions. But in order not to hurt others and myself while carrying out this experiment a few safety steps will be followed. * The Clamp stand will be placed away from the edge of the table.

  2. Carry out an experiment of simple harmonic motion using a simple pendulum and determine ...

    The amplitude was kept small so as not to move too fast and for ease of counting. We also tried to keep the amplitude at a similar size each time because although amplitude does not affect the time period, changing the length of the pendulum does.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work