Random Uncertainty Your friend asks you to measure their height. You use a tape measure (with centimeter markings) and get 180 cm. Your friend asks you to quantify how accurately you can determine their height. To answer this you decide to ask two more people to measure your friend's height. You record these multiple trials of the height measurement in a table. Trial Height (cm) 1 180 cm 2 179 cm 3 182 cm Average 180 cm You realize that by doing multiple trials and nding the average you've estimated the height, and gotten a sense of how accurately you've measured. Trial 3 is furthest from the average, 182 cm - 180 cm = 2 cm from the average to be precise. One way of quantifying the random uncertainty of the measurement is to quantify the range of measurements. The complete statement of the measurement of your friend's height is 180 cm :l: 2 cm .This means your friend's height is in the range between 178 cm and 182 cm. There is no way to measure your friend's height exactly. There's no way to make any measurement exactly. Every measurement has uncertainty. The rst step to estimating uncertainty is to do multiple trials of the measurement. Doing multiple trials doesn't determine the uncertainty in a measurement, it only estimates it. If you want to estimate the uncertainty better you can do even more trials. You nd one more person measure your friend's height. Trial What is the new average, in cm? Height (cm) 180 cm 179 cm 182 cm 184 cm Random Uncertainty (cont) What is the new random uncertainty from the previous question, in cm? Instrumental Uncertainty You ask the same 4 people to use a ruler (with millimeter markings) to measure the length of your phone. Trial Length (cm) 1 14.3 cm 2 14.3 cm 3 14.3 cm 4 14.3 cm Averageirandom uncertainty 14.3 cm i ??? All 4 trials ended up being the same. It is rare that this happens with hand held measuring tools, but common when taking measurements using simulations. If we used the method for determining random uncertainty we would get 0.0 cm, which is not reasonable. No measurement is exact. Notice that the length of the phone was measured with a ruler that has millimeter markings. In this case it's the precision of the measurement instrument that is determining the accuracy of the measurement. This is called instrument uncertainty, and it's equal to half the smallest increment. For the ruler this would be 0.5 mm. The measurement of the length of your phone with uncertainty would then be 14.30 cm i .05 cm. Your friend uses the same ruler to measure the length of your foot four times and gets 25.4 cm each time. What is the range that represents the length of your foot, based on the instrumental uncertainty? \fNow that you've determined your friend's height including uncertainty (181 cm :l: 3 cm) you decide to solve the following experimental problem: Determine the smallest rectangular volume that your friend could stand up in. The method you come up with is to ask the same 4 people to help measure your friend's left-to- right width and front-to-back depth. Together with the previously measured height, you'll determine the resulting volume . Trial Width (cm) 1 52 cm 2 50 cm 3 53 cm 4 52 cm What is the average value of the width, in cm? What is the random uncertainty on the width measurement, in cm