ARTICLES
Mathematics of A Freely-hanging Slinky Spring
By Malcolm Hooper (teacher), with Patrick Adji (student);
Normanhurst Boys’ High School
“Door meten tot weten” Through measurement to knowledge –
Dutch physicist/chemist Heike Kamerlingh-Onnes (1853-1926).
For this experiment, retort stands must be near the edge of the
bench but not dangling over the edge to slide easily. Due care
to be taken.
Aims: to observe and measure how the length of a freely-hanging
slinky spring, the dependent variable, depends on the number of
rings, the independent variable.
Equipment:
1 retort stand, 1 retort ring (with bosshead), 1 new metal slinky,
1 new plastic slinky, 1 clamp, 1 bosshead, 1 metre rule with mm
divisions, digital balance of centigram precision, laptop with
spreadsheet software for data analysis, … For further work: 5, 25
and 50 gram masses, blu-tack, light string, …
The teacher aimed to train students in:
• understanding the Year 11 Dynamics topic; the shape of
the slinky is determined by a balance of forces, the weight
hanging below any point and the stretch of the slinky at that
point.
Method:
• the science, art & attitude of measurement;
1. Attach the retort ring to the retort stand and hang the slinky
from the retort ring over the edge of the desk. Allow the slinky
to gradually support its own weight as you slowly lower your
hand supporting it. This minimises oscillations in the slinky.
• understanding the keywords accurate, precise, reliable, and
valid;
• using spreadsheets to analyse data more fully, often a
repetitive task;
2. Attach the clamp and bosshead. Hang the ruler vertically from
the clamp so that it just clears the slinky (to avoid disturbing it
while minimising parallax error), with the zero of the metre rule
level with the bottom of the slinky.
• imagining errors and estimating their size; and
• massaging data, a gentle art to recover realistic information
from mis-information.
Hypothesis:
A slinky is a really weak spring. Hooke’s Law describes the force
exerted by a spring to be proportional to the spring’s extension. At
the bottom of a freely-hanging slinky, the load is zero. The slinky’s
own weight provides the force that extends the slinky more and
more as the number of rings increases. Hooke’s Law predicts the
spacing between the rings to increase linearly with the number
of rings, so the length from the bottom should increase as the
square of the number of rings. This is mathematically homologous
to the distance travelled by a uniformly accelerating object from
a standing start increasing as the square of time.
Safety:
Risk
Eye injury
Falling retort
stand
How bad?
Always
serious
Bruising
How likely?
Low
Low
Mitigate
Safety
glasses
Leather
shoes, do
experiment
standing due
care, ...
Figure 1. The experimental setup minimised parallax error.
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SCIENCE EDUCATIONAL NEWS VOL 68 NO 3