Topic 11.2
Springs
Springs
Aims
In this experiment you will plot a force–extension graph for a spring. This will enable you to
measure the limit of proportionality and determine the spring constant of the spring.
Safety
 Attach the masses securely to the spring and ensure that, should the masses fall, they will
not fall on your feet. You may need to protect the floor.
 The clamp stand must be securely attached to the bench with a G-clamp.
Equipment, materials and method
1 For this experiment you will need a spring, a clamp stand, a G-clamp, some masses and a
mass hanger, some string, a metre ruler, a set square and a stand with two clamps.
2 Secure the first stand to the bench and hang the spring from the clamp. Tie a loop of string
through the bottom of the spring. Adjust the ruler and secure it in place as close to the
spring as possible, using the second stand and both its clamps. Use the set square to ensure
that the ruler is vertical.
3 Read the position of the top and the bottom ring of the spring. Use the set square to ensure
that the line between the spring and the ruler is horizontal. Subtract these values to
calculate the length of the spring. Estimate the precision of each reading.
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Topic 11.2
Springs
4 Add the mass hanger (whose mass should be the same as the individual masses to be
added later) to the loop of string and measure the new length of the spring.
5 Continue to add masses and measure the new length of the spring each time until it is
clear that the results are no longer linear. At this point caution must be taken.
6 For each measurement, calculate the extension of the spring by subtracting the original
length of the spring from the new length.
7 After the spring has been extended beyond its linear region, repeat the measurements as
you unload the spring.
Questions
1 What force does each of your masses exert on the spring?
2 How can you calculate the extension of the spring from your measurements?
Results
Tabulate your results. For each extension, calculate the force applied and the extension of the
spring. Enter these values in your table. Estimate the probable uncertainty in each extension
measurement. Plot a graph of force against extension. Differentiate, on your graph, between
the measurements taken when loading and when unloading the spring.
Discussion
1 Use your graph to find the values for the spring constant and the limit of proportionality of
your spring, and estimate the probable uncertainty of this limit.
2 When unloading the spring, what do you notice about the gradient (and hence the spring
constant) of the new line?
Springs
Aims
 To plot a force–extension graph for a spring and use it to determine the spring constant
and the limit of proportionality of the spring.
 To take suitable precautions to ensure that uncertainty due to experimental technique (for
example, parallax) is minimised.
Safety
 The clamp stand must be securely attached to the bench with a G-clamp.
 The floor may need protection from falling masses.
 Ensure that the spring is attached securely to the clamp.
 Warn pupils to take care with falling masses.
Teaching notes
3 This experiment should take about 25 minutes (although graph plotting may take longer).
AQA Physics A AS Level © Nelson Thornes Ltd 2008
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Topic 11.2
Springs
4 The number of masses added each time in order to ensure a suitable number of
measurements for the graph (8–10 minimum) should be determined by assessing how
much weight is needed to reach the elastic limit. This depends on the spring used.
5 More readings should be taken around the point where the spring reaches the elastic limit.
Answers to questions
1 Weight of mass in newton = number of kg × 9.81 N kg−1
2 Extension = length of extended spring − original length
Columns for both of these values should be added to the table of results.
Discussion
3 The spring constant is found by finding the gradient of the straight part of the graph.
Encourage students to extrapolate this line in order to draw a larger triangle to calculate
the gradient. This minimises error.
The limit of proportionality is the point at which the graph ceases to be a straight line.
Encourage students to draw a line of best fit for this region. Take account of the probable
uncertainty in each measurement to estimate the probable uncertainty in the gradient and
in the limit of proportionality.
4 As the spring is unloaded it will not return to its original length, thus a new line is formed
on the graph. However, the gradient (and hence the spring constant) should be
approximately the same for this second line.
Practical assessment opportunities
5 ISA preparation:
practical task – practice in recording measurements, estimating errors and plotting a graph
written task Section A and B – opportunities to draw conclusions and to evaluate the
strength of the conclusion
Springs
Equipment and materials required
Each student or pair of students will require the following equipment:
 a stand and clamp
 a spring (for which 1 N gives an extension of 2–3 cm)
 a 15 cm length of string
 some masses and mass hanger(s)
 a second stand with two clamps
 a metre ruler
 a set square
 a G-clamp
 graph paper
AQA Physics A AS Level © Nelson Thornes Ltd 2008
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Topic 11.2
Springs
The number of masses and mass hangers depends on the spring used. The spring needs to
extend beyond its elastic limit.
Safety
 The clamp stand must be securely attached to the bench with a G-clamp.
 The floor may need protection from falling masses.
 Ensure that the spring is attached securely to the clamp.
AQA Physics A AS Level © Nelson Thornes Ltd 2008
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