GOCE
Gravity field & steady state
Ocean
Circulation
Explorer
Pulling Power- Measuring g With a Pendulum
Background Information:
When Dutchman Christiaan Huygens invented the pendulum clock in 1656, it was
the first practical means of measuring ‘the rate of fall of a heavy body’ i.e. the
acceleration due to gravity. French astronomers then noted that pendulum clocks
lost time near the Equator when compared with observations made in Paris. This
observation implied that the strength of gravity was less at low latitudes and it
initiated a long debate on the shape of the Earth. It is now accepted that at the
Equator the acceleration due to gravity is slightly more, since the rotation of the
Earth makes it bulge at the centre. Similarly, the acceleration due to gravity is
slightly less at the poles, where the Earth is slightly flattened.
Textbooks quote often quote a fixed value for g, but in reality it varies across the
whole surface of the Earth, depending on the land masses underneath. In fact, the Himalayas
have a small influence on the value of g measured in Europe. Although invisible to the naked eye,
the sea surface actually has undulations that echo the topography of the ocean floor on a
reduced scale. For example, the extra mass of a 2 km high mountain in the sea attracts water
over it, causing a bulge in the sea surface about 2 m high and 40 km across. Similarly, the
reduced gravity over trenches in the sea floor means that less water is held by gravitational
attraction over these regions, so that locally the sea surface is depressed.
So the new scientific evidence gathered from this simple experiment made scientists reconsider
their model of the Earth’s shape and it greatly improved our understanding of the world we live
in. Nowadays, by using the GOCE satellite, scientists are continuing to try to improve upon this
model to one that is accurate to within a centimetre. They aim to measure the Earth’s
gravitational field strength to an accuracy of 10-5 m s-2.
Learning Objectives:
To be able to plan and conduct investigations. To be able to plot and draw graphs, calculate
gradients and manipulate formulae. To appreciate that the gravitational field strength at that
location depends on several factors including the density of the local rocks.
Outcomes:
To find the value of the gravitational field strength at a specific location on Earth.
Curriculum Links:
Edexcel GCSE in Physics (2109)
P3 6.10: Use the equation frequency = 1/time period
Mathematical Skills: Students should be able to “manipulate formulae, equations and
expressions; plot and draw graphs from suitable data, selecting appropriate scales for the axes;
interpret graphs in terms of general trends and by interpolation; interpret a range of graphs
and diagrams; understand and use direct and inverse proportion”
AO2 Plan a scientific task, such as a practical procedure
AO3 Carry out practical tasks safely and skilfully; evaluate the methods they use when
collecting first-hand and secondary data; analyse and interpret qualitative and quantitative data
from different sources; consider the validity and reliability of data in presenting and justifying
conclusions.
The Twenty First Century Science suite GCSE Physics A (J635)
Higher Tier: Recognise and use expressions in standard form, manipulate equations, select
appropriate axes and scales for graph plotting, determine the intercept of a linear graph,
understand and use inverse proportion and calculate the gradient of a graph
AQA Physics 2009 (4451)
10.4 Designing an investigation - A fair test is one in which only the independent variable affects
the dependent variable, as all other variables are kept the same.
Materials:
Retort Stand
Stop clocks
Metre rule
String
Plumb bob
Rubber stopper with slit through it
Suggested activities:
Revise the definition of time period - the time for one complete cycle to pass. Explain that the
aim of the investigation is to find the relationship between the length of a pendulum and its time
period and, through doing so, to find the acceleration due to gravity. Discuss fair testing. What
factors would you need to keep the same if you are looking at the relationship between time
period and the length of a pendulum? Explain that as the amplitude of oscillation does not
actually have an effect, you do not need to use a protractor to precisely release the bob from
the same position each time. Pupils plan the investigation, selecting suitable apparatus, table
headings, range and step sizes.
1. Feed the string through the slit in the rubber stopper and places the stopper in the clamp
stand. Measure the length of the string with a metre rule. Pull the string through the stopper
until the length is 20 cm.
2. A complete swing is from the release position to the other side and back. Use the stop clock
to measure the time it takes for ten complete swings.
3. Repeat for lengths of 40 cm. 60 cm. 80 cm and 100 cm.
Pupils will choose to plot T versus l. Ask them to suggest a possible relationship by looking at the
shape obtained. Lead them towards plotting a graph of T2 versus l for the pendulum. Calculate
the gradient of the graph.
Given that T = 2π√(l/g), use the gradient of the graph to determine the acceleration due to
gravity.
Extension:
The apparatus for uniform circular motion experiments (a rubber
stopper, string, glass tube, paper clip, washers and stopclock) could
also be used to determine g. The paper clip is used to set the
orbital radius. When spinning the stopper, the paper clip should be
just below the glass tube. The time period could be measured for
various values of radius of rotation. A graph of T2 against r could be
plotted. Since T = π(r/g)1/2, the gradient of the graph could be used
to determine g.