The paperclip as a teaching object: mass, moment and failure
The paperclip appears in school physics more often than almost any other object, and it appears
with the wrong number attached. Textbook exercises state a mass of one gram. The most common
office clip weighs 0.38 g, and no clip the Institute has weighed, in any class, reaches one
gram except at the extreme upper end of class BR-05.
The error is harmless in arithmetic and unhelpful in teaching, because the whole value of the
object is that a pupil can check the figure. This page gives the measured values, the three
demonstrations they support, and the places where the object misleads.
The figures a teacher actually needs
Class
Mass
Wire diameter
Developed length
Sheets held
BR-01 Extra-fine
0.20 g
0.62 mm
8.4 cm
6
BR-02 Standard
0.38 g
0.78 mm
9.6 cm
12
BR-03 Administrative
0.55 g
0.90 mm
10.8 cm
18
BR-04 Reinforced
0.81 g
1.05 mm
12.1 cm
28
BR-05 Non-series
1.31 g
1.24 mm
13.8 cm
40
Masses from 1,200 units weighed; capacities from the same series, failure defined as
permanent set beyond 0.5 mm. Full method on the mass
page and the capacity page.
Three demonstrations that work
Counting by weighing
Weigh twenty clips, divide, then weigh a full box and predict the count. The prediction will
be close and will not be exact, and the discrepancy is the lesson: boxes are filled by weight, not
counted. The Institute counted 24 boxes marked 100 and found a mean of
98.4.
Elastic and plastic deformation
Open a clip slightly and it returns; open it further and it does not. The transition is
visible, repeatable, and happens at a load a pupil can apply by hand. The Institute's failure
criterion — permanent set beyond 0.5 mm — is precisely this transition, and it can be measured
with a ruler.
Fatigue
Bend a clip back and forth at one point and count the cycles to fracture. Steel clips exceeded
200 openings of the working kind without failing, but repeated reversal at a single point breaks
them in well under twenty. The difference between the two numbers is the whole of what fatigue
means.
Where the object misleads
It is not one gram. Nor is it a uniform object: the five measured classes span 0.20 g
to 1.31 g, a factor of six and a half.
Its capacity is not proportional to its mass. A BR-05 weighs three and a half times a
BR-02 and holds three and a third times as many sheets — close, but the relation breaks at both
ends of the range and the Institute publishes no formula.
A plastic clip is not a lighter version of a steel one. It has a rectangular section,
no BR class, and it fractures rather than deforming — polystyrene units failed at a median of six
openings. See plastic or metal.
There is no standard to appeal to. A pupil who asks what the official size is should be
told the truth: no national standards body has ever ratified a diameter class for the office
paperclip. The measurement is the only authority available, which is an unusually honest
position for a school exercise to be in.
Measuring it properly
Wire diameter is measured at the outer loop, at three points, discarding any reading that differs
from the other two by more than 0.04 mm. The
eight-step protocol sets out the four sources of error
that are larger than the instrument — the commonest being that the clip is measured where it has
been flattened by use, which is not a diameter at all.