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DATA ANALYSIS AND INTERPRETATION (ME 102)

ASSIGNMENT 4

PROPOGATION OF ERRORS

1) In a hypothetical scenario, the National Institute of Standards and Technology has received

a new replica of The Kilogram. It is weighed five times. The measurements are as follows, in

units of micrograms above 1 kg: 114.3, 82.6, 136.4, 126.8, 100.7.

a. Is it possible to estimate the uncertainty in these measurements? If so, estimate it. If not,

explain why not.

b. Is it possible to estimate the bias in these measurements? If so, estimate it. If not, explain

why not.

2) The length of a rod was measured eight times. The measurements in centimeters, in the

order they were taken, were 21.20, 21.22, 21.25, 21.26, 21.28, 21.30, 21.32, 21.35.

a. Do these measurements appear to be a random sample from a population of possible

measurements? Why or why not?

b. Is it possible to estimate the uncertainty in these measurements? Explain

3) According to Newtons law of cooling, the temperature T of a body at time t is given by

T = Ta + (T0 Ta)ekt

, where Ta is the ambient temperature, T0 is the initial temperature, and

k is the cooling rate constant. For a certain type of beverage container, the value of k is

known to be 0.025 min1.

a. Assume that Ta = 36F exactly and that T0 = 72.0 0.5F. Estimate the temperature T at

time t = 10 min, and find the uncertainty in the estimate.

b. Assume that T0 = 72F exactly and that Ta = 36.0 0.5F. Estimate the temperature T at

time t = 10 min, and find the uncertainty in the estimate.

4) Nine independent measurements are made of the length of a rod. The average of the nine

measurements is X = 5.238 cm, and the standard deviation is s = 0.081 cm.

a. Is the uncertainty in the value 5.238 cm closest to 0.009, 0.027, or 0.081 cm? Explain.

b. Another rod is measured once by the same process. The measurement is 5.423 cm. Is the

uncertainty in this value closest to 0.009, 0.027, or 0.081 cm? Explain.

5) A certain chemical process is run 10 times at a temperature of 65C and 10 times at a

temperature of 80C. The yield at each run was measured as a percent of a theoretical

maximum. The data are presented in the following table.

a) For each temperature, estimate the mean yield and find the uncertainty in the estimate.

b. Estimate the difference between the mean yields at the two temperatures, and find the

uncertainty in the estimate.

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6) The friction velocity F of water flowing through a pipe is given by l

gdhF

4 , where g is

the acceleration due to gravity, d is the diameter of the pipe, l is the length of the pipe, and h

is the head loss. Estimate F, and find the uncertainty in the estimate, assuming that g = 9.80

m/s2 exactly, and that

a. d = 0.15 m and l = 30.0 m, both with negligible uncertainty, and h = 5.33 0.02 m.

b. h = 5.33 m and l = 30.0 m, both with negligible uncertainty, and d = 0.15 0.03 m.

c. d = 0.15 m and h = 5.33 m, both with negligible uncertainty, and l = 30.00 0.04 m.

Estimate F, and find the relative uncertainty in the estimate, assuming that g = 9.80 m/s2

exactly and that

d. d = 0.20 m and l = 35.0 m, both with negligible uncertainty, and h = 4.51 0.03 m.

e. h = 4.51 m and l = 35.0 m, both with negligible uncertainty, and d = 0.20 0.008 m.

f. d = 0.20 m and h = 4.51 m, both with negligible uncertainty, and l = 35.00 0.4 m.