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
& '
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