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Paper Clip Fatigue

October 27 1999

The first year engineering students, at the University of Waterloo performed a paper clip fatigue experiment.  The results of this experiment is enclosed in this memorandum, in the form of a line-column graph (Figure 1) , which shows the values of the frequency observed by the students, and the Gaussian distribution of the data.

The Gaussian distribution plays an important role in statistics, and is an excellent model for continuous distributions that occur in real situations.  The results of this experiment follows a similar pattern to that of the Gauss model.  Observations from the experiment follow the Gauss model, since the graph begins at low values and gradually increases until a peak is reached near the mean value, then the values of the dependent variable decreases as the values of the independent variable increases.

Although the data from the experiment follows similar trends of a Gaussian curve, there are differences.  The Gaussian curve is symmetrical, about the highest point at the mean, whereas the graph of the observation is not perfectly symmetric.  A reason for this inconsistency between the Gaussian curve and the observed curve is due to errors in conducting the experiment.  It is inconceivable to believe that every student used the same techniques, or applied the exact same force, and bent the paperclip to the same angle.  Another possible source of errors is from the construction of the paperclip.  The material of which the paperclips are made is generally not uniform throughout the box of paperclips.  In other words the metal is not standardised.  Therefore, the resistance of the paperclip to the applied force will vary depending on the purity, and the strength, of the material of which it is comprised.

The results obtained from the experiment, and the conclusion made from the graph, can be used to reveal general trends and properties of metal fatigue.  This type of data can be used to generate reports when dealing with the safety of designs, such as bridges, buildings, cars, and aircraft.  These results can lead to similar results in other metals.  These values provide engineers with a standard, which the can use when dealing with similar materials.