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\phantom{1}\\  Do \textbf{not} argue with your colleague in front of the students! Even if you think that your colleague is wrong. Please have a word with him/her when he/she walks away from the student. Many times I have seen how demonstrators correct each other in front of the students, and students always get confused as they don’t know who is right and who is wrong. Sometimes they ask the same question to different demonstrators and when they get different answers they don’t know what to think. If they say that another demonstrator told you something else and you think it is wrong, ask them to wait, have a word with your colleague and then explain the agreed-upon approach to the student together!\\  \phantom{1}\\  Finally, make the distinction between random errors and measurement uncertainty. Just because a student places \textit{the same weight on the same scale} 10 times does not mean they can increase their precision using $\sigma_{\bar{X}} = \frac{\sigma_{X}}{\sqrt{N}}$ - if the base uncertainty of the scale is much larger than any gaussian fluctuations, it is difficult (or impossible) to justify applying normal-distribution tricks such as adding variances rather than absolute uncertainties. uncertainties.\\  \phantom{1}\\  \textbf{Practice Problem - Approach and Solutions}  \begin{enumerate} 
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Based on data from Reserve Bank Coinage Specifications[1], the densities for 10 cent, 20 cent, 50 cent, 1 dollar and 2 dollar coins should come out as 6328, 6901, 6113, 7027, 6715 kg/m3 respectively. Having said this, values should roughly fall within 6000-8000 $kgm^{-3}$. Diameters and masses are pretty consistent between testing one coin and five coins, but thicknesses are very dependent on exactly where you test the coins. Students will probably need to measure the thickness of the coin at the *rim* to get a density in the Specification range. By measuring thicknesses at the center of each coin, the calculated densities are closer to 7500$kgm^{-3}$.\\  \begin{table} \begin{table}[!h]  \begin{tabular}{c|c|c|c|c|c}  & 10c & 20c & 50c & \$1 & \$2 \\ \hline   Thickness($\pm0.01$mm) & 1.37 & 1.48 & 1.39 & 2.59 & 2.37 \\ \hline 
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\phantom{1}\\  It is assumed that all of the measurements lie within the scale uncertainty of the calipers - if this is not the case, then adding the relative errors in quadrature, rather than linearly, is an acceptable approach.  \phantom{1}\\  \begin{table} \begin{table}[!h]  \begin{tabular}{ c|c|c|c|c|c }  $\rho=\frac{M}{V}$ & 10c & 20c & 50c & \$1 & \$2 \\ \hline  V (m$^3$) & $4.51\times10^{-7}$ & $5.47\times10^{-7}$ & $6.69\times10^{-7}$ & $1.07\times10^{-6}$ & $1.312\times10^{-6}$ \\ \hline 
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\phantom{1}\\  In part 3 (measuring reaction time), the free-fall distance associated with a reaction time of 0.18s is 16.2cm. This should be what people aim for, but it is difficult to test this in a reliable manner in the lab, so expect results to vary wildly - results will most likely be within the range of 10cm - 40cm.\\  \phantom{1}\\  \textbf{Key Discussion Points} Points}\\  Again, it is worth emphasising that students should `add errors in quadrature' when the errors are generated by random fluctuations. If the fundamental uncertainty of the measuring equipment is the limiting factor, the quadrature approach is no longer appropriate. This is covered in appendix A4.1 under the discussion of dependent and independent quantities.\\  \phantom{1}\\  Section 1.3 - Archimedean method of determining volume by placing the coin in water and measuring the volume of displaced water would be good example. A reasonable way to do this is to use a graduated (marked) cylinder. Pour water into the graduated cylinder until it reaches a known level (seen by markings on the cylinder’s surface). Add the object to the water and record the new water level. The difference between the new water level and the original level will be the object's volume. This measurement is taken in milliliters, which are interchangeable with cubic centimeters. Once volume is determined, then weigh the object on a scale and do the same calculations as before. \\ 
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\phantom{1}\\  Section 5.3 - Firstly, students should distinguish between measuring their own reaction, and the average reaction time. Secondly, students should realise that their experiment cannot prove or disprove the reference value, only give evidence in support of or against it. Thirdly, students should realise that taking everyone’s value in the class would introduce sampling bias.\\  \phantom{1}\\  \textbf{References} \textbf{References}\\  [1] Retreived from http://www.rbnz.govt.nz/notes-and-coins/coins/new-zealand-coinage-specifications on 25th February 2016