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Question: need help with 1 b c d e and f...

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PRE-LAB EXERCISES average size. If d is the diameter in millimeters, some pebbles will be bigger and some smaller than the desired average do. Suppose you have a rock crusher. The pebbles it makes have different sizes, but you can adjust the 1. (a) In the histogram below, about how many pebbles are shown to have diameter of greater 150 100 (b) In this distribution (same histogram,) approximately how many pebbles are represented 50 altogether, including all sizes? 20 40 60 80 Pebble Diameter d in Millimeters

e you made a batch of 7 x107pebbles crushed by the same rock crusher, using the same same raw material. Estimate how many pebbles would have diameter of greater (c) Suppos settings and the Remember to explain your reasoning in sentences.) (d) Let do represent the average pebble diameter. About half of the pebbles will have diameters less than do and about half will have greater diameter, but this is not always precisely true. For example, consider the set of numbers {1,2,3,4,5,15). Calculate the mean or average value and show that this value does not fall in the middle of the distribution, where middle means the middle number or median. About where would the middle be?

Nevertheless, it is often reasonable to suppose the mean value is above approximately at the center of the set of values. (e) Let us consider the spread of distribution in pebble size. How much spread is there around the mean value? You cant just average the difference d -do for each data point, because that average is always zero. So, what you do first is square the differences, then average the s (all positive numbers) and then take the square root. Here we write this quantity A, size N is large enough usually the symbol ơ the standard deviation. Actually, A is a root mean square difference. The quantity befo the square root is called variance. So, loosely speaking Δ quares if the sample is used because it is approximately what they call is the standard deviation. For o ur 2-2 UND Physics CPSL

Nature of Measurement Uncertainty purposes, lets just call A the rms for short. It turns out that when the distribution looks sort of bell-shaped, about 68% of the data fall between d- and d, +A, Also about 95% of the data fall between d, -2A and d +2A. So, the point of the rms (or in other words A) is that it measures how spread out the distribution is. For the following (short!) list of pebble sizes, find the mean value and the rms (Sizes d in mm) 1 5.846 2 10.057 3 4.98 4. 7.104 5. 7.856 6. 9.392 7 5.927 8 12.301 9 10.159 10 9.507 11 3.442 12. 3.476

(f) Compose two sentences to give the practical meaning (more than a definition) of the mean value and the rms of some data. In other words, what does each of these two statistics actually tell you about the data? The next problem also has to do with multiple measurements. It has to do with time measurements rather than diameter measurements, but the ideas are the same. From your reading, write down formulas for the distance traveled and for the velocity, each as a function of time, in terms of initial speed and the acceleration a, assuming the acceleration is constant. This situation applies to a falling object or a car skidding to a stop 2.

Need help with 1: b, c, d, e and f. And 2. Thanks!

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