University physics 1

,ent Uncertainty mm: Bring solutionstoithe ' E . ourTA will check to see that you have mitten them up. Later you will pass'the'm PRE~LAB EXERCISES ' 1. Suppose you have a rock crusher. The pebbles it makes have different sizes. but you can adjust the average size. If 6 is the diameter in millimeters, some pebbles will be bigger and some smaller than the desired average do- (a) In the histogram below. about how many pebbles are shown 1,; to have diameter of greater than 6.5 cm? (b) In this distribution (same histogram) approximately how many pebbles are represented altogether, including all sizes? Number of Pebbles Pebble Diameter d in Miltimeters (c) Suppose you made a batch of 7 x 107 pebbles crushed by the same rock crusher, using the same settings and the same raw material. Estimate how many pebbles would have diameter of greater than 65 mm. (Remember to explain your reasoning in sentences.) (d) Let do represent the average pebble diameter. About half of the pebbles wilt 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 can't just average the difference d do for each data point. because that average is always zero. 80, what you do rst is square the differences. then average the squares (all positive numbers) and then take the square root. Here we write this quantity A . ifthe sample srze N is large enough usually the symbol a is used because it is approximately what they call the standard deviation. Actually, A is a root mean square dierenee. The quantity before talking the square mat is called variance. So, loosely speaking A is the standard deviation. For our W0 Physics CPSL 2-2 v t. ' - . a