YEARS 7 – 12 IDEAS ARTICLES FOR THE CLASSROOM
Using Real Data, and Analysing Errors
By Malcolm Hooper, Normanhurst Boys’ High School
Unexpected experimental results can provoke further exploration and promote deeper physical understanding. The new syllabus explicitly mentions both systematic and random errors; both are found in experimental data. The challenges are to tease them apart, to identify the sources, and then to minimise each type of error. In this work, observations and physical arguments are used to create auxiliary hypotheses about the experiment, then mathematical models are used to examine the systematic errors.
This experiment aimed to measure gravitational acceleration by using the fall of a glider along a linear air track. With negligible air resistance at low speeds and long fall times, the experiment was expected to measure gravitational acceleration g to good precision and accuracy. The independent variable was the angle θ of the track and dependent variable was the fall time, t. aa = $%
The data were expected to lie on a single straight line, a = g · sin( θ)
≈ gθ, where θ is in radians. This hypothesis is based on the usual splitting of forces into components parallel and perpendicular to the surface of the linear air track. The experimental data showed
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the glider accelerating right-to-left and then left-to-right, with the results on nearly parallel lines, with neither going through the origin. The challenge was to explain this result.
Method
The track was first leveled by adjusting a screw thread at one end of the I-beam support until the glider remained stationary on the track. The screw thread was identified as 16 threads per inch, using an old imperial units ruler and noting the perfect alignment with the threads, giving a pitch of 25.4 mm / 16 = 1.5875 mm.
The glider was timed as it moved 1.626 m from rest, hence u = 0 in the equation for uniformly accelerated motion; s = ut + ½at 2 = ½at 2. The acceleration a along the track was calculated from the measured fall time t, using a = 2s / t 2. The gradient was determined by counting the screw thread turns(– 10 to + 10) from the horizontal position. The distance from the single slope-adjusting leg to the other two legs was measured as 1.534 m. For these very small angles the approximation θ( in radian) = sin( θ) = tan( θ) contributed negligibly to the error.
Linear air track glider
I-beam to
Adjusting screws
Figure 1: The experimental setup
54 SCIENCE EDUCATIONAL NEWS VOL 67 NO 3