Help with #26 and #27*** MacBook Pro LAB 107A LABORATORY MANUAL ection VIl: Comb

Question

Help with #26 and #27***

MacBook Pro LAB 107A LABORATORY MANUAL ection VIl: Combining addition/subtraction and multiplication/division of quantities questions, the ask is to determine the quantity (a-b)/c, where a = 17.3 m ± For the next two 0.2 m, b = 15.4 m ± 0.3 m, and c = 10.1 s ± 0.1 s. Question #26. Using the max/min method, show that (a b)/c2 equals 0.018728 m/s2 ± 0.005272 F11 minimum possible value and maximum possible value (note: the largest value in this case would use the largest value of a, the smallest value of b and the smallest value of c). Then use those two values to figure out the range. m/s?. First figure out the maximum and minimum of each individual value, then determine the Question #27. Using the short-cut method for addition subtract and the relative uncertainty method for multiplication/division, show that (a - b)/c2 equals 0.018626 m/s+ 0.00527 m/s. First get the middle value by carrying out the calculation without the uncertainties. Then figure out the value of (a b) by adding up the numerical uncertainties (using the short-cut method for subtraction). Then treat the remaining part of the problem as a division problem, where you add up all of the relative uncertainties to get the relative uncertainty in the answer (remember that the relative uncertainty associated with the 0.1 s is present twice). You'll need to multiply that by the final answer to get the numerical uncertainty. Instructor's Signature 50pts

Explanation / Answer

#26 . a = 17.3 +- 0.2 m

b = 15.4 +- 0.3 m

c = 10.1 +- 0.1 s

x = (a - b)/c^2

now, xmax = (amax - bmin)/cmin^2 = (17.5 - 15.1)/10^2 = 0.024

xmin = (amin - bmax)/cmax^2 = (17.1 - 15.7)/10.2^2 = 0.013456362

average x = (xmax + xmin)/2 = 0.018728181

error = (xmax - xmin)/2 = 0.0052718

hence x = 0.018728 +- 0.005272

#27 x = (a - b)/c^2 = (17.3 - 15.4)/10.1^2 = 0.018625

dx/x = d(a - b)/(a - b) + 2dc/c

d(a - b) = (0.2 + 0.3) = 0.5

dx/x = 0.5/(17.3 - 15.4) + 2*0.1/10.1 = 0.2829598

dx = 0.005270

hence

x = 0.018625 +- 0.00527

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